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Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds
Image Segmentation With Maximum Cuts
"... This paper presents an alternative approach to the image segmentation problem. Similar to other recent proposals a graph theoretic framework is used: Given an image a weighted undirected graph is constructed, where each pixel becomes a vertex of the graph and edges measure a relationship between pix ..."
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regions of isolated nodes and therefore a normalization is needed in order to enforce a more balanced partitioning. We propose to fix this shortcoming by using a maximum cut approach, because a maximum cut is usually achieved when the clusters are of similar size. Our edge weights measure the pixel
On the complexity of the Maximum Cut problem
 Nordic Journal of Computing
, 1991
"... The complexity of the simple maxcut problem is investigated for several special classes of graphs. It is shown that this problem is NPcomplete when restricted to one of the following classes: chordal graphs, undirected path graphs, split graphs, tripartite graphs, and graphs that are the complement ..."
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Cited by 18 (4 self)
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polynomial time algorithms for the simple max cut problem. 1 Introduction One of the best known combinatorial graph problems is the max cut problem. In this problem, we have a weighted, undirected graph G = (V; E) and we look for a partition of the vertices of G into two disjoint sets, such that the total
Approximation Algorithms for the Maximum Cut Problem
"... Consider the problem of keeping closely related objects together and seperating unrelated objects from each other. This idea has clear applications to statistics, computer science, mathematics, social studies, and natural sciences just to name a few. To model this idea, we de ne the maximum cut prob ..."
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Consider the problem of keeping closely related objects together and seperating unrelated objects from each other. This idea has clear applications to statistics, computer science, mathematics, social studies, and natural sciences just to name a few. To model this idea, we de ne the maximum cut
New Convex Relaxations for the Maximum Cut . . .
, 2001
"... It is well known that many of the optimization problems which arise in applications are “hard”, which usually means that they are NPhard. Hence much research has been devoted to finding “good” relaxations for these hard problems. Usually a “good” relaxation is one which can be solved (either exac ..."
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exactly or within a prescribed numerical tolerance) in polynomialtime. Nesterov and Nemirovskii showed that by this criterion, many convex optimization problems are good relaxations. This thesis presents new convex relaxations for two such hard problems, namely the MaximumCut (MaxCut) problem
Approximation Algorithms for Connected Maximum Cut and Related Problems
"... Abstract. An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V,E) and the goal is to find a subset of vertices S ⊆ V that maximizes the number of edges in the cut δ(S) such that the induced graph G[S] is connected. We present the first nontrivial Ω ( 1 logn) appr ..."
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Abstract. An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V,E) and the goal is to find a subset of vertices S ⊆ V that maximizes the number of edges in the cut δ(S) such that the induced graph G[S] is connected. We present the first nontrivial Ω ( 1 logn
THE MAXIMUM CUT PROBLEM ON BLOWUPS OF MULTIPROJECTIVE SPACES.
"... Abstract. The maximum cut problem for a quintic del Pezzo surface Bl4(P2) asks: Among all partitions of the 10 exceptional curves into two disjoint sets, what is the largest possible number of pairwise intersections? In this article we show that the answer is twelve. More generally, we obtain bounds ..."
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Abstract. The maximum cut problem for a quintic del Pezzo surface Bl4(P2) asks: Among all partitions of the 10 exceptional curves into two disjoint sets, what is the largest possible number of pairwise intersections? In this article we show that the answer is twelve. More generally, we obtain
The Method of Extremal Structure on the kMaximum Cut Problem
"... Using the Method of Extremal Structure, which combines the use of reduction rules as a preprocessing technique and combinatorial extremal arguments, we will prove the fixedparameter tractability and find a problem kernel for kMAXIMUM CUT. This kernel has 2k edges, the same as that found by Mahajan ..."
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Cited by 8 (0 self)
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Using the Method of Extremal Structure, which combines the use of reduction rules as a preprocessing technique and combinatorial extremal arguments, we will prove the fixedparameter tractability and find a problem kernel for kMAXIMUM CUT. This kernel has 2k edges, the same as that found
A Note on Polyhedral Relaxations for the Maximum Cut Problem
"... We consider three wellstudied polyhedral relaxations for the maximum cut problem: the metric polytope of the complete graph, the metric polytope of a general graph, and the relaxation of the bipartite subgraph polytope. The metric polytope of the complete graph can be described with a polynomial nu ..."
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Cited by 1 (1 self)
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We consider three wellstudied polyhedral relaxations for the maximum cut problem: the metric polytope of the complete graph, the metric polytope of a general graph, and the relaxation of the bipartite subgraph polytope. The metric polytope of the complete graph can be described with a polynomial
Results 1  10
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759,486