No sublogarithmic-time approximation scheme for bipartite vertex cover

@article{Gs2012NoSA,
  title={No sublogarithmic-time approximation scheme for bipartite vertex cover},
  author={Mika G{\"o}{\"o}s and Jukka Suomela},
  journal={Distributed Computing},
  year={2012},
  volume={27},
  pages={435-443}
}
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 $$\epsilon > 0$$ϵ>0 there exists a constant-time distributed algorithm that finds a $$(1+\epsilon )$$(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 $$\delta > 0$$δ>0 so… 
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13 Citations
Background Citations
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Methods Citations
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13 Citations

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Approximating Bipartite Minimum Vertex Cover in the CONGEST Model

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  • Yi-Jun ChangSeth Pettie
  • Computer Science, Mathematics
    2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
  • 2017
It is proved that any randomized algorithm that solves an LCL problem in sublogarithmic time can be sped up to run in O(T_{LLL}) time, which is the complexity of the distributed Lovasz local lemma problem, currently known to be Ω( log log n) and 2^{O(sqrt{log log n})} on bounded degree graphs.

Local coordination and symmetry breaking

An informal overview of the techniques that can be used to prove lower bounds for distributed graph algorithms and a roadmap for future research are proposed, with the aim of resolving some of the major open questions of the field.

Polynomial Lower Bound for Distributed Graph Coloring in a Weak LOCAL Model

An \(\varOmega \big (\varDelta ^{\frac{1}{3}-\frac{\eta }{3}}\big )\) lower bound on the runtime of any deterministic distributed graph coloring algorithm in a weak variant of theLOCAL model is shown.

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No sublogarithmic-time approximation scheme for bipartite vertex cover

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\documentclass[12pt]{minimal}…

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