# Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs

@article{Kaplan2005ApproximationAF, title={Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs}, author={Haim Kaplan and Moshe Lewenstein and Nira Shafrir and Maxim Sviridenko}, journal={J. ACM}, year={2005}, volume={52}, pages={602-626} }

- Published in J. ACM 2005
DOI:10.1145/1082036.1082041

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… CONTINUE READING

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