Two 6-approximation Algorithms for the Stochastic Score Classification Problem

TL;DR

This paper introduces two constant-factor approximation algorithms for the stochastic score classification problem with arbitrary costs, improving existing bounds and leveraging information theory insights.

Contribution

It presents two 6-approximation non-adaptive algorithms for the SSClass problem, improving the approximation factor of a previous algorithm from 2(B-1) to 6.

Findings

Both algorithms are 6-approximation non-adaptive solutions.

The first algorithm uses a modified round-robin approach inspired by recent work.

The second algorithm improves the approximation factor from 2(B-1) to 6.

Abstract

We study the arbitrary cost case of the unweighted Stochastic Score Classification (SSClass) problem. We show two constant approximation algorithms and both algorithms are 6-approximation non-adaptive algorithms with respect to the optimal adaptive algorithm. The first algorithm uses a modified round-robin approach among three sequences, which is inspired by a recent result on the unit cost case of the SSClass problem. The second algorithm is originally from the work of Gkenosis et al. In our work, we successfully improve its approximation factor from 2(B-1) to 6. Our analysis heavily uses the relation between computation and verification of functions, which was studied in the information theory literature.