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- W2017288734 abstract "A complete partition of a graph G is a partition of V(G) such that any two 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 [18], and is known to be NP-hard on several classes of graphs. We obtain the first, and 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 produces a complete partition of size Ω(cp(G)/√lg|V(G)|). 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 problem whose approximation threshold has been determined to be of the form θ((lg n)c) for some constant c strictly between 0 and 1." @default.
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- W2017288734 date "2005-01-23" @default.
- W2017288734 modified "2023-09-26" @default.
- W2017288734 title "Complete partitions of graphs" @default.
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- W2017288734 doi "https://doi.org/10.5555/1070432.1070553" @default.
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