1 research outputs found
Mildly Exponential Time Approximation Algorithms for Vertex Cover, Uniform Sparsest Cut and Related Problems
In this work, we study the trade-off between the running time of
approximation algorithms and their approximation guarantees. By leveraging a
structure of the `hard' instances of the Arora-Rao-Vazirani lemma [JACM'09], we
show that the Sum-of-Squares hierarchy can be adapted to provide `fast', but
still exponential time, approximation algorithms for several problems in the
regime where they are believed to be NP-hard. Specifically, our framework
yields the following algorithms; here denote the number of vertices of the
graph and can be any positive real number greater than 1 (possibly
depending on ).
(i) A -approximation algorithm for Vertex
Cover that runs in time.
(ii) An -approximation algorithms for Uniform Sparsest Cut, Balanced
Separator, Minimum UnCut and Minimum 2CNF Deletion that runs in
time.
Our algorithm for Vertex Cover improves upon Bansal et al.'s algorithm
[arXiv:1708.03515] which achieves -approximation in time
. For the remaining problems, our
algorithms improve upon -approximation
-time algorithms that follow from a
work of Charikar et al. [SIAM J. Comput.'10].Comment: An extended abstract of this work will appear in APPROX'1