TY - GEN

T1 - The traveling salesman problem

T2 - 44th Annual ACM Symposium on Theory of Computing, STOC '12

AU - Bartal, Yair

AU - Gottlieb, Lee Ad

AU - Krauthgamer, Robert

PY - 2012

Y1 - 2012

N2 - The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1 + ε)-approximation to the optimal tour, for any fixed ε > 0, in TSP instances that form an arbitrary metric space with bounded intrinsic dimension. The celebrated results of Arora [Aro98] and Mitchell [Mit99] prove that the above result holds in the special case of TSP in a fixed-dimensional Euclidean space. Thus, our algorithm demonstrates that the algorithmic tractability of metric TSP depends on the dimensionality of the space and not on its specific geometry. This result resolves a problem that has been open since the quasi-polynomial time algorithm of Talwar [Tal04].

AB - The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1 + ε)-approximation to the optimal tour, for any fixed ε > 0, in TSP instances that form an arbitrary metric space with bounded intrinsic dimension. The celebrated results of Arora [Aro98] and Mitchell [Mit99] prove that the above result holds in the special case of TSP in a fixed-dimensional Euclidean space. Thus, our algorithm demonstrates that the algorithmic tractability of metric TSP depends on the dimensionality of the space and not on its specific geometry. This result resolves a problem that has been open since the quasi-polynomial time algorithm of Talwar [Tal04].

KW - doubling metrics

KW - traveling salesman problem

UR - http://www.scopus.com/inward/record.url?scp=84862634866&partnerID=8YFLogxK

U2 - 10.1145/2213977.2214038

DO - 10.1145/2213977.2214038

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AN - SCOPUS:84862634866

SN - 9781450312455

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 663

EP - 672

BT - STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing

Y2 - 19 May 2012 through 22 May 2012

ER -