The Power of Local Search: Maximum Coverage over a Matroid

Yuval Filmus & Justin Ward
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...