Mika Göös · Jukka Suomela

No sublogarithmic-time approximation scheme for bipartite vertex cover

Distributed Computing · volume 27, issue 6, pages 435–443, 2014 · doi:10.1007/s00446-013-0194-z

authors’ version publisher’s version arXiv.org


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 bounded-degree graphs. 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 run-time 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.


Conference Version

© Springer 2014

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