Optimal Graph Constraint Reduction for Symbolic Layout Compaction

The symbolic layout compaction problem is often formulated as a linear program (LP). In order to reduce the execution time and memory usage, it is very important to reduce the size of the LP. Since most of the constraints in the LP are derived from physical separation and electrical connectivity requirements which can be expressed in the form of "graph constraints", we study the problem of graph constraint reduction, i.e. the problem of producing, for a given system of graph constraints, an "equivalent" system with fewer constraints. In this paper we first show a previous formulation of the graph constraint reduction problem is NP-complete. We also observe that such a formulation is overly restrictive in the sense that a maximum possible reduction is not always attainable. We then propose a new formulation of the problem and present a polynomial-time algorithm which always produces a maximum possible reduction.