The traveling salesman problem in bounded degree graphs

Authors:
Andreas Björklund;Thore Husfeldt;Petteri Kaski;Mikko Koivisto
Affiliations:
Lund University, Sweden;IT University of Copenhagen, Denmark and Lund University, Sweden;Helsinki Institute for Information Technology and University of Helsinki, Finland;Helsinki Institute for Information Technology and University of Helsinki, Finland
Venue:
ACM Transactions on Algorithms (TALG)
Year:
2012

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Abstract

We show that the traveling salesman problem in bounded-degree graphs can be solved in time O((2-ε)n), where ε 0 depends only on the degree bound but not on the number of cities, n. The algorithm is a variant of the classical dynamic programming solution due to Bellman, and, independently, Held and Karp. In the case of bounded integer weights on the edges, we also give a polynomial-space algorithm with running time O((2-ε)n) on bounded-degree graphs. In addition, we present an analogous analysis of Ryser's algorithm for the permanent of matrices with a bounded number of nonzero entries in each column.