Jukka Suomela: Publications: No sublogarithmic-time approximation scheme for bipartite vertex cover
Conference paper
| Authors: | Mika Göös and Jukka Suomela |
| Title: | No sublogarithmic-time approximation scheme for bipartite vertex cover |
| Conference: | 26th International Symposium on Distributed Computing (DISC), Salvador, Brazil, October 2012 |
| Proceedings: | Marcos K. Aguilera (Ed.): Distributed Computing. 26th International Symposium, DISC 2012. Salvador, Brazil, October 16–18, 2012. Proceedings |
| Lecture Notes in Computer Science, volume 7611 Springer, Berlin, Germany, 2012 ISBN: 978-3-642-33650-8 pages 181–194 doi:10.1007/978-3-642-33651-5_13 |
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| Links: | publisher’s version · authors’ version © Springer 2012 — The original publication is available at www.springerlink.com. |
| extended version | |
| presentation, 17 October 2012 | |
| conference · proceedings · series · DBLP · arXiv.org | |
| Abstract: | König's theorem states that on bipartite graphs the size of a maximum matching equals the size of a minimum vertex cover. It is known from prior work that for every ε > 0 there exists a constant-time distributed algorithm that finds a (1+ε)-approximation of a maximum matching on 2-coloured graphs of bounded degree. In this work, we show—somewhat surprisingly—that no sublogarithmic-time approximation scheme exists for the dual problem: there is a constant δ > 0 so that no randomised distributed algorithm with running time o(log n) can find a (1+δ)-approximation of a minimum vertex cover on 2-coloured graphs of maximum degree 3. In fact, a simple application of the Linial–Saks (1993) decomposition demonstrates that this lower bound is tight. Our lower-bound construction is simple and, to some extent, independent of previous techniques. Along the way we prove that a certain cut minimisation problem, which might be of independent interest, is hard to approximate locally on expander graphs. |