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 -