Exactly Solving the Maximum Weight Independent Set Problem on Large Real-World Graphs

TL;DR

This paper introduces new reduction techniques for the maximum weight independent set problem, enabling exact solutions on large real-world graphs and outperforming existing algorithms in speed and solution quality.

Contribution

The authors develop a comprehensive set of reductions for weighted independent set problems and demonstrate their effectiveness on large-scale real-world graphs.

Findings

Outperforms state-of-the-art algorithms on large graphs

Solves many instances within 15 minutes

Combining kernelization with local search yields better solutions

Abstract

One powerful technique to solve NP-hard optimization problems in practice is branch-and-reduce search---which is branch-and-bound that intermixes branching with reductions to decrease the input size. While this technique is known to be very effective in practice for unweighted problems, very little is known for weighted problems, in part due to a lack of known effective reductions. In this work, we develop a full suite of new reductions for the maximum weight independent set problem and provide extensive experiments to show their effectiveness in practice on real-world graphs of up to millions of vertices and edges. Our experiments indicate that our approach is able to outperform existing state-of-the-art algorithms, solving many instances that were previously infeasible. In particular, we show that branch-and-reduce is able to solve a large number of instances up to two orders of magnitude faster than existing (inexact) local search algorithms---and is able to solve the majority of instances within 15 minutes. For those instances remaining infeasible, we show that combining kernelization with local search produces higher-quality solutions than local search alone.