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7th Latin-American algorithms, Graphs, and Optimization Symposium (LAGOS)

作者： Cameron, Kathie Chaplick, Steven Hoang, Chinh T. Wilfrid Laurier Univ Dept Math Waterloo ON Canada Tech Univ Berlin Inst Math Berlin Germany Wilfrid Laurier Univ Dept Phys & Comp Sci Waterloo ON Canada

In this paper we continue the study of the edge intersection graphs of one (or zero) bend paths on a rectangular grid. That is, the edge intersection graphs where each vertex is represented by one of the following shapes left perpendicular inverted right perpendicular, right perpendicular inverted left perpendicular, and we consider zero bend paths (i.e., vertical bar and -) to be degenerate left perpendicular 's. These graphs, called B-1-EPG graphs, were first introduced by Golumbic et al. (2009). We consider the natural subclasses of B-1-EPG formed by the subsets of the four single bend shapes (i.e., {left perpendicular }, {left perpendicular, inverted right perpendicular }, {left perpendicular , inverted left perpendicular}, and {left perpendicular , inverted right perpendicular, inverted left perpendicular}) and we denote the classes by [left perpendicular], [left perpendicular, inverted right perpendicular], [left perpendicular , inverted left perpendicular], and [left perpendicular , inverted right perpendicular, inverted left perpendicular] respectively. Note: all other subsets are isomorphic to these up to 90 degree rotation. We show that testing for membership in each of these classes is NP-complete and observe the expected strict inclusions and incomparability (i.e., [left perpendicular] not subset of [left perpendicular, inverted right perpendicular], [left perpendicular, inverted left perpendicular] not subset of [left perpendicular, inverted right perpendicular, inverted left perpendicular] not subset of B-1-EPG and [left perpendicular, inverted right perpendicular] is incomparable with [left perpendicular, inverted left perpendicular] ). Additionally, we give characterizations and polytime recognition algorithms for special subclasses of Split boolean AND[left perpendicular]. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Edge intersection graphs Grid paths Split graphs NP-completeness recognition algorithms L-graphs

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recognition of Unipolar and Generalised Split Graphs

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algorithms 2015年第1期8卷 46-59页

作者： McDiarmid, Colin Yolov, Nikola Univ Oxford Dept Stat Oxford OX1 3TG England Univ Oxford Dept Comp Sci Wolfson BldgPk Rd Oxford OX1 3QD England

A graph is unipolar if it can be partitioned into a clique and a disjoint union of cliques, and a graph is a generalised split graph if it or its complement is unipolar. A unipolar partition of a graph can be used to find efficiently the clique number, the stability number, the chromatic number, and to solve other problems that are hard for general graphs. We present an O(n(2))-time algorithm for recognition of n-vertex generalised split graphs, improving on previous O(n(3))-time algorithms.

关键词： generalised split graphs perfect graphs recognition algorithms representations unipolar graphs

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On the hereditary (p, q)-Helly property of hypergraphs, cliques, and bicliques

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Electronic Notes in Discrete Mathematics 2015年 50卷 361-366页

作者： Dourado, Mitre C. Grippo, Luciano N. Safe, Martín D. Instituto de Matemática Universidade Federal do Rio de Janeiro Rio de Janeiro Brazil Instituto de Ciencias Universidad Nacional de General Sarmiento Los Polvorines Buenos Aires Argentina

We prove several characterizations of hereditary (p, q)-Helly hypergraphs, including one by minimal forbidden partial subhypergraphs, and show that the recognition of hereditary (p, q)-Helly hypergraphs can be solved in polynomial time for fixed p but is co-NP-complete if p is part of the input. We also give several characterizations of hereditary (p, q)-clique-Helly graphs, including one by forbidden induced subgraphs, and prove that the recognition of hereditary (p, q)-clique-Helly graphs can be solved in polynomial time for fixed p and q but is NP-hard if p or q is part of the input. We prove similar results for hereditary (p, q)-biclique-Helly graphs. © 2015 Elsevier B.V.

关键词： (p, q)-Helly property Forbidden induced subgraphs Forbidden partial subhypergraphs Maximal bicliques Maximal cliques recognition algorithms

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Using SPQR-trees to speed up algorithms based on 2-cutset decompositions

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Electronic Notes in Discrete Mathematics 2015年 50卷 169-174页

作者： de Figueiredo, C.M.H. de Macêdo Filho, H.B. Li, Z. Machado, R.C.S. Trotignon, N. COPPE UFRJ Rio de Janeiro Brazil LIENS ENS-Paris Paris France Dimci Inmetro Rio de Janeiro Brazil LIP ENS-Lyon Lyon France

We propose the use of SPQR-trees as a data structure to encode the 3-connected components of a graph and to obtain linear-time recognition algorithms for graph classes structurally characterized by 2-cutset decomposit... 详细信息

关键词： Chordless graphs Graph decomposition Propeller-subgraph-free graphs recognition algorithms SPQR-tree

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Linear Time recognition algorithms and Structure Theorems for Bipartite Tolerance Graphs and Bipartite Probe Interval Graphs

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DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE 2010年第5期12卷 63-82页

作者： Brown, David E. Busch, Arthur H. Isaak, Garth Utah State Univ Dept Math & Stat Logan UT 84341 USA Univ Dayton Dept Math Dayton OH 45465 USA Lehigh Univ Dept Math Bethlehem PA 18015 USA

A graph is a probe interval graph if its vertices can be partitioned into probes and nonprobes with an interval associated to each vertex so that vertices are adjacent if and only if their corresponding intervals intersect and at least one of them is a probe. A graph G = (V, E) is a tolerance graph if each vertex v is an element of V can be associated to an interval I-v of the real line and a positive real number t(v) such that uv is an element of E if and only if vertical bar I-u boolean AND I-v vertical bar >= min {t(u), t(v)}. In this paper we present O(vertical bar V vertical bar + vertical bar E vertical bar) recognition algorithms for both bipartite probe interval graphs and bipartite tolerance graphs. We also give a new structural characterization for each class which follows from the algorithms.

关键词： tolerance graphs probe interval graphs recognition algorithms

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Clique-perfectness and balancedness of some graph classes

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2014年第10期91卷 2118-2141页

作者： Bonomo, Flavia Duran, Guillermo Safe, Martin D. Wagler, Annegret K. Univ Buenos Aires CONICET Buenos Aires DF Argentina Univ Buenos Aires FCEN Dept Comp Buenos Aires DF Argentina Univ Buenos Aires CONICET Inst Calculo Buenos Aires DF Argentina Univ Buenos Aires FCEN Dept Matemat Buenos Aires DF Argentina Univ Chile FCFM Dept Ingn Ind Santiago Chile Univ Nacl Gen Sarmiento Inst Ciencias Los Polvorines Argentina Univ Blaise Pascal CNRS Aubiere France Univ Blaise Pascal LIMOS UFR Sci & Tech Aubiere France

A graph is clique-perfect if the maximum size of a clique-independent set (a set of pairwise disjoint maximal cliques) and the minimum size of a clique-transversal set (a set of vertices meeting every maximal clique) coincide for each induced subgraph. A graph is balanced if its clique-matrix contains no square submatrix of odd size with exactly two ones per row and column. In this work, we give linear-time recognition algorithms and minimal forbidden induced subgraph characterizations of clique-perfectness and balancedness of P-4-tidy graphs and a linear-time algorithm for computing a maximum clique-independent set and a minimum clique-transversal set for any P-4-tidy graph. We also give a minimal forbidden induced subgraph characterization and a linear-time recognition algorithm for balancedness of paw-free graphs. Finally, we show that clique-perfectness of diamond-free graphs can be decided in polynomial time by showing that a diamond-free graph is clique-perfect if and only if it is balanced.

关键词： 05C75 05C17 05C85 clique-perfect graphs balanced graphs diamond-free graphs recognition algorithms paw-free graphs P-4-tidy graphs

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recognition AND COMBINATORIAL OPTIMIZATION algorithms FOR BIPARTITE CHAIN GRAPHS

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COMPUTING AND INFORMATICS 2013年第2期32卷 313-329页

作者： Talmaciu, Mihai Nechita, Elena Iantovics, Barna Vasile Alecsandri Univ Bacau Dept Math & Informat Bacau Romania Petru Maior Univ Targu Mures Dept Informat Targu Mures Romania

In this paper we give a recognition algorithm in O(n(n + m)) time for bipartite chain graphs, and directly calculate the density of such graphs. For their stability number and domination number, we give algorithms comparable to the existing ones. We point out some applications of bipartite chain graphs in chemistry and approach the Minimum Chain Completion problem.

关键词： Bipartite chain graphs weakly decomposition recognition algorithms combinatorial optimization algorithms

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A Method of recognition of Human Hand and Body Gestures for Task-Level Learning from Demonstration

A Method of Recognition of Human Hand and Body Gestures for ...

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2014 4th International Conference on Materials,Mechatronics and Automation(ICMMA 2014)

作者： Vladimir Popov Ural Federal University

Different problems of robot learning and planning have received considerable attention, recently. In particular, we can mention robot task learning. Robot learning from demonstration is especially important for robots that operate in unstructured environments. The effectiveness of such learning depends strongly on the quality of vision-based analysis of human hand and body gestures. In this paper, we consider a method of recognition of human hand and body gestures that based on a modified longest common subsequence algorithm with adaptive parameters.

关键词： Robot Longest common subsequence Learning from demonstration recognition algorithms Task-level learning

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Complexity of Finding Graph Roots with Girth Conditions

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ALGORITHMICA 2012年第1-2期62卷 38-53页

作者： Farzad, Babak Lau, Lap Chi Van Bang Le Nguyen Ngoc Tuy Brock Univ Dept Math St Catharines ON L2S 3A1 Canada Chinese Univ Hong Kong Dept Comp Sci & Engn Hong Kong Hong Kong Peoples R China Univ Rostock Inst Informat Rostock Germany Hong Duc Univ Dept Comp Sci Thanh Hoa City Vietnam

Graph G is the square of graph H if two vertices x,y have an edge in G if and only if x,y are of distance at most two in H. Given H it is easy to compute its square H (2), however Motwani and Sudan proved that it is NP-complete to determine if a given graph G is the square of some graph H (of girth 3). In this paper we consider the characterization and recognition problems of graphs that are squares of graphs of small girth, i.e. to determine if G=H (2) for some graph H of small girth. The main results are the following. There is a graph theoretical characterization for graphs that are squares of some graph of girth at least 7. A corollary is that if a graph G has a square root H of girth at least 7 then H is unique up to isomorphism. There is a polynomial time algorithm to recognize if G=H (2) for some graph H of girth at least 6. It is NP-complete to recognize if G=H (2) for some graph H of girth 4.

关键词： Graph roots Graph powers recognition algorithms NP-completeness

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Distance-hereditary comparability graphs

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DISCRETE APPLIED MATHEMATICS 2012年第18期160卷 2669-2680页

作者： Di Stefano, Gabriele Univ Aquila Dipartimento Ingn Elettr & Informaz I-67100 Laquila Italy

In this paper, we study the class of distance-hereditary comparability graphs, that is, those graphs which admit a transitive orientation and are completely decomposable with respect to the split decomposition. We provide a characterization based on a restricted number of forbidden subgraphs. We also provide further characterizations and one of them, based on the split decomposition, is used to devise a recognizing algorithm working in linear time. Finally, we show how to build distance-hereditary comparability graphs. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Comparability graphs Distance-hereditary graphs Split decomposition recognition algorithms Building algorithms

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