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48
A Sufficiently Fast Algorithm for Finding Close to Optimal Junction Trees
, 1996
"... An algorithm is developed for finding a close to optimal junction tree of a given graph G. ..."
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Cited by 77 (3 self)
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An algorithm is developed for finding a close to optimal junction tree of a given graph G.
An improved approximation algorithm for multiway cut
 Journal of Computer and System Sciences
, 1998
"... Given an undirected graph with edge costs and a subset of k nodes called terminals, a multiway cut is a subset of edges whose removal disconnects each terminal from the rest. Multiway Cut is the problem of finding a multiway cut of minimum cost. Previously, a very simple combinatorial algorithm due ..."
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Cited by 74 (5 self)
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Given an undirected graph with edge costs and a subset of k nodes called terminals, a multiway cut is a subset of edges whose removal disconnects each terminal from the rest. Multiway Cut is the problem of finding a multiway cut of minimum cost. Previously, a very simple combinatorial algorithm due to Dahlhaus, � Johnson, Papadimitriou, Seymour, and Yannakakis gave a performance guarantee of 2 1 − 1 k. In this paper, we present a new linear programming relaxation for Multiway Cut and a new approximation algorithm based on it. The algorithm breaks the threshold of 2 for approximating Multiway Cut, achieving a. This improves the previous result for every value of k. performance ratio of at most 1.5 − 1 k In particular, for k = 3 we get a ratio of 7
Approximating Clique and Biclique Problems
, 1998
"... We present here 2approximation algorithms for several node deletion and edge deletion biclique problems and for an edge deletion clique problem. The biclique problem is to find a node induced subgraph that is bipartite and complete. The objective is to minimize the total weight of nodes or edges de ..."
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Cited by 44 (2 self)
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We present here 2approximation algorithms for several node deletion and edge deletion biclique problems and for an edge deletion clique problem. The biclique problem is to find a node induced subgraph that is bipartite and complete. The objective is to minimize the total weight of nodes or edges deleted so that the remaining subgraph is bipartite complete. Several variants of the biclique problem are studied here, where the problem is defined on bipartite graph or on general graphs with or without the requirement that each side of the bipartition forms an independent set. The maximum clique problem is formulated as maximizing the number Ž or weight. of edges in the complete subgraph. A 2approximation algorithm is given for the minimum edge deletion version of this problem. The approximation algorithms given here are derived as a special case of an approximation technique devised for a class of formulations introduced by Hochbaum. All approximation algorithms described Žand the polynomial algorithms for two versions of the node biclique problem. involve calls to a minimum cut algorithm. One conclusion of our analysis of the NPhard problems here is that all of these problems are MAX SNPhard and at least as difficult to approximate as the vertex cover problem. Another conclusion is that the problem of finding the minimum node cutset, the removal of which leaves two cliques in the graph, is NPhard and 2approximable.
Dynamic QoSAware Multimedia Service Configuration in Ubiquitous Computing Environments
 In Proc. of IEEE ICDCS
, 2002
"... Ubiquitous computing promotes the proliferation of various stationary, embedded and mobile devices interconnected by heterogeneous networks. It leads to a highly dynamic distributed system with many devices and services coming and going frequently. Many emerging distributed multimedia applicatio ..."
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Cited by 30 (12 self)
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Ubiquitous computing promotes the proliferation of various stationary, embedded and mobile devices interconnected by heterogeneous networks. It leads to a highly dynamic distributed system with many devices and services coming and going frequently. Many emerging distributed multimedia applications are being deployed in such a computing environment. In order to make the experience for a user truly seamless and to provide soft performance guarantees, we must meet the following challenges: (1) users should be able to perform tasks continuously, despite changes of resources, devices and locations; (2) users should be able to efficiently utilize all accessible resources within runtime environments to receive the best possible QualityofService (QoS). In this paper, we propose an integrated QoSaware service configuration model to address the above problems. The configuration model includes two tiers: (1) service composition tier, which is responsible for choosing and composing current available service components appropriately and coordinating arbitrary interactions between them to achieve the user’s objectives; and (2) service distribution tier, which is responsible for dividing an application into several partitions and distributing them to different available devices appropriately. Our initial experimental results based on both prototype and simulations show the soundness of our model and algorithms.
FPT algorithms for pathtransversals and cycletransversals problems in graphs
"... Abstract. In this article, we consider problems on graphs of the following form: given a graph, remove p edges/vertices to achieve some property. The first kind of problems are separation problems on graphs, where we aim at separating distinguished vertices in a graph. The second kind of problems ar ..."
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Cited by 23 (2 self)
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Abstract. In this article, we consider problems on graphs of the following form: given a graph, remove p edges/vertices to achieve some property. The first kind of problems are separation problems on graphs, where we aim at separating distinguished vertices in a graph. The second kind of problems are feedback set problems on grouplabelled graphs, where we aim at breaking nonnull cycles in a graph. We obtain new FPT algorithms for these different problems. A building stone for our algorithms is a general O ∗ (4 p) algorithm for a class of problems aiming at breaking a set of paths in a graph, provided that the set of paths has a special property called homogeneity. 1
Multicuts in Unweighted Graphs and Digraphs with Bounded Degree and Bounded TreeWidth
, 1998
"... this paper. Also, we show that Directed Edge Multicut is NPhard in digraphs with treewidth one and maximum in and out degree three. Other hardness results indicate why we cannot eliminate any of the three restrictionsunweighted, bounded degree and bounded treewidthon the input graph and sti ..."
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Cited by 23 (0 self)
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this paper. Also, we show that Directed Edge Multicut is NPhard in digraphs with treewidth one and maximum in and out degree three. Other hardness results indicate why we cannot eliminate any of the three restrictionsunweighted, bounded degree and bounded treewidthon the input graph and still obtain a PTAS. It is known [1] that for a Max SNPhard problem, unless P=NP, no PTAS exists. We have already seen that Unweighted Edge Multicut is Max SNPhard in stars [9], so letting the input graph have unbounded degree makes the problem harder. We show that Weighted Edge Multicut is Max SNPhard in binary trees, therefore letting the input graph be weighted makes the problem harder. Finally, we show that Unweighted Edge Multicut is Max SNPhard if the input graphs are walls. Walls, to be formally defined in Section 6, have degree at most three and unbounded treewidth. We conclude that letting the input graph have unbounded treewidth makes the problem significantly harder
Algorithm Engineering for Optimal Graph Bipartization
, 2009
"... We examine exact algorithms for the NPhard Graph Bipartization problem. The task is, given a graph, to find a minimum set of vertices to delete to make it bipartite. Based on the “iterative compression ” method introduced by Reed, Smith, and Vetta in 2004, we present new algorithms and experimental ..."
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Cited by 21 (4 self)
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We examine exact algorithms for the NPhard Graph Bipartization problem. The task is, given a graph, to find a minimum set of vertices to delete to make it bipartite. Based on the “iterative compression ” method introduced by Reed, Smith, and Vetta in 2004, we present new algorithms and experimental results. The worstcase time complexity is improved. Based on new structural insights, we give a simplified correctness proof. This also allows us to establish a heuristic improvement that in particular speeds up the search on dense graphs. Our best algorithm can solve all instances from a testbed from computational biology within minutes, whereas established methods are only able to solve about half of the instances within reasonable time.
Approximating Minimum Subset Feedback Sets in Undirected Graphs with Applications to Multicuts
, 1996
"... Let G = (V; E) be a weighted undirected graph where all weights are at least one. We consider the following generalization of feedback set problems. Let S ae V be a subset of the vertices. A cycle is called interesting if it intersects the set S. A subset feedback edge (vertex) set is a subset of th ..."
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Cited by 19 (0 self)
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Let G = (V; E) be a weighted undirected graph where all weights are at least one. We consider the following generalization of feedback set problems. Let S ae V be a subset of the vertices. A cycle is called interesting if it intersects the set S. A subset feedback edge (vertex) set is a subset of the edges (vertices) that intersects all interesting cycles. In minimum subset feedback problems the goal is to find such sets of minimumweight. The case in which S consists of a single vertex is equivalent to the multiway cut problem, in which the goal is to separate a given set of terminals. Hence, the subset feedback problem is NPcomplete, and also generalizes the multiway cut problem. We provide a polynomialtime algorithm for approximating the subset feedback edge set problem that achieves an approximation factor of two. For the subset feedback vertex set problem we achieve an approximation factor of minf2\Delta; O(log jSj); O(log ø )g, where \Delta is the maximum degree in G and ø ...
Multiway cuts in node weighted graphs
 JOURNAL OF ALGORITHMS
, 2004
"... A (2 — 2/k) approximation algorithm is presented for the node multiway cut problem, thus matching the result of Dahlhaus et al. (SIAM J. Comput. 23 (4) (1994) 864894) for the edge version of this problem. This is done by showing that the associated LPrelaxation always has a halfintegral optimal s ..."
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Cited by 19 (0 self)
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A (2 — 2/k) approximation algorithm is presented for the node multiway cut problem, thus matching the result of Dahlhaus et al. (SIAM J. Comput. 23 (4) (1994) 864894) for the edge version of this problem. This is done by showing that the associated LPrelaxation always has a halfintegral optimal solution.
Multicut is FPT
 In STOC
, 2011
"... Let G = (V,E) be a graph on n vertices and R be a set of pairs of vertices in V called requests. A multicut is a subset F of E such that every request xy of R is separator by F, i.e.every xypath of G intersects F. We show that there exists an O(f(k)nc) algorithm which decides if there exists a mult ..."
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Let G = (V,E) be a graph on n vertices and R be a set of pairs of vertices in V called requests. A multicut is a subset F of E such that every request xy of R is separator by F, i.e.every xypath of G intersects F. We show that there exists an O(f(k)nc) algorithm which decides if there exists a multicut of size at most k. In other words, the MULTICUT problem parameterized by the solution size k is FixedParameter Tractable. 1