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Algorithms & Randomness Center (ARC)
Vera Traub (ETH Zurich)
Monday, September 28, 2020
Virtual via Bluejeans - 11:00 am
Title: Reducing Path TSP to TSP
Abstract: In this talk we present a black-box reduction from the path version of the Traveling Salesman Problem (Path TSP) to the classical tour version (TSP). More precisely, we show that given an α-approximation algorithm for TSP, then, for any ϵ>0, there is an (α+ϵ)-approximation algorithm for the more general Path TSP. This reduction implies that the approximability of Path TSP is the same as for TSP, up to an arbitrarily small error. This avoids future discrepancies between the best known approximation factors achievable for these two problems, as they have existed until very recently.
To obtain our result we use a novel way to set up a recursive dynamic program to guess significant parts of an optimal solution. At the core of our dynamic program we deal with instances of a new generalization of (Path) TSP which combines parity constraints with certain connectivity requirements. This problem, which we call Φ-TSP, has a constant-factor approximation algorithm and can be reduced to TSP in certain cases when the dynamic program would not make sufficient progress.
This is joint work with Jens Vygen and Rico Zenklusen.
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