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Approximation Algorithms and Hardness of the kRoute Cut Problem
, 2011
"... We study the kroute cut problem: given an undirected edgeweighted graph G = (V, E), a collection {(s1, t1), (s2, t2),..., (sr, tr)} of sourcesink pairs, and an integer connectivity requirement k, the goal is to find a minimumweight subset E ′ of edges to remove, such that the connectivity of eve ..."
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Cited by 5 (0 self)
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We study the kroute cut problem: given an undirected edgeweighted graph G = (V, E), a collection {(s1, t1), (s2, t2),..., (sr, tr)} of sourcesink pairs, and an integer connectivity requirement k, the goal is to find a minimumweight subset E ′ of edges to remove, such that the connectivity
Improved RegionGrowing and Combinatorial Algorithms for kRoute Cut Problems
"... We study the kroute generalizations of various cut problems, the most general of which is kroute multicut (kMC) problem, wherein we have r sourcesink pairs and the goal is to delete a minimumcost set of edges to reduce the edgeconnectivity of every sourcesink pair to below k. The kroute exte ..."
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extensions of multiway cut (kMWC), and the minimum st cut problem (k(s, t)Cut), are similarly defined. We present various approximation and hardness results for kMC, kMWC, and k(s, t)Cut that improve the stateoftheart for these problems in several cases. Our contributions are threefold. • For kroute
Multicommodity maxflow mincut theorems and their use in designing approximation algorithms
 J. ACM
, 1999
"... In this paper, we establish maxflow mincut theorems for several important classes of multicommodity flow problems. In particular, we show that for any nnode multicommodity flow problem with uniform demands, the maxflow for the problem is within an O(log n) factor of the upper bound implied by ..."
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Cited by 357 (6 self)
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to design the first polynomialtime (polylog ntimesoptimal) approximation algorithms for wellknown NPhard optimization problems such as graph partitioning, mincut linear arrangement, crossing number, VLSI layout, and minimum feedback arc set. Applications of the flow results to path routing problems
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
The Complexity of Multiterminal Cuts
 SIAM Journal on Computing
, 1994
"... In the Multiterminal Cut problem we are given an edgeweighted graph and a subset of the vertices called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the mincut, maxflow problem, and ..."
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Cited by 194 (0 self)
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, and can be solved in polynomial time. We show that the problem becomes NPhard as soon as k = 3, but can be solved in polynomial time for planar graphs for any fixed k. The planar problem is NPhard, however, if k is not fixed. We also describe a simple approximation algorithm for arbitrary graphs
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
Approximation and Hardness Results for Label Cut and Related Problems
"... We investigate a natural combinatorial optimization problem called the Label Cut problem. Given an input graph G with a source s and a sink t, the edges of G are classified into different categories, represented by a set of labels. The labels may also have weights. We want to pick a subset of labels ..."
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Cited by 8 (0 self)
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of labels of minimum cardinality (or minimum total weight), such that the removal of all edges with these labels disconnects s and t. We give the first nontrivial approximation and hardness results for the Label Cut problem. Firstly, we present an O ( √ m)approximation algorithm for the Label Cut problem
Nearoptimal hardness results and approximation algorithms for edgedisjoint paths and related problems
 Journal of Computer and System Sciences
, 1999
"... We study the approximability of edgedisjoint paths and related problems. In the edgedisjoint paths problem (EDP), we are given a network G with sourcesink pairs (si, ti), 1 ≤ i ≤ k, and the goal is to find a largest subset of sourcesink pairs that can be simultaneously connected in an edgedisjo ..."
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Cited by 108 (12 self)
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disjoint manner. We show that in directed networks, for any ɛ> 0, EDP is NPhard to approximate within m 1/2−ɛ. We also design simple approximation algorithms that achieve essentially matching approximation guarantees for some generalizations of EDP. Another related class of routing problems that we study
Combination Can Be Hard: Approximability of the Unique Coverage Problem
 In Proceedings of the 17th Annual ACMSIAM Symposium on Discrete Algorithms
, 2006
"... Abstract We prove semilogarithmic inapproximability for a maximization problem called unique coverage:given a collection of sets, find a subcollection that maximizes the number of elements covered exactly once. Specifically, assuming that NP 6 ` BPTIME(2n " ) for an arbitrary "> ..."
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Cited by 77 (2 self)
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hypothesis concerning the hardness of another problem, balanced bipartite independent set. We establish an \Omega (1 / log n)approximation algorithm, even for a moregeneral (budgeted) setting, and obtain an \Omega (1 / log B)approximation algorithm when every set hasat most B elements. We also show
On the Hardness of Approximating MAX kCUT and its Dual
, 1995
"... We study the Max kCut problem and its dual, the Min kPartition problem: given G = (V; E) and w : E ! R + , find an edge set of minimum weight whose removal makes G kcolorable. For the Max kCut problem we show that, if P 6= NP, no polynomial time approximation algorithm can achieve a relative ..."
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Cited by 31 (2 self)
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We study the Max kCut problem and its dual, the Min kPartition problem: given G = (V; E) and w : E ! R + , find an edge set of minimum weight whose removal makes G kcolorable. For the Max kCut problem we show that, if P 6= NP, no polynomial time approximation algorithm can achieve a relative
Results 1  10
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51,493