Results 1  10
of
20
LexBFS and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing
, 2000
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Efficient stepwise selection in decomposable models
 In Proc. UAI
, 2001
"... In this paper, we present an efficient algorithm for performing stepwise selection in the class of decomposable models. We focus on the forward selection procedure, but we also discuss how backward selection and the combination of the two can be performed efficiently. The main contributions of this ..."
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Cited by 33 (2 self)
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In this paper, we present an efficient algorithm for performing stepwise selection in the class of decomposable models. We focus on the forward selection procedure, but we also discuss how backward selection and the combination of the two can be performed efficiently. The main contributions of this paper are (1) a simple characterization for the edges that can be added to a decomposable model while retaining its decomposability and (2) an efficient algorithm for enumerating all such edges for a given decomposable model in O(n2) time, where n is the number of variables in the model. We also analyze the complexity of the overall stepwise selection procedure (which includes the complexity of enumerating eligible edges as well as the complexity of deciding how to “progress”). We use the KL divergence of the model from the saturated model as our metric, but the results we present here extend to many other metrics as well. 1
Private communication
, 1995
"... Given a graph G and positive integers b and w, the blackandwhite coloring problem asks about the existence of a partial vertexcoloring of G, with b vertices colored black and w white, such that there is no edge between a black and a white vertex. We suggest an improved algorithm for solving this ..."
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Cited by 7 (0 self)
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Given a graph G and positive integers b and w, the blackandwhite coloring problem asks about the existence of a partial vertexcoloring of G, with b vertices colored black and w white, such that there is no edge between a black and a white vertex. We suggest an improved algorithm for solving this problem on trees. Submitted:
The Knapsack Problem with Conflict Graphs
, 2009
"... We extend the classical 01 knapsack problem by introducing disjunctive constraints for pairs of items which are not allowed to be packed together into the knapsack. These constraints are represented by edges of a conflict graph whose vertices correspond to the items of the knapsack problem. Similar ..."
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Cited by 5 (2 self)
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We extend the classical 01 knapsack problem by introducing disjunctive constraints for pairs of items which are not allowed to be packed together into the knapsack. These constraints are represented by edges of a conflict graph whose vertices correspond to the items of the knapsack problem. Similar conditions were treated in the literature for bin packing and scheduling problems. For the knapsack problem with conflict graphs, exact and heuristic algorithms were proposed in the past. While the problem is strongly NPhard in general, we present pseudopolynomial algorithms for two special graph classes, namely graphs of bounded treewidth (including trees and seriesparallel graphs) and chordal graphs. From these algorithms we can easily derive fully polynomial time approximation schemes (FPTAS).
Maximal Common Connected Sets of Interval Graphs
 In Proceedings of Combinatorial Pattern Matching, Lecture Notes in Computer Science
, 2004
"... Abstract. Given a pair of graph G1 = (V, E1), G2 = (V, E2) on the same vertex set, a set S ⊆ V is a maximal common connected set of G1 and G2 if the subgraphs of G1 and G2 induced by S are both connected and S is maximal the inclusion order. The maximal Common Connected sets Problem (CCP for short) ..."
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Cited by 3 (0 self)
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Abstract. Given a pair of graph G1 = (V, E1), G2 = (V, E2) on the same vertex set, a set S ⊆ V is a maximal common connected set of G1 and G2 if the subgraphs of G1 and G2 induced by S are both connected and S is maximal the inclusion order. The maximal Common Connected sets Problem (CCP for short) consists in identifying the partition of V into maximal common connected sets of G1 and G2. This problem has many practical applications, notably in computational biology. Let n = V  and m = E1  + E2. We present an O((n + m) log n) worst case time algorithm solving CCP when G1 and G2 are two interval graphs. The algorithm combines maximal clique path decompositions of the two input graphs together with an Hopcroftlike partitioning approach. 1
Common connected components of interval graphs
 In CPM 2004, volume 3109 of LNCS
, 2004
"... The Common Connected Problem (CCP) consists in identifying common connected components in two or more graphs on the same vertices (or reduced to). More formally, let G1(V, E1) and G2(V, E2) be two such graphs and let V ′ ⊂ V. If G1[V ′ ] and G2[V ′] are both connected, V ′ is said a common connecte ..."
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Cited by 3 (3 self)
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The Common Connected Problem (CCP) consists in identifying common connected components in two or more graphs on the same vertices (or reduced to). More formally, let G1(V, E1) and G2(V, E2) be two such graphs and let V ′ ⊂ V. If G1[V ′ ] and G2[V ′] are both connected, V ′ is said a common connected component. The CCP problem is the identification of maximal (for the inclusion order) such components, that form a partition of V. Let n = V  and m = E1  + E2. We present an O((n + m)log n) worst case time algorithm solving the CCP problem when G1 and G2 are two interval graphs. The algorithm combines maximal clique path decompositions of the two input graphs together with an Hopcroft like partitioning approach. 1
The cliqueseparator graph for chordal graphs
, 2007
"... We present a new representation of a chordal graph called the cliqueseparator graph, whose nodes are the maximal cliques and minimal vertex separators of the graph. We present structural properties of the cliqueseparator graph and additional properties when the chordal graph is an interval graph, ..."
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Cited by 3 (0 self)
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We present a new representation of a chordal graph called the cliqueseparator graph, whose nodes are the maximal cliques and minimal vertex separators of the graph. We present structural properties of the cliqueseparator graph and additional properties when the chordal graph is an interval graph, proper interval graph, or split graph. We also characterize proper interval graphs and split graphs in terms of the cliqueseparator graph. We present an algorithm that constructs the cliqueseparator graph of a chordal graph in O(n³) time and of an interval graph in O(n²) time, where n is the number of vertices in the graph.
Canonical Data Structure for Interval Probe Graphs
, 2004
"... The class of interval probe graphs is introduced to deal with the physical mapping and sequencing of DNA as a generalization of interval graphs. The polynomial time recognition algorithms for the graph class are known. However, the complexity of the graph isomorphism problem for the class is still u ..."
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Cited by 2 (1 self)
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The class of interval probe graphs is introduced to deal with the physical mapping and sequencing of DNA as a generalization of interval graphs. The polynomial time recognition algorithms for the graph class are known. However, the complexity of the graph isomorphism problem for the class is still unknown. In this paper, extended MPQtrees are proposed to represent the interval probe graphs. An extended MPQtree is canonical and represents all possible permutations of the intervals. The extended MPQtree can be constructed from a given interval probe graph in O(n 2 + m) time. Thus we can solve the graph isomorphism problem for the interval probe graphs in O(n 2 + m) time. Using the tree, we can determine that any two nonprobes are independent, overlapping, or their relation cannot be determined without an experiment. Therefore, we can heuristically find the best nonprobe that would be probed in the next experiment. Also, we can enumerate all possible affirmative interval graphs for any interval probe graph.
Canonical Data Structure for Probe Interval Graphs
, 2004
"... The class of probe interval graphs is introduced to deal with the physical mapping and sequencing of DNA as a generalization of interval graphs. The polynomial time recognition algorithms for the graph class are known. However, the complexity of the graph isomorphism problem for the class is still u ..."
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Cited by 1 (0 self)
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The class of probe interval graphs is introduced to deal with the physical mapping and sequencing of DNA as a generalization of interval graphs. The polynomial time recognition algorithms for the graph class are known. However, the complexity of the graph isomorphism problem for the class is still unknown. In this paper, extended MPQtrees are proposed to represent the probe interval graphs. An extended MPQtree is canonical and represents all possible permutations of the intervals. The extended MPQtree can be constructed from a given probe interval graph in O(n 2 + m) time. Thus we can solve the graph isomorphism problem for the probe interval graphs in O(n 2 + m) time. Using the tree, we can determine that any two nonprobes are independent, overlapping, or their relation cannot be determined without an experiment. Therefore, we can heuristically find the best nonprobe that would be probed in the next experiment. Also, we can enumerate all possible affirmative interval graphs for given probe interval graph.
A POLYNOMIAL DELAY ALGORITHM FOR ENUMERATING MINIMAL DOMINATING SETS IN CHORDAL GRAPHS
, 2014
"... An outputpolynomial algorithm for the listing of minimal dominating sets in graphs is a challenging open problem and is known to be equivalent to the wellknown Transversal problem which asks for an outputpolynomial algorithm for listing the set of minimal hitting sets in hypergraphs. We give a ..."
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Cited by 1 (1 self)
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An outputpolynomial algorithm for the listing of minimal dominating sets in graphs is a challenging open problem and is known to be equivalent to the wellknown Transversal problem which asks for an outputpolynomial algorithm for listing the set of minimal hitting sets in hypergraphs. We give a polynomial delay algorithm to list the set of minimal dominating sets in chordal graphs, an important and wellstudied graph class where such an algorithm was open for a while.