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The Traveling Salesman Problem in Bounded Degree Graphs

Publiceringsår: 2012
Språk: Engelska
Publikation/Tidskrift/Serie: ACM Transactions on Algorithms
Volym: 8
Nummer: 2
Dokumenttyp: Artikel
Förlag: Association for Computing Machinery


We show that the traveling salesman problem in bounded-degree graphs can be solved in time O((2 - epsilon)(n)), where epsilon > 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 - epsilon)(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.



  • Computer Science
  • Counting
  • dynamic programming
  • inclusion-exclusion
  • permanent
  • Shearer's
  • entropy lemma
  • traveling salesman problem
  • trimming


  • ISSN: 1549-6325

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