Algorithms for Implicit Hitting Set Problems

Details Algorithms for Implicit Hitting Set Problems Algorithms for Implicit Hitting Set Problems

2011-02-07

arxiv.org/abs/1102.1472v1

Computer Science

Data Structures and Algorithms

Scientific paper

A hitting set for a collection of sets is a set that has a non-empty intersection with each set in the collection; the hitting set problem is to find a hitting set of minimum cardinality. Motivated by instances of the hitting set problem where the number of sets to be hit is large, we introduce the notion of implicit hitting set problems. In an implicit hitting set problem the collection of sets to be hit is typically too large to list explicitly; instead, an oracle is provided which, given a set H, either determines that H is a hitting set or returns a set that H does not hit. We show a number of examples of classic implicit hitting set problems, and give a generic algorithm for solving such problems optimally. The main contribution of this paper is to show that this framework is valuable in developing approximation algorithms. We illustrate this methodology by presenting a simple on-line algorithm for the minimum feedback vertex set problem on random graphs. In particular our algorithm gives a feedback vertex set of size n-(1/p)\log{np}(1-o(1)) with probability at least 3/4 for the random graph G_{n,p} (the smallest feedback vertex set is of size n-(2/p)\log{np}(1+o(1))). We also consider a planted model for the feedback vertex set in directed random graphs. Here we show that a hitting set for a polynomial-sized subset of cycles is a hitting set for the planted random graph and this allows us to exactly recover the planted feedback vertex set.

Affiliated with

Also associated with

No associations

Rating

Algorithms for Implicit Hitting Set Problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Algorithms for Implicit Hitting Set Problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Algorithms for Implicit Hitting Set Problems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-501825