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INCLUSION–EXCLUSION BASED ALGORITHMS FOR
"... Abstract. We present a deterministic algorithm producing the number of kcolourings of a graph on n vertices in time 2nnO(1). We also show that the chromatic number can be found by a polynomial space algorithm running in time O(2.2461n). Finally, we present a family of polynomial space approximatio ..."
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Abstract. We present a deterministic algorithm producing the number of kcolourings of a graph on n vertices in time 2nnO(1). We also show that the chromatic number can be found by a polynomial space algorithm running in time O(2.2461n). Finally, we present a family of polynomial space approxi
InclusionExclusion Algorithms for . . .
, 2006
"... Given a set U with n elements and a family of subsets S ⊆ 2 U we show how to count the number of kpartitions S1 ∪···∪Sk = U into subsets Si ∈ S in time 2 n n O(1). The only assumption on S is that it can be enumerated in time 2 n n O(1). In effect we get exact algorithms in time 2 n n O(1) for seve ..."
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Given a set U with n elements and a family of subsets S ⊆ 2 U we show how to count the number of kpartitions S1 ∪···∪Sk = U into subsets Si ∈ S in time 2 n n O(1). The only assumption on S is that it can be enumerated in time 2 n n O(1). In effect we get exact algorithms in time 2 n n O(1
Set partitioning via inclusionexclusion
 SIAM J. Comput
"... Abstract. Given a set N with n elements and a family F of subsets, we show how to partition N into k such subsets in 2nnO(1) time. We also consider variations of this problem where the subsets may overlap or are weighted, and we solve the decision, counting, summation, and optimisation versions of t ..."
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Cited by 60 (7 self)
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of these problems. Our algorithms are based on the principle of inclusion–exclusion and the zeta transform. In effect we get exact algorithms in 2nnO(1) time for several wellstudied partition problems including Domatic Number, Chromatic Number, Maximum kCut, Bin Packing, List Colouring, and the Chromatic
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
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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computational rule, the sumproduct algorithm operates in factor graphs to computeeither exactly or approximatelyvarious marginal functions by distributed messagepassing in the graph. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can
Efficient GraphBased Image Segmentation
"... This paper addresses the problem of segmenting an image into regions. We define a predicate for measuring the evidence for a boundary between two regions using a graphbased representation of the image. We then develop an efficient segmentation algorithm based on this predicate, and show that althou ..."
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Cited by 931 (1 self)
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This paper addresses the problem of segmenting an image into regions. We define a predicate for measuring the evidence for a boundary between two regions using a graphbased representation of the image. We then develop an efficient segmentation algorithm based on this predicate, and show
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
InclusionExclusion Algorithms for Counting Set Partitions
, 2006
"... Given an nelement set U and a family of subsets S ⊆ 2 U we show how to count the number of kpartitions S1 ∪ · · · ∪ Sk = U into subsets Si ∈ S in time 2 n n O(1). The only assumption on S is that it can be enumerated in time 2 n n O(1). In effect we get exact algorithms in time 2 n n O(1) fo ..."
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Cited by 36 (1 self)
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Given an nelement set U and a family of subsets S ⊆ 2 U we show how to count the number of kpartitions S1 ∪ · · · ∪ Sk = U into subsets Si ∈ S in time 2 n n O(1). The only assumption on S is that it can be enumerated in time 2 n n O(1). In effect we get exact algorithms in time 2 n n O(1
"GrabCut”  interactive foreground extraction using iterated graph cuts
 ACM TRANS. GRAPH
, 2004
"... The problem of efficient, interactive foreground/background segmentation in still images is of great practical importance in image editing. Classical image segmentation tools use either texture (colour) information, e.g. Magic Wand, or edge (contrast) information, e.g. Intelligent Scissors. Recently ..."
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Cited by 1140 (36 self)
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. Recently, an approach based on optimization by graphcut has been developed which successfully combines both types of information. In this paper we extend the graphcut approach in three respects. First, we have developed a more powerful, iterative version of the optimisation. Secondly, the power
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
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