DOI： 10.1007/978-3-031-52113-3_21

Scopus

Publisher：Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)  

In this study, we investigate the computational complexity of some variants of generalized puzzles. We are provided with two sets S1 and S2 of polyominoes. The first puzzle asks us to form the same shape using polyominoes in S1 and S2. We demonstrate that this is polynomial-time solvable if S1 and S2 have constant numbers of polyominoes, and it is strongly NP-complete in general. The second puzzle allows us to make copies of the pieces in S1 and S2. That is, a polyomino in S1 can be used multiple times to form a shape. This is a generalized version of the classical puzzle known as the common multiple shape puzzle. For two polyominoes P and Q, the common multiple shape is a shape that can be formed by many copies of P and many copies of Q. We show that the second puzzle is undecidable in general. The undecidability is demonstrated by a reduction from a new type of undecidable puzzle based on tiling. Nevertheless, certain concrete instances of the common multiple shape can be solved in a practical time. We present a method for determining the common multiple shape for provided tuples of polyominoes and outline concrete results, which improve on the previously known results in the puzzle community.

DOI： 10.1007/978-3-031-52113-3_4

Scopus

Publisher：Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)  

We consider a graph orientation problem that can be viewed as a generalization of Minimum Graph Coloring. Our problem takes as input an undirected graph G= (V, E) in which every edge { u, v} ∈ E has two (potentially different and not necessarily positive) weights representing the lengths of its two possible directions (u, v) and (v, u), and asks for an orientation, i.e., an assignment of a direction to each edge of G, such that the length of a longest simple directed path in the resulting directed graph is minimized. A longest path in a graph is not always a maximal path when some edges have negative lengths, so the problem has two variants depending on whether all simple directed paths or maximal simple directed paths only are taken into account in the definition. We prove that the problems are NP-hard to approximate even if restricted to subcubic planar graphs, and develop fast polynomial-time algorithms for both problem variants for three classes of graphs: path graphs, cycle graphs, and star graphs.

DOI： 10.1007/978-3-031-49190-0_10

Scopus

DOI： 10.1007/978-981-97-0566-5_29

Scopus

Language：English   Publisher：IJNC Editorial Committee  

For an undirected graph G = (V,E) and a k-non-negative integer vector p = (p1, . . . , pk), a mapping l : V → N∪{0} is called an L(p)-labeling of G if |l(u) − l(v)| ≥ pd for any two distinct vertices u, v ∈ V with distance d, and the maximum value of {l(v) | v ∈ V } is called the span of l. Originally, L(p)-labeling of G for p = (2, 1) is introduced in the context of frequency assignment in radio networks, where ‘close’ transmitters must receive different frequencies and ‘very close’ transmitters must receive frequencies that are at least two frequencies apart so that they can avoid interference. L(p)-Labeling is the problem of finding the minimum span λp among L(p)-labelings of G, which is NP-hard for every non-zero p. L(p)-Labeling is well studied for specific p’s; in particular, many (exact or approximation) algorithms for general graphs or restricted classes of graphs are proposed for p = (2, 1) or more generally p = (p, q). Unfortunately, most algorithms strongly depend on the values of p, and it is not apparent to extend algorithms for p to ones for another p′ in general. In this paper, we give a simple polynomial-time reduction of L(p)-Labeling on graphs with a small diameter to Metric (Path) TSP, which enables us to use numerous results on (Metric) TSP. On the practical side, we can utilize various high-performance heuristics for TSP, such as Concordo and LKH, to solve our problem. On the theoretical side, we can see that the problem for any p under this framework is 1.5-approximable, and it can be solved by the Held-Karp algorithm in O(2nn2) time, where n is the number of vertices, and so on.

DOI： 10.15803/ijnc.14.1_26

CiNii Research

Publishing type：Research paper (scientific journal)  

Other Link： https://dblp.uni-trier.de/db/journals/ijnc/ijnc14.html#HanakaOS24

Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.dam.2023.07.012

Web of Science

Scopus

Authorship：Last author   Language：English   Publishing type：Research paper (international conference proceedings)  

DOI： 10.48550/arXiv.2303.01290

Publishing type：Research paper (international conference proceedings)   Publisher：Springer  

DOI： 10.1007/978-3-031-23101-8_15

Web of Science

Scopus

Other Link： https://dblp.uni-trier.de/db/conf/sofsem/sofsem2023.html#KiyaOOO23

Publishing type：Research paper (international conference proceedings)  

DOI： 10.4230/LIPIcs.ISAAC.2023.37

Scopus

Other Link： https://dblp.uni-trier.de/db/conf/isaac/isaac2023.html#HanakaOSS23

Publisher：2023 IEEE International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2023  

For an undirected graph G=(V, E) and a k-nonnegative integer vector p=(p_1, L˙, p_k), a mapping l: V → N ∪0 is called an L(p)-labeling of G if |l(u)-l(v)| ≥ p_d for any two distinct vertices u, v in V with distance d, and the maximum value of l(v) mid v in V is called the span of l. Originally, L(p)-labeling of G for p=(2,1) is introduced in the context of frequency assignment in radio networks, where 'close' transmitters must receive different frequencies and 'very close' transmitters must receive frequencies that are at least two frequencies apart so that they can avoid interference. L(p) LABELING is the problem of finding the minimum span λp among L(p)-labelings of G, which is NP-hard for every non-zero p. L(p)-LABELING is well studied for specific p 's; in particular, many (exact or approximation) algorithms for general graphs or restricted classes of graphs are proposed for p=(2,1) or more generally p=(p, q). Unfortunately, most algorithms strongly depend on the values of p, and it is not apparent to extend algorithms for p to ones for another p' in general. In this paper, we give a simple polynomial-time reduction of L(p)-LABELING on graphs with a small diameter to METRIC (PATH) TSP, which enables us to use numerous results on (METRIC) TSP. On the practical side, we can utilize various high-performance heuristics for TSP, such as Concordo and LKH, to solve our problem. On the theoretical side, we can see that the problem for any p under this framework is 1.5 -approximable, and it can be solved by the Held-Karp algorithm in O2^n n^2) time, where n is the number of vertices, and so on.

DOI： 10.1109/IPDPSW59300.2023.00059

Web of Science

Scopus

Language：Japanese   Publisher：Discrete Applied Mathematics  

The competitive diffusion game is a game-theoretic model of information spreading on a graph proposed by Alon et al. (2010). It models the diffusion process of information in social networks where several competitive companies want to spread their information, for example. The nature of this game strongly depends on the graph topology, and the relationship is studied from several aspects. In this paper, we investigate the existence of a pure Nash equilibrium of the two-player competitive diffusion game on chordal and its related graphs. We show that a pure Nash equilibrium always exists on split graphs, block graphs, and interval graphs, all of which are well-known subclasses of chordal graphs. On the other hand, we show that a pure Nash equilibrium does not always exist on (strongly) chordal graphs; the boundary of the existence of a pure Nash equilibrium is found.

DOI： 10.1016/j.dam.2022.04.025

Web of Science

Scopus

Language：Japanese   Publisher：Leibniz International Proceedings in Informatics, LIPIcs  

The problem of computing the longest common subsequence of two sequences (LCS for short) is a classical and fundamental problem in computer science. In this paper, we study four variants of LCS: the Repetition-Bounded Longest Common Subsequence problem (RBLCS) [2], the Multiset-Restricted Common Subsequence problem (MRCS) [11], the Two-Side-Filled Longest Common Subsequence problem (2FLCS), and the One-Side-Filled Longest Common Subsequence problem (1FLCS) [5, 6]. Although the original LCS can be solved in polynomial time, all these four variants are known to be NP-hard. Recently, an exact, O(1.44225n)-time, dynamic programming (DP)-based algorithm for RBLCS was proposed [2], where the two input sequences have lengths n and poly(n). We first establish that each of MRCS, 1FLCS, and 2FLCS is polynomially equivalent to RBLCS. Then, we design a refined DP-based algorithm for RBLCS that runs in O(1.41422n) time, which implies that MRCS, 1FLCS, and 2FLCS can also be solved in O(1.41422n) time. Finally, we give a polynomial-time 2-approximation algorithm for 2FLCS.

DOI： 10.4230/LIPIcs.CPM.2022.15

Scopus

Language：Japanese   Publisher：Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS  

The cost-sharing connection game is a variant of routing games on a network. In this model, given a directed graph with edge costs and capacities, each agent wants to construct a path from a source to a sink with low cost. The cost of each edge is shared by the users based on a cost-sharing function. One of simple cost-sharing functions is defined as the cost divided by the number of users. It models an ideal setting, where no overhead arises when people share things, though it might be quite rare in real life. In this paper, we model more realistic scenarios of cost-sharing connection games by generalizing the cost-sharing function. The arguments do not depend on specific cost-sharing functions and are applicable for a class of all natural cost-sharing scenarios, which include equal divisions with any natural functional overheads. We show that many bounds of the Price of Anarchy and the Price of Stability under sum-cost and max-cost criteria inherit the no-overhead case.

Scopus

Language：Japanese   Publisher：Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)  

Airport problem is a classical and well-known model of fair cost-sharing for a single facility among multiple agents. This paper extends it to the so-called assignment setting, that is, for multiple facilities and agents, each agent chooses a facility to use and shares the cost with the other agents. Such a situation can be often seen in sharing economy, such as sharing fees for office desks among workers, and taxi fare among customers of possibly different destinations on a line. Our model is regarded as a coalition formation game, based on the fair cost-sharing of the airport problem; we call our model a fair ride allocation on a line. As the criteria of solution concepts, we incorporate Nash stability and envy-freeness into our setting. We show that a Nash-stable feasible allocation that minimizes the social cost of agents can be computed efficiently if a feasible allocation exists. For envy-freeness, we provide several structural properties of envy-free allocations. Based on these, we design efficient algorithms for finding an envy-free allocation when either (1) the number of facilities, (2) the number of agent types, or (3) the capacity of facilities, is small. Moreover, we show that a consecutive envy-free allocation can be computed in polynomial time. On the negative front, we show the NP-hardness of determining the existence of an allocation under two relaxed envy-free concepts.

DOI： 10.1007/978-3-031-15714-1_24

Scopus

Language：Japanese   Publisher：Journal of Graph Algorithms and Applications  

Given a graph, an L(p, 1)-labeling of the graph is an assignment f from the vertex set to the set of nonnegative integers such that for any pair of vertices u and v, |f(u) − f(v)| ≥ p if u and v are adjacent, and f(u) ≠ f(v) if u and v are at distance 2. The L(p, 1)-labeling problem is to minimize the span of f (i.e.,maxu∈V (f(u)) − minu∈V (f(u)) + 1). It is known to be NP-hard even for graphs of maximum degree 3 or graphs with tree-width 2, whereas it is fixed-parameter tractable with respect to vertex cover number. Since the vertex cover number is a kind of the strongest parameter, there is a large gap between tractability and intractability from the viewpoint of parameterization. To fill up the gap, in this paper, we propose new fixed-parameter algorithms for L(p, 1)-Labeling by the twin cover number plus the maximum clique size and by the tree-width plus the maximum degree. These algorithms reduce the gap in terms of several combinations of parameters.

DOI： 10.7155/jgaa.00592

Scopus

Publishing type：Research paper (international conference proceedings)  

DOI： 10.1007/978-3-031-22105-7_26

Web of Science

Scopus

Other Link： https://dblp.uni-trier.de/db/conf/cocoon/cocoon2022.html#IshiiKMO22

Language：Japanese   Publisher：一般社団法人電子情報通信学会  

DOI： 10.1587/ieiceissjournal.26.2_10

CiNii Research

Publisher：Brain  

Aquaporin 4 (AQP4)-IgG-positive neuromyelitis optica spectrum disorder (AQP4-IgG+NMOSD) is an autoimmune astrocytopathic disease pathologically characterized by the massive destruction and regeneration of astrocytes with diverse types of tissue injury with or without complement deposition. However, it is unknown whether this diversity is derived from differences in pathological processes or temporal changes. Furthermore, unlike for the demyelinating lesions in multiple sclerosis, there has been no staging of astrocytopathy in AQP4-IgG+NMOSD based on astrocyte morphology. Therefore, we classified astrocytopathy of the disease by comparing the characteristic features, such as AQP4 loss, inflammatory cell infiltration, complement deposition and demyelination activity, with the clinical phase. We performed histopathological analyses in eight autopsied cases of AQP4-IgG+NMOSD. Cases comprised six females and two males, with a median age of 56.5 years (range, 46-71 years) and a median disease duration of 62.5 months (range, 0.6-252 months). Astrocytopathy in AQP4-IgG+NMOSD was classified into the following four stages defined by the astrocyte morphology and immunoreactivity for GFAP: (i) astrocyte lysis: extensive loss of astrocytes with fragmented and/or dust-like particles; (ii) progenitor recruitment: loss of astrocytes except small nucleated cells with GFAP-positive fibre-forming foot processes; (iii) protoplasmic gliosis: presence of star-shaped astrocytes with abundant GFAP-reactive cytoplasm; and (iv) fibrous gliosis: lesions composed of densely packed mature astrocytes. The astrocyte lysis and progenitor recruitment stages dominated in clinically acute cases (within 2 months after the last recurrence). Findings common to both stages were the loss of AQP4, a decreased number of oligodendrocytes, the selective loss of myelin-associated glycoprotein and active demyelination with phagocytic macrophages. The infiltration of polymorphonuclear cells and T cells (CD4-dominant) and the deposition of activated complement (C9neo), which reflects the membrane attack complex, a hallmark of acute NMOSD lesions, were selectively observed in the astrocyte lysis stage (98.4% in astrocyte lysis, 1.6% in progenitor recruitment, and 0% in protoplasmic gliosis and fibrous gliosis). Although most of the protoplasmic gliosis and fibrous gliosis lesions were accompanied by inactive demyelinated lesions with a low amount of inflammatory cell infiltration, the deposition of complement degradation product (C3d) was observed in all four stages, even in fibrous gliosis lesions, suggesting the past or chronic occurrence of complement activation, which is a useful finding to distinguish chronic lesions in NMOSD from those in multiple sclerosis. Our staging of astrocytopathy is expected to be useful for understanding the unique temporal pathology of AQP4-IgG+NMOSD.

DOI： 10.1093/brain/awab102

Scopus

Language：Japanese   Publisher：Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS  

In this paper, we study a variant of hedonic games, called Seat Arrangement. The model is defined by a bijection from agents with preferences to vertices in a graph. The utility of an agent depends on the neighbors in the graph. In this paper, we study the price of stability and fairness in Seat Arrangement, and the computational complexity and the parameterized complexity of finding certain “good” seat arrangements, say Maximum Welfare Arrangement, Maximin Utility Arrangement, Stable Arrangement, and Envy-free Arrangement.

Scopus

CiNii Research

Publishing type：Research paper (international conference proceedings)  

DOI： 10.1609/aaai.v38i18.30060

Other Link： https://dblp.uni-trier.de/db/conf/aaai/aaai2024.html#HoriyamaK0SS24

Authorship：Corresponding author  

DOI： 10.1007/978-3-031-49611-0_28

Scopus

Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.dam.2023.01.026

Web of Science

Scopus

Publishing type：Part of collection (book)   Publisher：Springer International Publishing  

DOI： 10.1007/978-3-031-30448-4_19

Scopus

Publishing type：Research paper (scientific journal)  

DOI： 10.48550/arXiv.2305.10749

Publishing type：Research paper (scientific journal)  

DOI： 10.48550/arXiv.2308.16426

Publishing type：Research paper (international conference proceedings)  

DOI： 10.4230/LIPIcs.CPM.2023.2

Scopus

Other Link： https://dblp.uni-trier.de/db/conf/cpm/cpm2023.html#AsahiroEG0LMOT23

Publishing type：Research paper (scientific journal)  

DOI： 10.48550/arXiv.2312.10599

Publishing type：Research paper (scientific journal)  

DOI： 10.48550/arXiv.2307.02787

Publishing type：Research paper (scientific journal)  

DOI： 10.48550/arXiv.2310.01983

Language：English   Publishing type：Research paper (conference, symposium, etc.)  

DOI： 10.1007/s00453-021-00875-y

Web of Science

Scopus

Language：Japanese   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.tcs.2021.11.019

Web of Science

Scopus

Authorship：Last author   Language：English   Publishing type：Research paper (scientific journal)  

J-GLOBAL

Language：Japanese   Publishing type：Research paper (international conference proceedings)  

DOI： 10.1007/978-3-031-06678-8_37

Scopus

Other Link： https://dblp.uni-trier.de/db/conf/iwoca/iwoca2022.html#YoshiwatariKHO22

Publishing type：Research paper (international conference proceedings)   Publisher：International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)  

Other Link： https://dl.acm.org/doi/10.5555/3535850.3536053

Publishing type：Research paper (scientific journal)  

DOI： 10.48550/arXiv.2211.05307

Language：Japanese   Publisher：THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS  

DOI： 10.11509/isciesci.65.10_415

CiNii Research

Authorship：Last author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：The Institute of Electronics, Information and Communication Engineers  

<p>DAIHINMIN, which means Grand Pauper, is a popular playing-card game in Japan. TANHINMIN is a simplified variant of DAIHINMIN, which was proposed by Nishino in 2007 in order to investigate the mathematical properties of DAIHINMIN. In this paper, we consider a 2-player generalized TANHINMIN, where the deck size is arbitrary <i>n</i>. We present a linear-time algorithm that determines which player has a winning strategy after all cards are distributed to the players.</p>

DOI： 10.1587/transfun.2020dmp0026

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Scopus

Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：World Scientific Pub Co Pte Lt  

The goal of an outdegree-constrained edge-modification problem is to find a spanning subgraph or supergraph [Formula: see text] of an input undirected graph [Formula: see text] such that either: (Type I) the number of edges in [Formula: see text] is minimized or maximized and [Formula: see text] can be oriented to satisfy some specified constraints on the vertices’ resulting outdegrees; or: (Type II) among all subgraphs or supergraphs of [Formula: see text] that can be constructed by deleting or inserting a fixed number of edges, [Formula: see text] admits an orientation optimizing some objective involving the vertices’ outdegrees. This paper introduces eight new outdegree-constrained edge-modification problems related to load balancing called (Type I) MIN-DEL-MAX, MIN-INS-MIN, MAX-INS-MAX, and MAX-DEL-MIN and (Type II) [Formula: see text]-DEL-MAX, [Formula: see text]-INS-MIN, [Formula: see text]-INS-MAX, and [Formula: see text]-DEL-MIN. In each of the eight problems, the input is a graph and the goal is to delete or insert edges so that the resulting graph has an orientation in which the maximum outdegree (taken over all vertices) is small or the minimum outdegree is large. We first present a framework that provides algorithms for solving all eight problems in polynomial time on unweighted graphs. Next we investigate the inapproximability of the edge-weighted versions of the problems, and design polynomial-time algorithms for six of the problems on edge-weighted trees.

DOI： 10.1142/S012905412150012X

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Scopus

Language：Japanese   Publishing type：Part of collection (book)   Publisher：Springer International Publishing  

DOI： 10.1007/978-3-030-68211-8_17

Scopus

Language：Japanese   Publishing type：Research paper (scientific journal)  

DOI： 10.1186/s40649-021-00100-4

Scopus

Publishing type：Research paper (scientific journal)  

Other Link： https://dblp.uni-trier.de/db/journals/corr/corr2111.html#abs-2111-02579

Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.tcs.2020.07.013

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Scopus

Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.tcs.2020.07.042

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Scopus

Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.dam.2020.01.022

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Scopus

Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

DOI： 10.1007/s00453-020-00700-y

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Scopus

Other Link： http://link.springer.com/article/10.1007/s00453-020-00700-y/fulltext.html

Language：Japanese   Publishing type：Part of collection (book)   Publisher：Springer International Publishing  

DOI： 10.1007/978-3-030-48966-3_4

Scopus

Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Journal of Graph Algorithms and Applications  

DOI： 10.7155/jgaa.00528

Scopus

Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

DOI： 10.1007/s00224-018-09908-6

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Scopus

Other Link： http://link.springer.com/article/10.1007/s00224-018-09908-6/fulltext.html

Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：International Foundation for Autonomous Agents and Multiagent Systems  

Other Link： https://dblp.uni-trier.de/conf/atal/2020

Language：English   Publishing type：Research paper (scientific journal)   Publisher：The Japan Society of Mechanical Engineers  

<p>In this paper, we analyze the complexity of the gear placement problem (GPP). In the GPP, we are given a rectangular plane, called a gearbox, on which a torque generator source and a set of gears, called target gears, are placed. The task is to find a placement of a set of gears called sub-gears, to connect every target gear to the torque generator source so that every target gear rotates in a given direction. The objective is to minimize the number of sub-gears to be used. We prove that the GPP is NP-hard by giving a reduction from the Hamiltonian path problem on 3-regular planar graphs, which is known to be NP-complete, to the GPP. We also present an upper bound for the number of sub-gears to be placed.</p>

DOI： 10.1299/jamdsm.2020jamdsm0069

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CiNii Research

Language：Japanese   Publishing type：Part of collection (book)   Publisher：Springer International Publishing  

DOI： 10.1007/978-3-030-38919-2_52

Web of Science

Scopus

Publishing type：Research paper (scientific journal)  

Other Link： https://dblp.uni-trier.de/db/journals/corr/corr2007.html#abs-2007-08045

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.dam.2017.10.018

Web of Science

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.eneco.2017.09.012

Web of Science

Language：Japanese   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.disopt.2016.01.003

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Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.tcs.2016.08.016

Web of Science

Language：English   Publishing type：Research paper (scientific journal)  

Language：Japanese   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1007/s00224-014-9565-5

Web of Science

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.tcs.2015.07.037

Web of Science

Language：Japanese   Publishing type：Research paper (scientific journal)  

Language：Japanese   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.tcs.2015.01.007

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Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.tcs.2015.04.026

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Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.tcs.2014.11.001

Web of Science

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1137/140958682

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Language：English   Publishing type：Research paper (scientific journal)  

Web of Science

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1109/TCBB.2014.2372782

Web of Science

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1007/978-3-319-17142-5_19

Web of Science

Language：Japanese   Publishing type：Research paper (scientific journal)  

無向グラフに対するオリエンテーション(グラフ有向化)とは,各辺に対して向き付けを行うことである.オリエンテーションによる結果として得られる有向グラフにおいて,各頂点の出次数が事前に指定された下界あるいは上界を満たす場合に,それを次数制約オリエンテーションと呼ぶ.本稿では,次数制約オリエンテーションを求める問題の一種である,2つのお互いに関連するMIN W-LIGHT問題とMAX W-HEAVY問題について考える.任意の固定された非負整数Wに対して,MIN W-LIGHT(またはMAX W-HEAVY)問題は,入力された無向グラフGのオリエンテーションのうち,出次数W以下(またはWP以上)の頂点数を最小化(または最大化)するものを発見することを目的とする.これらの問題の計算複雑さはWの値によって変化する.本稿では,これらの問題の計算複雑さ(主に近似可能性)に関するいくつかの結果を示す.

Language：Japanese   Publishing type：Research paper (scientific journal)  

無向グラフに対するオリエンテーション(グラフ有向化)とは,各辺に対して向き付けを行うことである.オリエンテーションによる結果として得られる有向グラフにおいて,各頂点の出次数が事前に指定された下界あるいは上界を満たす場合に,それを次数制約オリエンテーションと呼ぶ.本稿では,次数制約オリエンテーションを求める問題の一種である,2つのお互いに関連するMIN W-LIGHT問題とMAX W-HEAVY問題について考える.任意の固定された非負整数Wに対して,MIN W-LIGHT(またはMAX W-HEAVY)問題は,入力された無向グラフGのオリエンテーションのうち,出次数W以下(またはWP以上)の頂点数を最小化(または最大化)するものを発見することを目的とする.これらの問題の計算複雑さはWの値によって変化する.本稿では,これらの問題の計算複雑さ(主に近似可能性)に関するいくつかの結果を示す.

Language：Japanese   Publishing type：Research paper (scientific journal)  

無向グラフに対するオリエンテーション （グラフ有向化） とは，各辺に対して向き付けを行うことである．オリエンテーションによる結果として得られる有向グラフにおいて，各頂点の出次数が事前に指定された下界あるいは上界を満たす場合に，それを次数制約オリエンテーションと呼ぶ．本稿では，次数制約オリエンテーションを求める問題の一種である，2 つのお互いに関連する Min W-Light 問題と Max W-Heavy 問題について考える．任意の固定された非負整数 W に対して，Min W-Light （または Max W-Heavy） 問題は，入力された無向グラフ G のオリエンテーションのうち，出次数 W 以下 （または W 以上） の頂点数を最小化 （または最大化） するものを発見することを目的とする．これらの問題の計算複雑さは W の値によって変化する．本稿では，これらの問題の計算複雑さ （主に近似可能性） に関するいくつかの結果を示す．

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DOI： 10.1016/j.tcs.2013.11.030

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DOI： 10.1016/j.tcs.2014.04.011

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DOI： 10.1016/j.dam.2012.11.015

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DOI： 10.1007/978-3-319-07001-8_50

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DOI： 10.1007/978-3-319-13075-0_44

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DOI： 10.1007/978-3-319-13075-0_17

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DOI： 10.1007/978-3-319-13075-0_31

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A degree-constrained graph orientation of an undirected graph is an assignment of a direction to each edge in the graph such that the outdegree of every vertex in the resulting directed graph satisfies a prescribed lower and/or upper bound. Such graph orientations have been studied in many literatures and various characterizations are known. We consider two related optimization problems introduced in [3]: For any fixed non-negative integer W, the problem MAX W-LIGHT (or MIN W-HEAVY) takes as input an undirected graph G and ask for an orientation of G that maximizes (or minimizes) the number of vertices with outdegree at most W (or at least W). The problems' computational complexities vary with W. In this paper we show several results related to their polynomial-time approximability.

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グラフGに対し,|I_b|=|I_r|であるような2つの独立点集合I_bとI_rが与えられたとする.また,Gにおいて,I_bに含まれる各点にはトークンが置かれているとする.スライディングトークン問題とは,I_bからI_rへのGの独立点集合の系列が存在するか判定する問題である.ただし,系列に含まれる各独立点集合は,その1つ前の独立点集合から,ただ1つのトークンをGの辺に沿ってスライドさせることで得られなければならない.この問題は,理想グラフに対してPSPACE完全であることが知られている.本論文では,理想グラフのいくつかの部分クラスに対して,この問題がO(n)時間で解けることを示す.ここで,nはグラフの点数である.また,これらのグラフに対しては,実際にI_bからI_rへ遷移させる最短の系列を多項式時間で見つけることができる.

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DOI： 10.1016/j.dam.2013.05.018

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DOI： 10.1007/s00453-012-9657-z

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DOI： 10.1587/transinf.E96.D.481

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DOI： 10.1007/s00453-011-9589-z

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DOI： 10.1137/120900368

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DOI： 10.1007/s00446-012-0173-9

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DOI： 10.1145/2287718.2287723

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DOI： 10.1016/j.disc.2012.01.007

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本論文では,ピクセルグリッドから最大重み領域を切り出す問題を扱う.ただし,切り出された領域は,基線に対して基単調図形に分割できなければならない.n×nピクセルグリッドと基線が与えられたとき,この問題はO(n^3)時間で解けることが知られている.これに対し本論文では,ピクセルグリッドのみが与えられたとき,k本の基線を最適に配置することはNP困難であることを示す.さらに,この配置問題に対し,O(n^3)時間の2倍近似アルゴリズムを与える。また,多項式時間で求解できるいくつかのケースや問題の変種も示す.

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DOI： 10.1016/j.tcs.2011.12.033

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証明書分散問題は，与えられた通信要求をセキュアに実現するために各計算機が保有しなければいけない証明書の枚数を最小化する組み合わせ最適化問題である．本研究では，通信要求グラフ，および証明書グラフが木の場合における証明書分散問題の計算困難性について論じる．通信要求グラフが木の場合，その最大次数によって計算困難さが変化すること，および証明書グラフが木の場合は多項式時間で最適解を求めることが可能であることを示す．

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In the context of designing a scalable overlay network to support decentralized topic-based pub/sub communication, the Minimum Topic-Connected Overlay problem(Min-TCO, for short) has been investigated:Given a set of t topics and a collection of n users together with the lists of topics they are intersted in, the aim is to collect these users to a network by a minimum number of edges such that every graph induced by users intersted in a common topic is connected.In this paper, we consider the complexity of Min-TCO.

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証明書分散問題は,与えられた通信要求をセキュアに実現するために各計算機が保有しなければいけない証明書の枚数を最小化する組み合わせ最適化問題である.本研究では,通信要求グラフ,および証明書グラフが木の場合における証明書分散問題の計算困難性について論じる.通信要求グラフが木の場合,その最大次数によって計算困難さが変化すること,および証明書グラフが木の場合は多項式時間で最適解を求めることが可能であることを示す.

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In the context of designing a scalable overlay network to support decentralized topic-based pub/sub communication, the Minimum Topic-Connected Overlay problem(Min-TCO, for short) has been investigated:Given a set of t topics and a collection of n users together with the lists of topics they are intersted in, the aim is to collect these users to a network by a minimum number of edges such that every graph induced by users intersted in a common topic is connected.In this paper, we consider the complexity of Min-TCO.

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DOI： 10.1109/IPDPSW.2012.107

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DOI： 10.1007/s10878-009-9276-z

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本論文では，パターン形成問題と呼ばれる，非同期的に動くロボット群を幾何的な配置に並ばせる問題を考察する．ここでは，各ロボットは各自固有の座標系に従って，他のロボットの配置と目的の配置を観測するできるものとする．n 点の座標からなる集合の対 A,B の間のマッチングを求めるアルゴリズム "clockwise matching" を構成し，"clockwise matching" によって任意のパターン形成問題を解くことができることを示す．A geometric pattern formation problem by autonomous mobile robots is investigated in this paper. In the "embedded pattern formation problem" disscussed in this paper, the target pattern is assumed to be visible from the robots via their own (local) coordinate system. We show that our matching algorithm "clockwise matching" which calculates the matching between a pair of patterns A and B both comprising of n coordinates, solves any embedded pattern formation problem.

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DOI： 10.1016/j.dam.2010.11.003

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DOI： 10.1142/S0129054111008246

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DOI： 10.1016/j.tcs.2010.09.028

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グラフにおける頂点/辺支配集合問題の新しい亜種について考える.ある頂点はその頂点自身と隣接点を支配すると言い,同様にある辺はその辺自身と隣接する辺を支配すると言う.グラフG=(V,E)と正整数kが与えられたとき,k-頂点(k-辺)支配問題(それぞれ以下k-MaxVD, k-MaxEDと呼ぶ)は高々サイズkの頂点の部分集合D_V&subE;V(D_E&subE;E)の中で,支配する頂点集合(また辺集合)のサイズを最大化するものを求める問題である.本論文では,まずこの問題に対して単純な貪欲アルゴリズムがk-MaxVD, k-MaxEDいずれに対しても近似比(1-1/e)を達成することを示す.次にP≠NPの条件下で,k-MaxVEに対してこの近似比が多項式時間アルゴリズムの最善であることを示す.さらにP≠NPの条件下で,k-MaxEDに対して1303/1304よりも良い近似比の多項式時間アルゴリズムが存在しないことを示す.一方,kがグラフの最小最大マッチングのサイズを超えないという条件下では,k-MaxEDに対して近似比3/4の多項式時間アルゴリズムが存在することを示す.

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本論文は，自己安定リーダー選挙メディエイテッドポピュレーションプロトコル (SS-LE MPP) の領域複雑度に関する研究結果である．Cai，Izumi and Wada (2009) は n エージェントに対する自己安定リーダー選挙ポピュレーションプロトコル (SS-LE PP) は少なくとも n 個のエージェント状態を必要とすることを示した．さらに n エージェントに対する SS-LE MPP のうちエージェント状態数が n であるプロトコルを与えた．MPP は Chatzigiannakis，Michail and Spirakis (2009) によって紹介された．MPP は分散ネットワークモデルの 1 つで，各エージェント間に局所的なメモリを追加した PP の拡張モデルである．一般的に MPP は PP よりも計算能力が高いことが知られている．一方で SS-LE のエージェント状態に対する空間複雑度の減少可能性については知られていない．本稿では，n エージェントの SS-LE MPP のうちエージェント状態数が n-1 であり，各エージェント間に 1 ビットのメモリが与えられたプロトコルを与える．This paper investigates the space complexity of a self stabilizing leader election in a mediated population protocol (SS-LE MPP). Cai, Izumi and Wada (2009) showed that SS-LE in a population protocol (SS-LE PP) for n agents requires at least n agent-states, and gave a SS-LE PP with n agent-states for n agents. MPP is a model of distributed computation, introduced by Chatzigiannakis, Michail and Spirakis (2009) as an extension of PP allowing an extra memory on every agents pair. While they showed that MPP is stronger than PP in general, it was not known if a MPP can really reduce the space complexity of SS-LE with respect to agent-states. We in this paper give a SS-LE MPP with n - 1 agent-states and a single bit memory on every agents pair for n agents.

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グラフ G の k-(p,q)-全ラベリングとは，G の節点と辺への 0 から k までの整数値の割当てであり，節点とそれに接続する辺の間では少なくとも p，隣接する 2 節点間または 2 辺間では少なくとも q の差があるもののことをいう．G の (p, q)-全ラベリング数 λTp;q(G) は，k がとりうる値の最小値として定義される．G の (p, q)-全ラベリング問題とは，ラベリング数 λTp;q(G) を求める問題である．本研究では，いくつかのグラフクラスのグラフの (p, q)-全ラベリング数に対して新しい上界と下界を与える．とくに，グラフが木の場合にはタイトな上界と下界を与える．また，グラフが木で p≦3q/2 の場合に (p, q)-全ラベリング問題を解く線形時間アルゴリズムを与え，さらに最大次数が 4 以上という仮定が加わった場合，λTp;q(T) を実現する木Tを完全に特徴づけられることも示す．この結果は，(p; q)-全ラベリング問題の一般化である L (p; q)-ラベリング問題が q が p の約数でないすべての (p; q) の組に対し NP 困難であることと対照的である．A (p,q)-total labeling of a graph G is an assignment f from the vertex set V(G) and the edge set E(G) to the set of nonnegative integers such that |f(x)-f(y)| ≧ p if x is a vertex and y is an edge incident to x, and |f(x)-f(y)| ≧ q if x and y are a pair of adjacent vertices or a pair of adjacent edges, for all x and y in V(G) ∪ E(G). A k-(p,q)-total labeling is a (p,q)-total labeling f:V(G) ∪ E(G) → {0,...,k}, and the (p,q)-total labeling problem asks the minimum k, which we denote by λTp,q(G), among all possible assignments. In this paper, we first give new upper and lower bounds on λTp,q(G) for some classes of graphs G, in particular, tight bounds on λTp,q(T) for trees T. We then show that if p ≦ 3q/2, the problem for trees T is linearly solvable, and give a complete characterization of trees achieving λTp,q(T) if in addition Δ ≧ 4 holds, where Δ is the maximum degree of T. It is contrasting to the fact that the L(p,q)-labeling problem, which is a generalization of the (p,q)-total labeling problem, is NP-hard for any two positive integers p and q such that q is not a divisor of p.

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DOI： 10.1016/j.disc.2010.02.015

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DOI： 10.1016/j.tcs.2010.03.029

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DOI： 10.1142/S0129054110007349

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DOI： 10.1016/j.tcs.2010.01.032

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グラフの k-L(2, 1) -ラベリングとは，頂点への 0 から k までの整数値の割り当てであり，隣接頂点間では少なくとも 2，距離 2 の頂点間では少なくとも 1 の差があるもののことを言う．L(2, 1) -ラベリング問題とは，グラフに対する k-L(2, 1) ラベリングの中で最小の k を求めるものである．この問題は，木幅が 2 のグラフに対してでも NP 困難であることが知られている．一方，多項式時間アルゴリズムは，路や閉路，木といった限られたクラスにしか知られておらず，木に対するアルゴリズムの計算量も 10 年以上 O(Δ4.5n) 時間であった （ただし，Δ はグラフの最大次数，n は木の頂点数）．この計算量は最近になって O(min{n1.75, Δ1.5n}) 時間へと改善されたが，線形時間で解けるかどうかは未解決であった．本論文では，これを解決する木の L(2, 1) -ラベリングに対する線形時間アルゴリズムを提案する．An L(2, 1)-labeling of a graph G is an assignment f from the vertex set V(G) to the set of nonnegative integers such that |f (x)− f (y)| ≥ 2 if x and y are adjacent and |f (x)− f (y)| ≥ 1 if x and y are at distance 2, for all x and y in V(G). A k-L(2, 1)-labeling is an L(2, 1)-labeling f : V(G) → {0, . . . , k}, and the L(2, 1)-labeling problem asks the minimum k, which we denote by λ(G), among all possible assignments. It is known that this problem is NP-hard even for graphs of treewidth 2, and tree is one of very few classes for which the problem is polynomially solvable. The running time of the best known algorithm for trees had been O(Δ4.5n) for more than a decade, and an O(min{n1.75, Δ1.5n})-time algorithm has appeared recently, where Δ is the maximum degree of T and n = |V(T)|, however, it has been open if it is solvable in linear time. In this paper, we finally settle this problem for L(2, 1)-labeling of trees by establishing a linear time algorithm.

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DOI： 10.1016/j.tcs.2009.04.025

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MAXMINO という無向グラフの向き付け問題の一種について考える．無向枝重みつきグラフの向き付けを与えることにより，重み付き出次数を定義する （枝重みは正整数であるとする）．この問題は，グラフ中の最小重み付き出次数を最大化する問題である．本研究ではまず，MAXMINO は枝重みを {1 , 2} に限定し，かつ各頂点の （重みなし） 次数が高々 3，さらにグラフが平面二部であるような場合でも強 NP 困難であり，P= NP でない限り，任意の定数 E ＞ 0 に対して多項式時間では 2 - E 近似不可能であることを示す．次にすべての枝重みが 1 である場合には，多項式時間で解くことができることを示す．これにより，枝重みが wmin よりも大きい枝数が O (log n)であるときにも，多項式時間で解くことができる．さらに，この手法により MAXMINO に対する単純な wmax / wmin 近似多項式時間アルゴリズムを得ることができる （wmax，wmin はそれぞれ枝重みの最大値，最小値)．最後に，入力グラフがカクタスである場合にも MAXMINO は多項式時間で解くことができることを示す．We study a new variant of the graph orientation problem called MAXMINO where the input is an undirected, edge-weighted graph and the objective is to assign a direction to each edge so that the minimum weighted outdegree (taken over all vertices in the resulting directed graph) is maximized. All edge weights are assumed to be positive integers. First, we prove that MAXMINO is strongly NP-hard and cannot be approximated within a ratio of 2 - E for any constant E > 0 in polynomial time unless P=NP, even if all edge weights belong to {1, 2}, every vertex has degree at most three, and the input graph is bipartite or planar. Next, we show how to solve MAXMINO exactly in polynomial time for the special case in which all edge weights are equal to 1. This technique gives us a simple polynomial-time wmax / wmin -approximation algorithm for MAXMINO where wmax and wmin denote the maximum and minimum weights among all the input edges. Furthermore, we also observe that this approach yields an exact algorithm for the general case of MAXMINO whose running time is polynomial whenever the number of edges having weight larger than wmin is at most logarithmic in the number of vertices. Finally, we show that MAXMINO is solvable in polynomial time if the input is a cactus graph.

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Assume that G is a graph and that R is a set of requests which is represented by a reachable ordered pair of nodes in G. The problem discussed in this paper requires us to assign edges to each node such that all requests in R are satisfied and the total number of edges all nodes have is minimized for a given G and R. To satisfy a request (u, v), a set of assigned edges to u and v must contain a path from u to v in G. This problem is called the Minimum Certificate Dispersal problem (MCD) and is NP-hard even if the input graph is restricted to a strongly connected one. In this paper, we consider approximability of MCD. We clarify an optimal approximability/inapproximability bound in terms of order: we prove the approximation ratio of MCD for strongly connected graphs is Ω(log n) and MCD has a polynomial time approximation algorithm whose factor is O(log n) (n is the number of nodes in G). In addition, we prove that when a given graph is restricted to an undirected graph, the MCD algorithm proposed in [11] guarantees 3/2 approximation ratio.

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A spreadsheet, especially MS Excel, is probably one of the most popular software applications for personal-computer users and gives us convenient and user-friendly tools for drawing tables. Using spreadsheets, we often wish to draw several vertical and horizontal black lines on selective gridlines to enhance the readability of our spreadsheet. Such situations we frequently encounter are formulated as the Border Drawing Problem (BDP). Given a layout of black line segments, we study how to draw it efficiently from an algorithmic view point, by using a set of border styles and investigate its complexity. (i) We first define a formal model based on MS Excel, under which the drawability and the efficiency of border styles are discussed, and then (ii) show that unfortunately the problem is -hard for the set of the Excel border styles and for any reasonable subset of the styles. Moreover, in order to provide potentially more efficient drawing, (iii) we propose a new compact set of border styles and show a necessary and sufficient condition of its drawability.

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1007/s00224-008-9117-y

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ゲノム配列から，ある機能発現に関わる遺伝子を発見したいという要望がある．このような遺伝子は対象となるゲノム配列集合においてエラーを含んだ形で頻出する配列パターンの形をとることがしばしばある．本研究では，エラーを含む文字列集合から，ある長さの頻出部分文字列パターンを高速に全列挙するアルゴリズムを提案する．エラーの影響から通常のパターン列挙と異なり，入力文字列には現れないパターンも列挙の対象となる．提案手法ではパターン頻出性の必要条件を利用して最小限の候補パターンをハッシュ格納することにより，高速な全列挙を実現する．We propose a practically fast algorithm that enumerates all m-length substring patterns appearing in at least θ sequences among a given set of string sequences, where at most k errors are allowed for each appearance. The problem of enumerating such substring patterns is derived from the genome science, where frequent substring patterns allowing errors are candidates of a gene related to a certain function. From this context, some pattern should be enumerated even if it does not appear in any sequence, because it may match a sufficient number of sequences by allowing errors. In order to prevent overlooking such potential patterns, we propose a hash-based enumeration algorithm. The algorithm stores not only a substring pattern appearing in a sequence but also its neighboring patterns. By using several techniques/conditions to exclude non-frequent patterns, our algorithm achieves an efficient enumeration of frequent substring patterns allowing errors.

Language：Japanese   Publishing type：Research paper (scientific journal)  

For an undirected graph G=(V,E), an edge cover is defined as a set of edges that covers all vertices of V. It is known that a minimum edge cover can be found in polynomial time and forms a collection of star graphs. Previously, the authors of this paper consider the problem of finding a balanced edge cover where the degrees of star center vertices are balanced, and present an O(n^<1/2>m log Δ)-time polynomial time algorithm, where n, m and Δ are the number of vertices, the number of edges and the maximum degree of vertices, respectively. In this paper, for an edge-weighted graph, we consider the problem of finding a minimum weight balanced edge cover, that is, a balanced edge cover in which the total weights of edges is minimized. By characterizing the optimality as the existence of a certain path structure, we develop an O(n^3 m)-time algorithm.

Language：Japanese   Publishing type：Research paper (scientific journal)  

A random walk on a finite graph is a model that a token on a vertex repeatedly moves to an adjacent vertex randomly chosen according to some transition probability. The cover time of a random walk is a criterion of its speed, and roughly speaking, it is the expected number of steps in which the token visits all the vertices. Given a graph, we consider to design a fast random walk in terms of the cover time, by properly setting the transition probability. In this paper, we give necessary conditions for that the given graph has the cover time of O(n), where n is the number of vertices.

Language：Japanese   Publishing type：Research paper (scientific journal)  

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Given an undirected graph with edge weights, we are asked to find an orientation, i.e., an assignment of a direction to each edge, so as to minimize the weighted maximum outdegree in the resulted directed graph. The problem is called MMO. As previous studies, it is shown that MMO is in P for trees, weak NP-hard for planar bipartite graphs, and strong NP-hard for general graphs. There are still gaps between those graph classes. The objective of this paper is to show tight thresholds of complexity: We show that MMO is (i) in P for cactuses, (ii) weakly NP-hard for multi outerplanar graphs and series-parallel graphs, and also (iii) strongly NP-hard for planar graphs and bipartite graphs.

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正方-八方格子の双対グラフ上の単連結部分グラフにおける完全マッチングについて,局所変形連結性の観点から研究する.これらのグラフは二部性を持たずある意味で不純物を含んでいるため,従来の研究で使われてきた高さ関数を用いた手法を利用することは出来ない.本研究では組合せ的手法を用いて,連結性を保証する最小の局所変形集合を与える:すなわち,これらのグラフ上の任意の完全マッチング同士が,二辺だけを動かす局所変形を繰り返すことにより移りあうことを示す.この結果から完全マッチング全体を状態集合とする簡易なマルコフ連鎖を構成でき,またその定常状態を一様とすることができる.計算シミュレーションでは顕著な統計的性質が観測された.

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本論文ではホーン知識ベースの内包・外包に対する演繹推論について考える.知識ベースの内包・外包はその安定性を測るものとして,Makino, Ibaraki [11]により提案された.本論文ではホーン関数(式表現)の内包に対する演繹推論を行う線形時間アルゴリズムを与え,外包に対する演繹推論がco-NP完全であることを示す.またホーン知識がモデル表現で与えられた場合,演繹推論は内包・外包共に計算困難であることを示す.外包のホーン包絡に関しては,モデル表現においては線形時間で解くことができる一方,式表現においてはco-NP完全となることを示す.また各計算困難なクラスにおいて,多項式時間で解ける部分クラスについても議論する.

Language：English   Publishing type：Research paper (scientific journal)  

無向グラフG=(V,E)において,全ての頂点が少なくとも1つの枝に接しているような枝の集合を枝被覆と呼ぶ.特に最小枝被覆は多項式時間で得られ,またスターグラフの集合により構成されることが知られている.本研究では,各スターの枝数が均等になるような枝被覆を求める負荷分散枝被覆問題を扱う.この問題の応用例として,センサーネットワークの構造最適化などが挙げられる.この目的達成のために,被覆枝における次数に関する狭義単調増加凸関数の和の最小化問題として問題を定式化し,その最適性がある種の交互パスの非存在として特徴付けられることを示す.またこの特徴付けを利用し,最適な枝被覆が最小枝被覆であること,被覆枝における次数列の辞書順が最小となること,最大次数が最小化されることを示す.さらに,この特徴を基にしたO(|V||E|)時間のアルゴリズムを提案する.

Language：Japanese   Publishing type：Research paper (scientific journal)  

Consider a rooted directed acyclic graph G=(V,E)with root r, representing a collection V of web pages connected via a set E of hyperlinks. Each node v is associated with the probability that a user wants to access the node v. The access cost is defined as the expected number of steps required to reach a node from the root r. A bookmark is an additional shortcut from r to a node of G, which may reduce the access cost. The bookmark assignment problem is to find a set of bookmarks that achieves the greatest improvement in the access cost. For the problem, the paper presents a polynomial time approximation algorithm with factor(1-1/e), and shows that there exists no polynomial time approximation algorithm with a better constant factor than(1-1/e)unless NP&subE;DTIME(N^<o(loglogN)>), where is the size of the inputs.

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Failure detectors are distributed oracles that provide each process with information about failures of other processes in distributed systems. It is known that many problems are unsolvable in asynchronous distributed systems if crash failures occur. For such unsolvable problems, failure detectors can be used to make them solvable. How strong information failure detectors should provide, that is, the weakest failure detectors for a certain problem are intensively studied from both theoretical and practical viewpoints. In this paper, we propose two new failure detectors classes, (k-Ω,Σ) and (Ω,Σ_k>), for solving k-Set Agreement problem, where both are generalizations of (Ω,Σ) that is a class of the weakest failure detectors for consensus problem. Furthermore, we consider the reducibility between these failure detector classes and another failure detector class, (Ω^k,Σ), which is also proposed for k-Set Agreement in a related study.

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DOI： 10.1016/j.dam.2006.04.020

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In recent years, DNA sequence sets are used in various fields such as nanotechnology and nanocomputing. Since there are several applications using the sequence sets, the sequence sets need to satisfy several constraints depending on the applications. Since several constraints are combinatorial, we consider the sequence sets design problem where the sequence sets are used to solve combinatorial problems. For the purpose, we focus on the overlapping measure which is more combinatorial than other constraints. Then, we propose a local-search based approximation algorithm. To deal with this, we adopt a dynamic neighorhood search frame work, called Variable Neighborhood Search and Variable Depth Search. The computational experiments show that generated sequence sets are as good as the ones generated by exiting methods, or better.

Language：Japanese   Publishing type：Research paper (scientific journal)  

DNA computing is a new computation paradigm to take reaction process of DNA as computation. The design of DNA sequence is a one of crucial research topics in DNA computing. We have to prepare DNA sequences that satisfy many constraints to react DNA as we expected. In our research, we propose sequence design using Hidden Markov Models. Hidden Markov Model is a stochastic model utilizing Markov process. In this paper, as a test of this method, we show experiments and their results of sequence design of DNA whose minimum free energy is small.

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Other Link： https://dl.acm.org/doi/10.5555/3535850.3536053

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Other Link： https://dl.acm.org/doi/10.5555/3535850.3536053

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