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Improved Inapproximability for TSP
, 2014
"... The Traveling Salesman Problem is one of the most studied problems in the theory of algorithms and its approximability is a longstanding open question. Prior to the present work, the best known inapproximability threshold was 220/219, due to Papadimitriou and Vempala. Here, using an essentially di ..."
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Cited by 9 (1 self)
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The Traveling Salesman Problem is one of the most studied problems in the theory of algorithms and its approximability is a longstanding open question. Prior to the present work, the best known inapproximability threshold was 220/219, due to Papadimitriou and Vempala. Here, using an essentially different construction and also relying on the work of Berman and Karpinski on boundedoccurrence CSPs, we give an alternative and simpler inapproximability proof which improves the bound to 185/184.
On integrality ratios for asymmetric tsp in the sheraliadams hierarchy
 In Automata, Languages, and Programming
, 2013
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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 ..."
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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
NoWait Flowshop Scheduling is as Hard as Asymmetric Traveling Salesman Problem
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