Document Open Access Logo

The Power of Local Search: Maximum Coverage over a Matroid

Authors Yuval Filmus, Justin Ward

Thumbnail PDF


  • Filesize: 0.51 MB
  • 12 pages

Document Identifiers

Author Details

Yuval Filmus
Justin Ward

Cite AsGet BibTex

Yuval Filmus and Justin Ward. The Power of Local Search: Maximum Coverage over a Matroid. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 601-612, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)


We present an optimal, combinatorial 1-1/e approximation algorithm for Maximum Coverage over a matroid constraint, using non-oblivious local search. Calinescu, Chekuri, Pál and Vondrák have given an optimal 1-1/e approximation algorithm for the more general problem of monotone submodular maximization over a matroid constraint. The advantage of our algorithm is that it is entirely combinatorial, and in many circumstances also faster, as well as conceptually simpler. Following previous work on satisfiability problems by Alimonti, as well as by Khanna, Motwani, Sudan and Vazirani, our local search algorithm is *non-oblivious*. That is, our algorithm uses an auxiliary linear objective function to evaluate solutions. This function gives more weight to elements covered multiple times. We show that the locality ratio of the resulting local search procedure is at least 1-1/e. Our local search procedure only considers improvements of size 1. In contrast, we show that oblivious local search, guided only by the problem's objective function, achieves an approximation ratio of only (n-1)/(2n-1-k) when improvements of size k are considered. In general, our local search algorithm could take an exponential amount of time to converge to an *exact* local optimum. We address this situation by using a combination of *approximate* local search and the same partial enumeration techniques as Calinescu et al., resulting in a clean 1 - 1/e-approximation algorithm running in polynomial time.
  • approximation algorithms; maximum coverage; matroids; local search


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail