Gerhard Reinelt

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where x e {0, 1} n, Q c ~( , , , i is an u p p e r t r i angu la r mat r ix and c c R" is a co lumn vector. Since x~-x i we can assume that the d i agona l of Q is zero. Our p r o b l e m is to find the m i n i m u m o f f This is an N P h a r d p rob lem, cf. G a r e y and Johnson (1979). It is po lynomia l ly so lvable if all the e lements of Q are nonpos(More)
In this article we consider a variant of the classical asymmetric traveling salesman problem (ATSP), namely the ATSP in which precedence constraints require that certain nodes must precede certain other nodes in any feasible directed tour. This problem occurs as a basic model in scheduling and routing and has a wide range of applications varying from(More)
Cutting plane algorithms have turned out to be practically successful computational tools in combinatorial optimization, in particular, when they are embedded in a branch and bound framework. Implementations of such \branch and cut" algorithms are rather complicated in comparison to many purely combinatorial algorithms. The purpose of this article is to(More)