Research output: Working paper
Research output: Working paper
}
TY - UNPB
T1 - Polynomial-time separation of simple comb inequalities
AU - Letchford, A N
AU - Lodi, A
N1 - This was eventually published as: L.K. Fleischer, A.N. Letchford & A. Lodi (2006) Polynomial-time separation of a superclass of simple comb inequalities. Math. Oper. Res., 31(4), 696-713.
PY - 2003
Y1 - 2003
N2 - The comb inequalities are a well-known class of facet-inducing inequalities for the Travelling Salesman Problem, defined in terms of certain vertex sets called the handle and the teeth. We say that a comb inequality is simple if the following holds for each tooth: either the intersection of the tooth with the handle has cardinality one, or the part of the tooth outside the handle has cardinality one, or both. The simple comb inequalities generalize the classical 2-matching inequalities of Edmonds, and also the so-called Chvatal comb inequalities. In 1982, Padberg and Rao [29] gave a polynomial-time algorithm for separating the 2-matching inequalities - i.e., for testing if a given fractional solution to an LP relaxation violates a 2-matching inequality. We extend this significantly by giving a polynomial-time algorithm for separating the simple comb inequalities. The key is a result due to Caprara and Fischetti.
AB - The comb inequalities are a well-known class of facet-inducing inequalities for the Travelling Salesman Problem, defined in terms of certain vertex sets called the handle and the teeth. We say that a comb inequality is simple if the following holds for each tooth: either the intersection of the tooth with the handle has cardinality one, or the part of the tooth outside the handle has cardinality one, or both. The simple comb inequalities generalize the classical 2-matching inequalities of Edmonds, and also the so-called Chvatal comb inequalities. In 1982, Padberg and Rao [29] gave a polynomial-time algorithm for separating the 2-matching inequalities - i.e., for testing if a given fractional solution to an LP relaxation violates a 2-matching inequality. We extend this significantly by giving a polynomial-time algorithm for separating the simple comb inequalities. The key is a result due to Caprara and Fischetti.
KW - travelling salesman problem
KW - cutting planes
KW - separation
M3 - Working paper
T3 - Management Science Working Paper Series
BT - Polynomial-time separation of simple comb inequalities
PB - The Department of Management Science
CY - Lancaster University
ER -