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Algorithmic Metatheorems for Graphs of Bounded Vertex Cover
, 2009
"... Possibly the most famous algorithmic metatheorem is Courcelle’s theorem, which states that all MSOexpressible graph properties are decidable in linear time for graphs of bounded treewidth. Unfortunately, the running time’s dependence on the MSO formula describing the problem is in general an expo ..."
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Possibly the most famous algorithmic metatheorem is Courcelle’s theorem, which states that all MSOexpressible graph properties are decidable in linear time for graphs of bounded treewidth. Unfortunately, the running time’s dependence on the MSO formula describing the problem is in general
Algorithmic Metatheorems for Restrictions of
"... Abstract. Possibly the most famous algorithmic metatheorem is Courcelle’s theorem, which states that all MSOexpressible graph properties are decidable in linear time for graphs of bounded treewidth. Unfortunately, the running time’s dependence on the formula describing the problem is in general ..."
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treewidth graphs: graphs of bounded vertex cover and graphs of bounded maxleaf number. We prove stronger algorithmic metatheorems for these more restricted classes of graphs. More specifically, we show it is possible to decide any FO property in both of these classes with a singly exponential parameter
Algorithmic Metatheorems for Restrictions of Treewidth
"... Possibly the most famous algorithmic metatheorem is Courcelle’s theorem, which states that all MSOexpressible graph properties are decidable in linear time for graphs of bounded treewidth. Unfortunately, the running time’s dependence on the formula describing the problem is in general a tower of e ..."
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Cited by 21 (4 self)
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of bounded vertex cover and graphs of bounded maxleaf number. We prove stronger algorithmic metatheorems for these more restricted classes of graphs. More specifically, we show it is possible to decide any FO property in both of these classes with a singly exponential parameter dependence
Graphbased algorithms for Boolean function manipulation
 IEEE TRANSACTIONS ON COMPUTERS
, 1986
"... In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on th ..."
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Cited by 3499 (47 self)
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In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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hard. We prove that (1 \Gamma o(1)) ln n is a threshold below which set cover cannot be approximated efficiently, unless NP has slightly superpolynomial time algorithms. This closes the gap (up to low order terms) between the ratio of approximation achievable by the greedy algorithm (which is (1 \Gamma
Interprocedural Slicing Using Dependence Graphs
 ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS
, 1990
"... ... This paper concerns the problem of interprocedural slicinggenerating a slice of an entire program, where the slice crosses the boundaries of procedure calls. To solve this problem, we introduce a new kind of graph to represent programs, called a system dependence graph, which extends previou ..."
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Cited by 822 (85 self)
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... This paper concerns the problem of interprocedural slicinggenerating a slice of an entire program, where the slice crosses the boundaries of procedure calls. To solve this problem, we introduce a new kind of graph to represent programs, called a system dependence graph, which extends
AN n 5/2 ALGORITHM FOR MAXIMUM MATCHINGS IN BIPARTITE GRAPHS
, 1973
"... The present paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to (m + n)x/. ..."
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Cited by 712 (1 self)
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The present paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to (m + n)x/.
Results 1  10
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283,340