Boosting Data Reduction for the Maximum Weight Independent Set Problem Using Increasing Transformations

Abstract

Given a vertex-weighted graph, the maximum weight independent set problem asks for a pair-wise non-adjacent set of vertices such that the sum of their weights is maximum. The branch-and-reduce paradigm is the de facto standard approach to solve the problem to optimality in practice. In this paradigm, data reduction rules are applied to decrease the problem size. These data reduction rules ensure that given an optimum solution on the new (smaller) input, one can quickly construct an optimum solution on the original input. We introduce new generalized data reduction and transformation rules for the problem. A key feature of our work is that some transformation rules can increase the size of the input. Surprisingly, these so-called increasing transformations can simplify the problem and also open up the reduction space to yield even smaller irreducible graphs later throughout the algorithm. In experiments, our algorithm computes significantly smaller irreducible graphs on all except one instance, solves more instances to optimality than previously possible, is up to two orders of magnitude faster than the best state-of-the-art solver, and finds higher-quality solutions than heuristic solvers DynWVC and HILS on many instances. While the increasing transformations are only efficient enough for preprocessing at this time, we see this as a critical initial step towards a new branch-and-transform paradigm.