# Routing in Grid Graphs by Cutting Planes

## Publication Details

Abstract

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*w*_{e} ∈ ℝ_{+} and letN,*N* ≥ 1, be a list of node sets. The weighted routing problem consists in finding mutually disjoint edge sets*S*_{1},...,*S*_{N} such that, for each*k* ∈ {1, ...,*N*}, the subgraph (*V*(*S*_{k}),*S*_{k}) contains an [*s, t*]-path for all*s, t ∈ T*_{k} and 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 describe 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 switchbox routing 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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How to cite

APA: | Grötschel, M., Martin, A., & Weismantel, R. (1993). Routing in Grid Graphs by Cutting Planes. In G. Rinaldi, L.A. Wolsey (Eds.), Integer Programming and Combinatorial Optimization (pp. 447 - 463). |

MLA: | Grötschel, Martin, Alexander Martin, and Robert Weismantel. "Routing in Grid Graphs by Cutting Planes." Integer Programming and Combinatorial Optimization Ed. G. Rinaldi, L.A. Wolsey, 1993. 447 - 463. |

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