A note on the generalized min-sum set cover problem

TL;DR

This paper improves the approximation guarantee for the generalized min-sum set cover problem from 485 to 28 by adapting existing algorithms and employing concepts from alpha-point scheduling.

Contribution

The authors significantly enhance the approximation ratio for the problem by modifying previous algorithms and analysis techniques, achieving an order of magnitude improvement.

Findings

Achieved a 28-approximation algorithm for the problem.

Demonstrated the effectiveness of alpha-point scheduling in this context.

Improved upon the previous 485-approximation guarantee.

Abstract

In this paper, we consider the generalized min-sum set cover problem, introduced by Azar, Gamzu, and Yin. Bansal, Gupta, and Krishnaswamy give a 485-approximation algorithm for the problem. We are able to alter their algorithm and analysis to obtain a 28-approximation algorithm, improving the performance guarantee by an order of magnitude. We use concepts from $\alpha$-point scheduling to obtain our improvements.