Routing in grid graphs by cutting planes
نویسندگان
چکیده
In this paper we study the following problem, which we call the weighted routing problem. Let be given a graph G = (V, E) with non-negative edge weights we € R+ and integer edge capacities ce 6 IN and let M = {Ti,.. .,Tjv}, N > 1, be a list of node sets. The weighted routing problem consists in finding edge sets S\,...,Sjq such that, for each A € { 1 , . . . , N}, the subgraph (V(Sk),Sk) contains an [s,i]-path for all s, t € Tk, at most ce of these edge sets use edge e for each e € E, and such that the sum of the weights of the edge sets is minimal. Our motivation for studying this problem arises from the routing problem in VLSI-design, where given sets of points have to be connected by wires. We consider the weighted routing problem from a polyhedral point of view. We define an appropriate polyhedron and try to (partially) describe this polyhedron by means of inequalities. We briefly sketch our separation algorithms for some of the presented classes of inequalities. Based on these separation routines we have implemented a branch and cut algorithm. Our algorithm is applicable to an important subclass of routing problems arising in VLSI-design, namely to problems where the underlying graph is a grid graph and the list of node sets is located on the outer face of the grid. We report on our computational experience with this class of problem instances.
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