# WeGotYouCovered: The Winning Solver from the PACE 2019 Implementation Challenge, Vertex Cover Track

## TL;DR

This paper introduces the winning solver from the PACE 2019 Challenge for the vertex cover problem, combining kernelization, local search, and branch-and-bound techniques, with novel insights on their interactions.

## Contribution

It presents a new solver that integrates techniques from related problems and provides empirical insights on their effectiveness and interactions.

## Key findings

- Kernelization can enhance branch-and-bound clique solvers.
- Local search significantly improves branch-and-reduce solver performance.
- Kernelization can sometimes degrade branch-and-bound algorithms.

## Abstract

We present the winning solver of the PACE 2019 Implementation Challenge, Vertex Cover Track. The minimum vertex cover problem is one of a handful of problems for which kernelization---the repeated reducing of the input size via data reduction rules---is known to be highly effective in practice. Our algorithm uses a portfolio of techniques, including an aggressive kernelization strategy, local search, branch-and-reduce, and a state-of-the-art branch-and-bound solver. Of particular interest is that several of our techniques were not from the literature on the vertex over problem: they were originally published to solve the (complementary) maximum independent set and maximum clique problems. Aside from illustrating our solver's performance in the PACE 2019 Implementation Challenge, our experiments provide several key insights not yet seen before in the literature. First, kernelization can boost the performance of branch-and-bound clique solvers enough to outperform branch-and-reduce solvers. Second, local search can significantly boost the performance of branch-and-reduce solvers. And finally, somewhat surprisingly, kernelization can sometimes make branch-and-bound algorithms perform worse than running branch-and-bound alone.