منابع مشابه
Maximum Cut Problem, MAX-CUT
The MAXIMUM CUT problem (MAX-CUT) is one of the simplest graph partitioning problems to conceptualize, and yet it is one of the most difficult combinatorial optimization problems to solve. The objective of MAX-CUT is to partition the set of vertices of a graph into two subsets, such that the sum of the weights of the edges having one endpoint in each of the subsets is maximum. This problem is k...
متن کامل2 Maximum Cut Problem
2.1 Greedy algorithm We can think of the cut as a partition of verticesl C = (S, V \ S) whiere S ⊆ V . We can switch between different cuts by moving vertices across the cut, in to or out of S. Moving v across the cut swaps its cut edges with its non-cut edges. This increase the value of the cut when the total weight of its non-cut edges exceeds the weight of the cut edges. If v ∈ S (and simila...
متن کاملApproximation 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 problem that is simple to state but di cult to solve. The aim of this report is to provide two known ...
متن کاملLaplacian eigenvalues and the maximum cut problem
We introduce and study an eigenvalue upper bound p(G) on the maximum cut mc (G) of a weighted graph. The function ~o(G) has several interesting properties that resemble the behaviour of mc (G). The following results are presented. We show that q~ is subadditive with respect to amalgam, and additive with respect to disjoint sum and 1-sum. We prove that ~(G) is never worse that 1.131 mc(G) for a ...
متن کاملSpectral bounds for the maximum cut problem
The maximum cut problem this paper deals with can be formulated as follows. Given an undirected simple graph G = (V,E) where V and E stand for the node and edge sets respectively, and given weights assigned to the edges: (wij)ij∈E , a cut δ(S), with S ⊆ V is de ned as the set of edges in E with exactly one endnode in S, i.e. δ(S) = {ij ∈ E | |S ∩ {i, j}| = 1}. The weight w(S) of the cut δ(S) is...
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ژورنال
عنوان ژورنال: An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
سال: 2020
ISSN: 2146-5703,2146-0957
DOI: 10.11121/ijocta.01.2020.00826