This paper surveys the theory of bidimensionality. This theory characterizes a broad range of graph problems ('bidimensional') that admit efficient approximate or fixed-parameter solutions in a broad range of ...
详细信息
This paper surveys the theory of bidimensionality. This theory characterizes a broad range of graph problems ('bidimensional') that admit efficient approximate or fixed-parameter solutions in a broad range of graphs. These graph classes include planar graphs, map graphs, bounded-genus graphs and graphs excluding any fixed minor. In particular, bidimensionality theory builds on the graph Minor Theory of Robertson and Seymour by extending the mathematical results and building new algorithmic tools. Here, we summarize the known combinatorial and algorithmic results of bidimensionality theory with the high-level ideas involved in their proof;we describe the previous work on which the theory is based and/or extends;and we mention several remaining open problems.
The inertia of a graph is an integer triple specifying the number of negative, zero,and positive eigenvalues of the adjacency matrix of the graph. A unicyclic graph is a simple connected graph with an equal number of ...
详细信息
The inertia of a graph is an integer triple specifying the number of negative, zero,and positive eigenvalues of the adjacency matrix of the graph. A unicyclic graph is a simple connected graph with an equal number of vertices and edges. This paper characterizes the inertia of a unicyclic graph in terms of maximum matchings and gives a linear-time algorithm for computing it. Chemists are interested in whether the molecular graph of an unsaturated hydrocarbon is (properly) closed-shell. having exactly half of its eigenvalues greater than zero, because this designates a stable electron configuration. The inertia determines whether a graph is closed-shell, and hence the reported result gives a linear-time algorithm for determining this for unicyclic graphs. (C) 2008 Elsevier Inc. All rights reserved.
We show how to use the split decomposition to solve some NP-hard optimization problems on graphs. We give algorithms for clique problem and domination-type problems. Our main result is an algorithm to compute a colora...
详细信息
We show how to use the split decomposition to solve some NP-hard optimization problems on graphs. We give algorithms for clique problem and domination-type problems. Our main result is an algorithm to compute a coloration of a graph using its split decomposition. Finally we show that the clique-width of a graph is bounded if and only if the clique-width of each representative graph in its split decomposition is bounded. (C) 2007 Elsevier B.V. All rights reserved.
We investigate a special case of the graph partitioning problem: the partitioning of a sibling graph which is an ordered tree augmented with edges connecting consecutive nodes that share a common parent. We describe t...
详细信息
We investigate a special case of the graph partitioning problem: the partitioning of a sibling graph which is an ordered tree augmented with edges connecting consecutive nodes that share a common parent. We describe the algorithm, XS, and present a proof of its correctness. (C) 2008 Elsevier B.V. All rights reserved.
With the ever-growing competition in telecommunications markets, operators have to increasingly rely on business intelligence to offer the right incentives to their customers. Existing approaches for telecorn business...
详细信息
With the ever-growing competition in telecommunications markets, operators have to increasingly rely on business intelligence to offer the right incentives to their customers. Existing approaches for telecorn business intelligence have almost solely focused on the individual behavior of customers. In this paper, we use the Call Detail Records of a mobile operator to construct call graphs, that is, graphs induced by people calling each other. We determine the structural properties of these graphs and also introduce the Treasure-Hunt model to describe the shape of mobile call graphs. Moreover, we determine how the structure of these call graphs evolve over time. Finally, since Short Messaging Service (SMS) is becoming a preferred mode of communication among many sections of the society, we study the properties of the SMS graph. Our analysis indicates several interesting similarities and differences between the SMS graph and the corresponding call graph. We believe that our analysis techniques can allow telecom operators to better understand the social behavior of their customers and potentially provide major insights for designing effective incentives.
Reference counting is the memory management technique of most widespread use today, Its cyclic version is used from implementations of languages such as Java to the consistent management of web pages. This paper intro...
详细信息
Reference counting is the memory management technique of most widespread use today, Its cyclic version is used from implementations of languages such as Java to the consistent management of web pages. This paper introduces the concept of "critical link" to largely optimize cyclic reference counting. (C) 2008 Elsevier B.V. All rights reserved.
We introduce a simple, linear time algorithm for recognizing trivially perfect (T?) graphs. It improves upon the algorithm of Yan et al. [J.-H. Yan, J.-J. Chen, G.J. Chang, Quasi-threshold graphs, Discrete Appl. Math....
详细信息
We introduce a simple, linear time algorithm for recognizing trivially perfect (T?) graphs. It improves upon the algorithm of Yan et al. [J.-H. Yan, J.-J. Chen, G.J. Chang, Quasi-threshold graphs, Discrete Appl. Math. 69 (3) (1996) 247-255] in that it is certifying, producing a P-4 or a C-4 when the graph is not TP. In addition, our algorithm can be easily modified to recognize the complement of TP graphs (co-TP) in linear time as well. It is based on lexicographic BFS, and in particular the technique of partition refinement, which has been used in the recognition of many other graph classes [D.G. Corneil, Lexicographic breadth first search-a survey, in: WG 2004, in: Lecture Notes in Comput. Sci., vol. 3353, Springer, 2004, pp. 1-19]. (C) 2008 Elsevier B.V. All rights reserved.
Falmagne recently introduced the concept of a medium, a combinatorial object encompassing hyperplane arrangements, topological orderings, acyclic orientations, and many other familiar structures. We find efficient sol...
详细信息
Falmagne recently introduced the concept of a medium, a combinatorial object encompassing hyperplane arrangements, topological orderings, acyclic orientations, and many other familiar structures. We find efficient solutions for several algorithmic problems on media: finding short reset sequences, shortest paths, testing whether a medium has a closed orientation, and listing the states of a medium given a black-box description. (c) 2007 Elsevier B.V. All rights reserved.
This paper is the second part of a study devoted to the mutual exclusion scheduling problem. Given a simple and undirected graph G and an integer k, the problem is to find a minimum coloring of G such that each color ...
详细信息
This paper is the second part of a study devoted to the mutual exclusion scheduling problem. Given a simple and undirected graph G and an integer k, the problem is to find a minimum coloring of G such that each color is used at most k times. The cardinality of such a coloring is denoted by chi(G, k). When restricted to interval graphs or related classes like circular-arc graphs and tolerance graphs, the problem has some applications in workforce planning. Unfortunately, the problem is shown to be N P-hard for interval graphs, even if k is a constant greater than or equal to four [H.L. Bodlaender, K. Jansen, Restrictions of graph partition problems. Part I. Theoret. Comput. Sci. 148 (1995) 93-109]. In this paper, the problem is approached from a different point of view by studying a non-trivial and practical sufficient condition for optimality. In particular, the following proposition is demonstrated: if an interval graph G admits a coloring such that each color appears at least k times, then chi(G, k) = inverted right perpendicular n/k inverted left perpendicular. This proposition is extended to several classes of graphs related to interval graphs. Moreover, all our proofs are constructive and provide efficient algorithms to solve the MES problem for these graphs, given a coloring satisfying the condition in input. (C) 2007 Elsevier B.V. All rights reserved.
The NP-complete POWER DOMINATING SET problem is an "electric power networks variant" of the classical domination problem in graphs: Given an undirected graph G = (V, E), find a minimum-size set P. V such tha...
详细信息
The NP-complete POWER DOMINATING SET problem is an "electric power networks variant" of the classical domination problem in graphs: Given an undirected graph G = (V, E), find a minimum-size set P. V such that all vertices in V are "observed" by the vertices in P. Herein, a vertex observes itself and all its neighbors, and if an observed vertex has all but one of its neighbors observed, then the remaining neighbor becomes observed as well. We show that POWER DOMINATING SET can be solved by "bounded-treewidth dynamic programs." For treewidth being upper-bounded by a constant, we achieve a linear-time algorithm. In particular, we present a simplified linear-time algorithm for POWER DOMINATING SET in trees. Moreover, we simplify and extend several NP-completeness results, particularly showing that POWER DOMINATING SET remains NP-complete for planar graphs, for circle graphs, and for split graphs. Specifically, our improved reductions imply that POWER DOMINATING SET parameterized by vertical bar P vertical bar is W[2]-hard and it cannot be better approximated than DOMINATING SET.
暂无评论