Improved approximation algorithms for the Min-Max Selecting Items problem

We give a simple deterministic O(log K/ log log K) approximation algorithm for the Min-Max Selecting Items problem, where K is the number of scenarios. While our main goal is simplicity, this result also improves over the previous best approximation ratio of O(log K) due to Kasperski, Kurpisz, and Zielinski (2013) [4]. Despite using the method of pessimistic estimators, the algorithm has a polynomial runtime also in the RAM model of computation. We also show that the LP formulation for this problem by Kasperski and Zielinski (2009) [6], which is the basis for the previous work and ours, has an integrality gap of at least Omega(log K / log log K). (C) 2013 Elsevier B.V. All rights reserved.