Home > Department of Mathematics > Seminars > OR Seminar Series > Academic year 2014-15 > Approximating ATSP by Relaxing Connectivity
How to contact us

 

LSE 10 logo master_6


Department of Management
London School of Economics and Political Science
Houghton Street

London WC2A 2AE

  

Enquiries: dom.events@lse.ac.uk 

  

Follow us online

Facebook-Square-38x38Twitter-square-38x38Youtube-square-38x38

 

Approximating ATSP by Relaxing Connectivity

Wednesday 10 June 2015
Ola Svensson

4pm - 5pm, OLD 3.24, Old Building, Houghton Street 


Abstract

The standard LP relaxation of the asymmetric traveling salesman problem has been conjectured to have a constant integrality gap in the metric case. We prove this conjecture when restricted to shortest path metrics of node-weighted digraphs. Our arguments are constructive and give a constant factor approximation algorithm for these metrics. We remark that the considered case is more general than the directed analog of the special case of the symmetric traveling salesman problem for which there were recent improvements on Christofides' algorithm.

The main idea of our approach is to first consider an easier problem obtained by relaxing the general connectivity requirements into local connectivity conditions. For this relaxed problem, it is quite easy to give an algorithm with a guarantee of 3 on node-weighted shortest path metrics. More surprisingly, we then show that any algorithm (irrespective of the metric) for the relaxed problem can be turned into an algorithm for the asymmetric traveling salesman problem by only losing a small constant factor in the performance guarantee. This leaves open the intriguing task of designing a "good" algorithm for the relaxed problem on general metrics.

 

Share:Facebook|Twitter|LinkedIn|