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COMBINATORICA
2007

Complete partitions of graphs

13 years 3 months ago
Complete partitions of graphs
A complete partition of a graph G is a partition of its vertex set in which any two distinct classes are connected by an edge. Let cp(G) denote the maximum number of classes in a complete partition of G. This measure was defined in 1969 by Gupta [G69], and is known to be NP-hard to compute for several classes of graphs. We obtain essentially tight lower and upper bounds on the approximability of this problem. We show that there is a randomized polynomial-time algorithm that given a graph G with n vertices, produces a complete partition of size Ω(cp(G)/ √ lg n). This algorithm can be derandomized. We show that the upper bound is essentially tight: there is a constant C > 1, such that if there is a randomized polynomial-time algorithm that for all large n, when given a graph G with n vertices produces a complete partition into at least C · cp(G)/ √ lg n classes, then NP ⊆ RTime(nO(lg lg n) ). The problem of finding a complete partition of a graph is thus the first natural...
Magnús M. Halldórsson, Guy Kortsarz,
Added 25 Dec 2010
Updated 25 Dec 2010
Type Journal
Year 2007
Where COMBINATORICA
Authors Magnús M. Halldórsson, Guy Kortsarz, Jaikumar Radhakrishnan, Sivaramakrishnan Sivasubramanian
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