Results 1  10
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318
Fixed Parameter Algorithms for Dominating Set and Related Problems on Planar Graphs
, 2002
"... We present an algorithm that constructively produces a solution to the kdominating set problem for planar graphs in time O(c . To obtain this result, we show that the treewidth of a planar graph with domination number (G) is O( (G)), and that such a tree decomposition can be found in O( (G)n) time. ..."
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Cited by 108 (24 self)
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We present an algorithm that constructively produces a solution to the kdominating set problem for planar graphs in time O(c . To obtain this result, we show that the treewidth of a planar graph with domination number (G) is O( (G)), and that such a tree decomposition can be found in O( (G)n) time. The same technique can be used to show that the kface cover problem ( find a size k set of faces that cover all vertices of a given plane graph) can be solved in O(c n) time, where c 1 = 3 and k is the size of the face cover set. Similar results can be obtained in the planar case for some variants of kdominating set, e.g., kindependent dominating set and kweighted dominating set.
The multivariate Tutte polynomial (alias Potts model) for graphs and matroids
 Surveys in Combinatorics (Cambridge
, 2005
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PolynomialTime Approximation Schemes for Geometric Graphs
, 2001
"... A disk graph is the intersection graph of a set of disks with arbitrary diameters in the plane. For the case that the disk representation is given, we present polynomialtime approximation schemes (PTASs) for the maximum weight independent set problem (selecting disjoint disks of maximum total weigh ..."
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Cited by 78 (4 self)
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A disk graph is the intersection graph of a set of disks with arbitrary diameters in the plane. For the case that the disk representation is given, we present polynomialtime approximation schemes (PTASs) for the maximum weight independent set problem (selecting disjoint disks of maximum total weight) and for the minimum weight vertex cover problem in disk graphs. These are the first known PTASs for NPhard optimization problems on disk graphs. They are based on a novel recursive subdivision of the plane that allows applying a shifting strategy on different levels simultaneously, so that a dynamic programming approach becomes feasible. The PTASs for disk graphs represent a common generalization of previous results for planar graphs and unit disk graphs. They can be extended to intersections graphs of other "disklike" geometric objects (such as squares or regular polygons), also in higher dimensions.
Graph Sandwich Problems
, 1994
"... The graph sandwich problem for property \Pi is defined as follows: Given two graphs G ) such that E ` E , is there a graph G = (V; E) such that E which satisfies property \Pi? Such problems generalize recognition problems and arise in various applications. Concentrating mainly o ..."
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Cited by 51 (8 self)
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The graph sandwich problem for property \Pi is defined as follows: Given two graphs G ) such that E ` E , is there a graph G = (V; E) such that E which satisfies property \Pi? Such problems generalize recognition problems and arise in various applications. Concentrating mainly on properties characterizing subfamilies of perfect graphs, we give polynomial algorithms for several properties and prove the NPcompleteness of others. We describe
ρQueries: Enabling Querying for Semantic Associations on the Semantic Web
 In Proceedings of the Twelfth International WorldWide Web Conference
, 2003
"... This paper presents the notion of Semantic Associations as complex relationships between resource entities. These relationships capture both a connectivity of entities as well as similarity of entities based on a specific notion of similarity called ρisomorphism. It formalizes these notions for the ..."
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Cited by 46 (8 self)
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This paper presents the notion of Semantic Associations as complex relationships between resource entities. These relationships capture both a connectivity of entities as well as similarity of entities based on a specific notion of similarity called ρisomorphism. It formalizes these notions for the RDF data model, by introducing a notion of a Property Sequence as a type. In the context of a graph model such as that for RDF, Semantic Associations amount to specific certain graph signatures. Specifically, they refer to sequences (i.e. directed paths) here called Property Sequences, between entities, networks of Property Sequences (i.e. undirected paths), or subgraphs of ρisomorphic Property Sequences. The ability to query about the existence of such relationships is fundamental to tasks in analytical domains such as national security and business intelligence, where tasks often focus on finding complex yet meaningful and obscured relationships between entities. However, support for such queries is lacking in contemporary query systems, including those for RDF. This paper discusses how querying for Semantic Associations might be enabled on the Semantic Web, through the use of an operator ρ. It also discusses two approaches for processing ρqueries on available persistent RDF stores and memory resident RDF data graphs, thereby building on current RDF query languages.
Complexity classification of some edge modification problems
, 2001
"... In an edge modification problem one has to change the edge set of a given graph as little as possible so as to satisfy a certain property. We prove the NPhardness of a variety of edge modification problems with respect to some wellstudied classes of graphs. These include perfect, chordal, chain, c ..."
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Cited by 43 (2 self)
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In an edge modification problem one has to change the edge set of a given graph as little as possible so as to satisfy a certain property. We prove the NPhardness of a variety of edge modification problems with respect to some wellstudied classes of graphs. These include perfect, chordal, chain, comparability, split and asteroidal triple free. We show that some of these problems become polynomial when the input graph has bounded degree. We also give a general constant factor approximation algorithm for deletion and editing problems on bounded degree graphs with respect to properties that can be characterized by a finite set of forbidden induced subgraphs.
Approximations for λColorings of Graphs
 THE COMPUTER JOURNAL
, 2004
"... A λcoloring of a graph G is an assignment of colors from the integer set {0,...,λ} to the vertices of the graph G such that vertices at distance of at most two get different colors and adjacent vertices get colors which are at least two apart. The problem of finding λcolorings with optimal or near ..."
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Cited by 42 (0 self)
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A λcoloring of a graph G is an assignment of colors from the integer set {0,...,λ} to the vertices of the graph G such that vertices at distance of at most two get different colors and adjacent vertices get colors which are at least two apart. The problem of finding λcolorings with optimal or nearoptimal λ arises in the context of radio frequency assignment. We show that the problem of finding the minimum λ for planar graphs, bipartite graphs, chordal graphs and split graphs is NPcomplete. We also give approximation algorithms for λcoloring and compute upper bounds on the best possible λ for outerplanar graphs, graphs of treewidth k, permutation and split graphs. Except in the case of split graphs, all the above bounds for λ are linear in ∆, the maximum degree of the graph. For split graphs, we give a bound of 1/2∆ 1.5 + 2 ∆ and we show that there are split graphs G with λ(G) = �(∆ 1.5). Similar results are also given for variations of the λcoloring problem.
Computing common intervals of K permutations, with applications to modular decomposition of graphs
, 2008
"... We introduce a new approach to compute the common intervals of K permutations based on a very simple and general notion of generators of common intervals. This formalism leads to simple and efficient algorithms to compute the set of all common intervals of K permutations, that can contain a quadrat ..."
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Cited by 35 (15 self)
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We introduce a new approach to compute the common intervals of K permutations based on a very simple and general notion of generators of common intervals. This formalism leads to simple and efficient algorithms to compute the set of all common intervals of K permutations, that can contain a quadratic number of intervals, as well as a linear space basis of this set of common intervals. Finally, we show how our results on permutations can be used for computing the modular decomposition of graphs.
Improved Tree Decomposition Based Algorithms for Dominationlike Problems
 in LATIN’02: Theoretical informatics (Cancun
, 2001
"... We present an improved dynamic programming strategy for dominating set and related problems on graphs that are given together with a tree decomposition of width k. We obtain an O(4 n) algorithm for dominating set, where n is the number of nodes of the tree decomposition. ..."
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Cited by 34 (9 self)
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We present an improved dynamic programming strategy for dominating set and related problems on graphs that are given together with a tree decomposition of width k. We obtain an O(4 n) algorithm for dominating set, where n is the number of nodes of the tree decomposition.
Fixed parameter algorithms for planar dominating set and related problems
, 2000
"... We present an algorithm that constructively produces a solution to the kdominating set problem for planar graphs in time O(c √ kn), where c = 36√34. To obtain this result, we show that the treewidth of a planar graph with domination number γ(G) is O ( � γ(G)), and that such a tree decomposition ca ..."
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Cited by 34 (10 self)
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We present an algorithm that constructively produces a solution to the kdominating set problem for planar graphs in time O(c √ kn), where c = 36√34. To obtain this result, we show that the treewidth of a planar graph with domination number γ(G) is O ( � γ(G)), and that such a tree decomposition can be found in O ( � γ(G)n) time. The same technique can be used to show that the kface cover problem (find a size k set of faces that cover all vertices of a given plane graph) can be solved √ k in O(c1 n + n2) time, where c1 = 236√34 and k is the size of the face cover set. Similar results can be obtained in the planar case for some variants of kdominating set, e.g., kindependent dominating set and kweighted dominating set. Keywords. NPcomplete problems, fixed parameter tractability, planar graphs, planar dominating set, face cover, outerplanarity, treewidth.