4 research outputs found
A Local Search Algorithm for the Min-Sum Submodular Cover Problem
We consider the problem of solving the Min-Sum Submodular Cover problem using
local search. The Min-Sum Submodular Cover problem generalizes the NP-complete
Min-Sum Set Cover problem, replacing the input set cover instance with a
monotone submodular set function. A simple greedy algorithm achieves an
approximation factor of 4, which is tight unless P=NP [Streeter and Golovin,
NeurIPS, 2008]. We complement the greedy algorithm with analysis of a local
search algorithm. Building on work of Munagala et al. [ICDT, 2005], we show
that, using simple initialization, a straightforward local search algorithm
achieves a -approximate solution in time
, provided that the monotone submodular set function is
also second-order supermodular. Second-order supermodularity has been shown to
hold for a number of submodular functions of practical interest, including
functions associated with set cover, matching, and facility location. We
present experiments on two special cases of Min-Sum Submodular Cover and find
that the local search algorithm can outperform the greedy algorithm on small
data sets
LIPIcs, Volume 248, ISAAC 2022, Complete Volume
LIPIcs, Volume 248, ISAAC 2022, Complete Volum