Paper Info
Title
Finding Large Set Covers Faster via the Representation Method.
Abstract
The worst-case fastest known algorithm for the Set Cover problem on universes with n elements still essentially is the simple O^*(2^n)-time dynamic programming algorithm, and no non-trivial consequences of an O^*(1.01^n)-time algorithm are known. Motivated by this chasm, we study the following natural question: Which instances of Set Cover can we solve faster than the simple dynamic programming algorithm? Specifically, we give a Monte Carlo algorithm that determines the existence of a set cover of size sigma*n in O^*(2^{(1-Omega(sigma^4))n}) time. Our approach is also applicable to Set Cover instances with exponentially many sets: By reducing the task of finding the chromatic number of a given n-vertex graph G to Set Cover in the natural way, we show there is an O^*(2^{(1-Omega(sigma^4))n})-time randomized algorithm that given integer s = sigma*n, outputs NO if u003e s and YES with constant probability if chi(G) u003c= s - 1.On a high level, our results are inspired by the representation method of Howgrave-Graham and Joux~[EUROCRYPTu002710] and obtained by only evaluating a randomly sampled subset of the table entries of a dynamic programming algorithm.
Year
DOI
Venue
2016
10.4230/LIPIcs.ESA.2016.69
european symposium on algorithms
DocType
Volume
Citations 
Journal
abs/1608.03439
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
Jesper Nederlof129424.22