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2003
IEEE

Approximation Algorithms for Asymmetric TSP by Decomposing Directed Regular Multigraphs

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Approximation Algorithms for Asymmetric TSP by Decomposing Directed Regular Multigraphs
A directed multigraph is said to be d-regular if the indegree and outdegree of every vertex is exactly d. By Hall’s theorem one can represent such a multigraph as a combination of at most n2 cycle covers each taken with an appropriate multiplicity. We prove that if the d-regular multigraph does not contain more than ⌊d/2⌋ copies of any 2-cycle then we can find a similar decomposition into n2 pairs of cycle covers where each 2-cycle occurs in at most one component of each pair. Our proof is constructive and gives a polynomial algorithm to find such a decomposition. Since our applications only need one such a pair of cycle covers whose weight is at least the average weight of all pairs, we also give an alternative, simpler algorithm to extract a single such pair. This combinatorial theorem then comes handy in rounding a fractional solution of an LP relaxation of the maximum Traveling Salesman Problem (TSP) problem. The first stage of the rounding procedure obtains two cycle cov...
Haim Kaplan, Moshe Lewenstein, Nira Shafrir, Maxim
Added 04 Jul 2010
Updated 04 Jul 2010
Type Conference
Year 2003
Where FOCS
Authors Haim Kaplan, Moshe Lewenstein, Nira Shafrir, Maxim Sviridenko
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