Simpler analysis of LP extreme points for traveling salesman and survivable network design problems

Authors:
Viswanath Nagarajan;R. Ravi;Mohit Singh
Affiliations:
IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA;Tepper School of Business, CMU, Pittsburgh, PA, USA;McGill University, Montreal, QC, Canada
Venue:
Operations Research Letters
Year:
2010

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Abstract

We consider the Survivable Network Design Problem (SNDP) and the Symmetric Traveling Salesman Problem (STSP). We give simpler proofs of the existence of a 12-edge and 1-edge in any extreme point of the natural LP relaxations for the SNDP and STSP, respectively. We formulate a common generalization of both problems and show our results by a new counting argument. We also obtain a simpler proof of the existence of a 12-edge in any extreme point of the set-pair LP relaxation for the element connectivitySurvivable Network Design Problem (SNDP"e"l"t).