Large Isolating Cuts Shrink the Multiway Cut
Abstract
We propose a preprocessing algorithm for the multiway cut problem that establishes its polynomial kernelizability when the difference between the parameter and the size of the smallest isolating cut is at most . To the best of our knowledge, this is the first progress towards kernelization of the multiway cut problem. We pose two open questions that, if answered affirmatively, would imply, combined with the proposed result, unconditional polynomial kernelizability of the multiway cut problem.
Cite
@article{arxiv.1104.5361,
title = {Large Isolating Cuts Shrink the Multiway Cut},
author = {Igor Razgon},
journal= {arXiv preprint arXiv:1104.5361},
year = {2011}
}
Comments
Marcin Piliczuk has communicated to me a negative answer to the first open question. The graph was designed for a different purpose in collaboration with Marek Cygan, Jakub Wojtaszczyk, Micha{\l} Pilipczuk but, after a slight modification, suited to answer the question