Probabilistic construction of deterministic algorithms: approximating packing integer programs
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Algorithmic Chernoff-Hoeffding inequalities in integer programming
Random Structures & Algorithms
Distributions on Level-Sets with Applications to Approximation Algorithms
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Generating randomized roundings with cardinality constraints and derandomizations
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Roundings respecting hard constraints
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Approximating the min-max (regret) selecting items problem
Information Processing Letters
| Hi-index | 0.89 |
We give a simple deterministic O(logK/loglogK) 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(logK) 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 @W(logK/loglogK).