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JOURNAL OF ALGEBRA 2012年第1期353卷 286-297页

作者： Brooksbank, Peter A. Wilson, James B. Bucknell Univ Dept Math Lewisburg PA 17837 USA Colorado State Univ Dept Math Ft Collins CO 80523 USA

A new algorithm is presented to compute the algebra of adjoints associated to a pair of forms on a common finite vector space. This algebra is used in several recent and ongoing projects to study central products, intersections of classical groups, and automorphism groups. The implementation of the new algorithms in MAGMA greatly outperforms its predecessor and hence, in restricted yet important settings, increases the practicality of the various algorithms that use adjoint algebras. (C) 2011 Elsevier Inc. All rights reserved.

关键词： -Algebra Bilinear map Isometry group polynomial-time algorithm

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HEURISTIC algorithm FOR FINDING THE MAXIMUM INDEPENDENT SET

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CYBERNETICS AND SYSTEMS ANALYSIS 2012年第5期48卷 673-680页

作者： Plotnikov, A. D. Volodymyr Dahl East Ukraine Natl Univ Minist Educ & Sci Youth & Sport Ukraine Lugansk Ukraine

A heuristic algorithm is developed for finding the maximum independent set of vertices in an undirected graph. To this end, the technique of finite partially ordered sets is used, in particular, the technique of partitioning such a set into a minimum number of chains. A special digraph is constructed and a solution algorithm is proposed on the basis of a hypothesis about its properties. Some experimental data are presented for well-known examples.

关键词： heuristic algorithm maximum independent set clique NP-hard NP-complete class NP polynomial-time algorithm finite partially ordered set

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Colouring vertices of triangle-free graphs without forests

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DISCRETE MATHEMATICS 2012年第7期312卷 1372-1385页

作者： Dabrowski, Konrad K. Lozin, Vadim Raman, Rajiv Ries, Bernard Univ Warwick DIMAP Coventry CV4 7AL W Midlands England Univ Warwick Math Inst Coventry CV4 7AL W Midlands England Univ Paris 09 LAMSADE Paris France

The VERTEX COLOURING problem is known to be NP-complete in the class of triangle-free graphs. Moreover, it is NP-complete in any subclass of triangle-free graphs defined by a finite collection of forbidden induced subgraphs, each of which contains a cycle. In this paper, we study the VERTEX COLOURING problem in subclasses of triangle-free graphs obtained by forbidding graphs without cycles, i.e., forests, and prove polynomial-time solvability of the problem in many classes of this type. In particular, our paper, combined with some previously known results, provides a complete description of the complexity status of the problem in subclasses of triangle-free graphs obtained by forbidding a forest with at most 6 vertices. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Vertex colouring Triangle-free graphs polynomial-time algorithm Clique-width

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polynomial-time recognition of clique-width ≤ 3 graphs

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DISCRETE APPLIED MATHEMATICS 2012年第6期160卷 834-865页

作者： Corneil, Derek G. Habib, Michel Lanlignel, Jean-Marc Reed, Bruce Rotics, Udi Netanya Acad Coll Sch Math & Comp Sci IL-42100 Netanya Israel Univ Toronto Dept Comp Sci Toronto ON Canada UMR 7089 CNRS LIAFA F-75205 Paris 13 France Univ Paris 07 UFR Informat F-75205 Paris 13 France Univ Montpellier 2 LIRMM UMR CNRS F-34392 Montpellier 5 France McGill Univ Sch Comp Sci Canada Res Chair Combinator Complex Networks Montreal PQ Canada

Clique-width is a relatively new parameterization of graphs, philosophically similar to treewidth. Clique-width is more encompassing in the sense that a graph of bounded treewidth is also of bounded clique-width (but not the converse). For graphs of bounded clique-width, given the clique-width decomposition, every optimization, enumeration or evaluation problem that can be defined by a monadic second-order logic formula using quantifiers on vertices, but not on edges, can be solved in polynomial time. This is reminiscent of the situation for graphs of bounded treewidth, where the same statement holds even if quantifiers are also allowed on edges. Thus, graphs of bounded clique-width are a larger class than graphs of bounded treewidth, on which we can resolve fewer, but still many, optimization problems efficiently. One of the major open questions regarding clique-width is whether graphs of clique-width at most k, for fixed k, can be recognized in polynomial time. In this paper, we present the first polynomial-time algorithm (O(n(2)m)) to recognize graphs of clique-width at most 3. (C) 2012 Elsevier B.V. with parts of the article (C) Bruce Reed. All rights reserved.

关键词： Clique-width computation polynomial-time algorithm

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Edge search number of cographs

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DISCRETE APPLIED MATHEMATICS 2012年第6期160卷 734-743页

作者： Golovach, Petr A. Heggernes, Pinar Mihai, Rodica Univ Bergen Dept Informat N-5020 Bergen Norway Univ Durham Sch Engn & Comp Sci Durham DH1 3LE England

We give a linear-time algorithm for computing the edge search number of cographs, thereby resolving the computational complexity of edge searching on this graph class. To achieve this we give a characterization of the edge search number of the join of two graphs. With our result, the knowledge on graph searching of cographs is now complete: node, mixed, and edge search numbers of cographs can all be computed efficiently. Furthermore, we are one step closer to computing the edge search number of permutation graphs. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Graph searching NP-hard problem polynomial-time algorithm Graph classes Cographs

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polynomial-time Isomorphism Test for Groups with Abelian Sylow Towers

Polynomial-time Isomorphism Test for Groups with Abelian Syl...

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29th International Symposium on Theoretical Aspects of Computer Science (STACS)

作者： Babai, Laszlo Qiao, Youming Univ Chicago Dept Comp Sci Chicago IL 60637 USA Tsinghua Univ Inst Interdisciplinary Informat Sci Beijing Peoples R China

ISBN: (纸本)9783939897354

We consider the problem of testing isomorphism of groups of order n given by Cayley tables. The trivial n(log) (n) bound on the time complexity for the general case has not been improved over the past four decades. Recently, Babai et al. (following Babai et al. in SODA 2011) presented a polynomial-time algorithm for groups without abelian normal subgroups, which suggests solvable groups as the hard case for group isomorphism problem. Extending recent work by Le Gall (STACS 2009) and Qiao et al. (STACS 2011), in this paper we design a polynomial-time algorithm to test isomorphism for the largest class of solvable groups yet, namely groups with abelian Sylow towers, defined as follows. A group G is said to possess a Sylow tower, if there exists a normal series where each quotient is isomorphic to a Sylow subgroup of G. A group has an abelian Sylow tower if it has a Sylow tower and all its Sylow subgroups are abelian. In fact, we are able to compute the coset of isomorphisms of groups formed as coprime extensions of an abelian group, by a group whose automorphism group is known. The mathematical tools required include representation theory, Wedderburn's theorem on semisimple algebras, and M.E. Harris's 1980 work on p'-automorphisms of abelian p-groups. We use tools from the theory of permutation group algorithms, and develop an algorithm for a parameterized version of the graph-isomorphism-hard setwise stabilizer problem, which may be of independent interest.

关键词： polynomial-time algorithm group isomorphism solvable group

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Edge search number of cographs

Edge search number of cographs

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4th Workshop on Graph Classes, Optimization, and Width Parameters (GROW)

作者： Golovach, Petr A. Heggernes, Pinar Mihai, Rodica Univ Bergen Dept Informat N-5020 Bergen Norway Univ Durham Sch Engn & Comp Sci Durham DH1 3LE England

关键词： Graph searching NP-hard problem polynomial-time algorithm Graph classes Cographs

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Finding Induced Paths of Given Parity in Claw-Free Graphs

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algorithmICA 2012年第1-2期62卷 537-563页

作者： van 't Hof, Pim Kaminski, Marcin Paulusma, Daniel Univ Durham Sch Engn & Comp Sci Sci Labs Durham DH1 3LE England Univ Libre Bruxelles Dept Comp Sci B-1050 Brussels Belgium

The Parity Path problem is to decide if a given graph contains both an induced path of odd length and an induced path of even length between two specified vertices. In the related problems Odd Induced Path and Even Induced Path, the goal is to determine whether an induced path of odd, respectively even, length between two specified vertices exists. Although all three problems are NP-complete in general, we show that they can be solved in O(n(5)) time for the class of claw-free graphs. Two vertices s and t form an even pair in G if every induced path from s to t in G has even length. Our results imply that the problem of deciding if two specified vertices of a claw-free graph form an even pair, as well as the problem of deciding if a given claw-free graph has an even pair, can be solved in O(n(5)) time and O(n(7)) time, respectively. We also show that we can decide in O(n(7)) time whether a claw-free graph has an induced cycle of given parity through a specified vertex. Finally, we show that a shortest induced path of given parity between two specified vertices of a claw-free perfect graph can be found in O(n(7)) time.

关键词： Induced path Parity path Claw-free graph polynomial-time algorithm

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Detecting Critical Links for Keeping Shortest Distance from Clients to Servers during Failures

Detecting Critical Links for Keeping Shortest Distance from ...

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12th IEEE/IPSJ International Symposium on Applications and the Internet (SAINT) / IEEE Annual Signature Conference on Computer Software and Applications (COMPSAC)

作者： Maeda, Nao Miwa, Hiroyoshi Kwansei Gakuin Univ Nishinomiya Hyogo 6691337 Japan

ISBN: (纸本)9780769547374

Recently, large-volume contents distributed by a content delivery service (CDS) on the Internet increase load of content delivery servers and networks, which is at the risk for degradation of quality of service. To overcome this problem, some mirror servers providing the same content are located on a network, and a request is navigated to one of the mirror servers. A reliable CDS must offer connectivity between a user and servers with small hop count even during link failure. Therefore, the introduction of mirror servers causes a new problem such as a high reliable network design which is appropriate for CDS. In this paper, we address a reliable network design problem by protection of critical links whose failures significantly degrade performance. The objective is to find the smallest number of the links to be protected so that all users can access servers within a small hop count even if non-protected links fail. First, we formulate this problem and prove that it is NP-hard. Second, we make clear the conditions that the problem is solvable in polynomial time. Specifically, we present a polynomial-time algorithm to solve the problem when the number of simultaneously failed link is restricted to one. Furthermore, we show that the problem can be solved also in polynomial time when hop count is restricted to one.

关键词： Network Graph theory Computational complexity Link failures Link protection Connectivity NP-hard polynomial-time algorithm

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polynomial-time recognition of clique-width ≤ 3 graphs

Polynomial-time recognition of clique-width ≤ 3 graphs

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4th Workshop on Graph Classes, Optimization, and Width Parameters (GROW)

关键词： Clique-width computation polynomial-time algorithm

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