Scheduling Resources for Executing a Partial Set of Jobs

TL;DR

This paper addresses resource scheduling for executing a subset of jobs with interval constraints, proposing approximation algorithms for partial covering and prize collecting versions to minimize costs and penalties.

Contribution

It introduces approximation algorithms for two variants of resource scheduling problems involving interval jobs and resources, with proven performance bounds.

Findings

O(log n)-factor approximation for partial covering problem

Constant factor approximation for prize collecting problem

Effective algorithms for cost-efficient resource allocation

Abstract

In this paper, we consider the problem of choosing a minimum cost set of resources for executing a specified set of jobs. Each input job is an interval, determined by its start-time and end-time. Each resource is also an interval determined by its start-time and end-time; moreover, every resource has a capacity and a cost associated with it. We consider two versions of this problem. In the partial covering version, we are also given as input a number k, specifying the number of jobs that must be performed. The goal is to choose k jobs and find a minimum cost set of resources to perform the chosen k jobs (at any point of time the capacity of the chosen set of resources should be sufficient to execute the jobs active at that time). We present an O(log n)-factor approximation algorithm for this problem. We also consider the prize collecting version, wherein every job also has a penalty associated with it. The feasible solution consists of a subset of the jobs, and a set of resources, to perform the chosen subset of jobs. The goal is to find a feasible solution that minimizes the sum of the costs of the selected resources and the penalties of the jobs that are not selected. We present a constant factor approximation algorithm for this problem