Abstract: We present a deterministic (1+sqrt(5))/2approximation algorithm for the st path TSP for an arbitrary metric. Given a symmetric metric cost on n vertices including two prespecified endpoints, the problem is to find a shortest Hamiltonian path between the two endpoints; Hoogeveen showed that the natural variant of Christofides' algorithm is a 5/3approximation algorithm for this problem, and this asymptotically tight bound in fact has been the best approximation ratio known until now. We modify this algorithm so that it chooses the initial spanning tree based on an optimal solution to the HeldKarp relaxation rather than a minimum spanning tree; we prove this simple but crucial modification leads to an improved approximation ratio, surpassing the 20yearold barrier set by the natural Christofides' algorithm variant. Our algorithm also proves an upper bound of (1+sqrt(5))/2 on the integrality gap of the pathvariant HeldKarp relaxation. The techniques devised in this paper can be applied to other optimization problems as well: these applications include improved approximation algorithms and improved LP integrality gap upper bounds for the prizecollecting st path problem and the unitweight graphical metric st path TSP. This is joint work with Robert Kleinberg and David Shmoys.
▶Speaker: HyungChan An(Cornell Univ.)
▶Organizer: HeeKap Ahn(POSTECH&GAIA)

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