Results 1 
3 of
3
LiftandProject Integrality Gaps for the Traveling Salesperson Problem
, 2011
"... We study the liftandproject procedures of LovászSchrijver and SheraliAdams applied to the standard linear programming relaxation of the traveling salesperson problem with triangle inequality. For the asymmetric TSP tour problem, Charikar, Goemans, and Karloff (FOCS 2004) proved that the integral ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We study the liftandproject procedures of LovászSchrijver and SheraliAdams applied to the standard linear programming relaxation of the traveling salesperson problem with triangle inequality. For the asymmetric TSP tour problem, Charikar, Goemans, and Karloff (FOCS 2004) proved that the integrality gap of the standard relaxation is at least 2. We prove that after one round of the LovászSchrijver or SheraliAdams procedures, the integrality gap of the asymmetric TSP tour problem is at least 3/2, with a small caveat on which version of the standard relaxation is used. For the symmetric TSP tour problem, the integrality gap of the standard relaxation is known to be at least 4/3, and Cheung (SIOPT 2005) proved that it remains at least 4/3 after o(n) rounds of the LovászSchrijver procedure, where n is the number of nodes. For the symmetric TSP path problem, the integrality gap of the standard relaxation is known to be at least 3/2, and we prove that it remains at least 3/2 after o(n) rounds of the LovászSchrijver procedure, by a simple reduction to Cheung’s result. 1
Multiple traveling salesmen in asymmetric metrics
 In Proceedings of APPROX
, 2013
"... ar ..."
(Show Context)