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1 LP for Multiway cut [1]
"... Last time we set up the following LP for the Multiway cut problem: uv xu − xv 1 · cuv min 1 2 s.t. xi = ei ∑ ∀terminal i j xuj =1 ∀u xu ≥ 0 ..."
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Last time we set up the following LP for the Multiway cut problem: uv xu − xv 1 · cuv min 1 2 s.t. xi = ei ∑ ∀terminal i j xuj =1 ∀u xu ≥ 0
Graph Clustering Using Multiway Ratio Cut
 PROC. OF GRAPH DRAWING, VOLUME 1353 OF LECT. NOTES IN COMPUT. SCI
, 1997
"... Identifying the natural clusters of nodes in a graph and treating them as supernodes or metanodes for a higher level graph (or an abstract graph) is a technique used for the reduction of visual complexity of graphs with a large number of nodes. In this paper we report on the implementation of a ..."
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Cited by 25 (2 self)
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clustering algorithm based on the idea of ratio cut, a well known technique used for circuit partitioning in the VLSI domain. The algorithm is implemented in WINDOWS95/NT environment. The performance of the clustering algorithm on some large graphs obtained from the archives of Bell Laboratories
Approximate Graph Coloring by Semidefinite Programming.
 In Proceedings of 35th Annual IEEE Symposium on Foundations of Computer Science,
, 1994
"... Abstract. We consider the problem of coloring kcolorable graphs with the fewest possible colors. We present a randomized polynomial time algorithm that colors a 3colorable graph on n vertices with min{O(⌬ 1/3 log 1/2 ⌬ log n), O(n 1/4 log 1/2 n)} colors where ⌬ is the maximum degree of any vertex ..."
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Cited by 210 (7 self)
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)} colors. Our results are inspired by the recent work of Goemans and Williamson who used an algorithm for semidefinite optimization problems, which generalize linear programs, to obtain improved approximations for the MAX CUT and MAX 2SAT problems. An intriguing outcome of our work is a duality
Rounding algorithms for a geometric embedding of minimum multiway cut
 In STOC ’99: Proceedings of the 31st Annual ACM Symposium on Theory of Computing
, 1999
"... Given an undirected graph with edge costs and a subset of k ≥ 3 nodes called terminals, a multiway, or kway, cut is a subset of the edges whose removal disconnects each terminal from the others. The multiway cut problem is to find a minimumcost multiway cut. This problem is MaxSNP hard. Recently ..."
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Cited by 50 (2 self)
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Given an undirected graph with edge costs and a subset of k ≥ 3 nodes called terminals, a multiway, or kway, cut is a subset of the edges whose removal disconnects each terminal from the others. The multiway cut problem is to find a minimumcost multiway cut. This problem is MaxSNP hard. Recently
Parameterized Tractability of Multiway Cut with Parity Constraints
"... Abstract. In this paper, we study a parity based generalization of the classical MULTIWAY CUT problem. Formally, we study the PARITY MULTIWAY CUT problem, where the input is a graph G, vertex subsets Te and To (T = Te ∪ To) called terminals, a positive integer k and the objective is to test whether ..."
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Cited by 6 (1 self)
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Abstract. In this paper, we study a parity based generalization of the classical MULTIWAY CUT problem. Formally, we study the PARITY MULTIWAY CUT problem, where the input is a graph G, vertex subsets Te and To (T = Te ∪ To) called terminals, a positive integer k and the objective is to test whether
Polynomial Time Approximation Schemes for Dense Instances of NPHard Problems
, 1995
"... We present a unified framework for designing polynomial time approximation schemes (PTASs) for "dense" instances of many NPhard optimization problems, including maximum cut, graph bisection, graph separation, minimum kway cut with and without specified terminals, and maximum 3satisfiabi ..."
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Cited by 189 (35 self)
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We present a unified framework for designing polynomial time approximation schemes (PTASs) for "dense" instances of many NPhard optimization problems, including maximum cut, graph bisection, graph separation, minimum kway cut with and without specified terminals, and maximum 3
A new approach to the minimum cut problem
 Journal of the ACM
, 1996
"... Abstract. This paper presents a new approach to finding minimum cuts in undirected graphs. The fundamental principle is simple: the edges in a graph’s minimum cut form an extremely small fraction of the graph’s edges. Using this idea, we give a randomized, strongly polynomial algorithm that finds th ..."
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Cited by 128 (9 self)
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with value within a multiplicative factor of � of the minimum cut’s in expected Õ(n 2 � ) time, or in �� � with n 2 � processors. The problem of finding a minimum multiway cut of a graph into r pieces is solved in expected Õ(n 2(r�1) ) time, or in �� � with n 2(r�1) processors. The “trace ” of the algorithm
Results 11  20
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873