TY - GEN

T1 - A near-optimal approximation algorithm for Asymmetric TSP on embedded graphs

AU - Erickson, Jeff

AU - Sidiropoulos, Anastasios

PY - 2014

Y1 - 2014

N2 - We present a near-optimal polynomial-time approximation algorithm for the asymmetric traveling salesman problem for graphs of bounded orientable or non-orientable genus. Given any algorithm that achieves an approximation ratio of f (n) on arbitrary n-vertex graphs as a black box, our algorithm achieves an approximation factor of O( f (g)) on graphs with genus g. In particular, the O(log n= log log n)-approximation algorithm for general graphs by Asadpour et al. [SODA 2010] immediately implies an O(log g= log log g)-approximation algorithm for genus-g graphs. Moreover, recent results on approximating the genus of graphs imply that our O(log g= log log g)-approximation algorithm can be applied to bounded-degree graphs even if no genus-g embedding of the graph is given. Our result improves and generalizes the O(√g log g)-approximation algorithm of Oveis Gharan and Saberi [SODA 2011], which applies only to graphs with orientable genus g and requires a genus-g embedding as part of the input, even for bounded-degree graphs. Finally, our techniques yield a O(1)-approximation algorithm for ATSP on graphs of genus g with running time 2O(g)· nO(1)

AB - We present a near-optimal polynomial-time approximation algorithm for the asymmetric traveling salesman problem for graphs of bounded orientable or non-orientable genus. Given any algorithm that achieves an approximation ratio of f (n) on arbitrary n-vertex graphs as a black box, our algorithm achieves an approximation factor of O( f (g)) on graphs with genus g. In particular, the O(log n= log log n)-approximation algorithm for general graphs by Asadpour et al. [SODA 2010] immediately implies an O(log g= log log g)-approximation algorithm for genus-g graphs. Moreover, recent results on approximating the genus of graphs imply that our O(log g= log log g)-approximation algorithm can be applied to bounded-degree graphs even if no genus-g embedding of the graph is given. Our result improves and generalizes the O(√g log g)-approximation algorithm of Oveis Gharan and Saberi [SODA 2011], which applies only to graphs with orientable genus g and requires a genus-g embedding as part of the input, even for bounded-degree graphs. Finally, our techniques yield a O(1)-approximation algorithm for ATSP on graphs of genus g with running time 2O(g)· nO(1)

KW - Approximation algorithms

KW - Topological graph algorithms

KW - Traveling salesman

UR - http://www.scopus.com/inward/record.url?scp=84904430730&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904430730&partnerID=8YFLogxK

U2 - 10.1145/2582112.2582136

DO - 10.1145/2582112.2582136

M3 - Conference contribution

AN - SCOPUS:84904430730

SN - 9781450325943

T3 - Proceedings of the Annual Symposium on Computational Geometry

SP - 130

EP - 135

BT - Proceedings of the 30th Annual Symposium on Computational Geometry, SoCG 2014

PB - Association for Computing Machinery

T2 - 30th Annual Symposium on Computational Geometry, SoCG 2014

Y2 - 8 June 2014 through 11 June 2014

ER -