Approximation Algorithms for Covering and Packing Problems on Paths

TL;DR

This paper develops approximation algorithms for NP-hard routing and scheduling problems, specifically focusing on unsplittable flow and resource allocation, to efficiently produce near-optimal solutions for large instances.

Contribution

It introduces new approximation algorithms and analyses for the Unsplittable Flow Problem and Resource Allocation in Job Scheduling, addressing their complexity on paths.

Findings

Algorithms achieve near-optimal solutions efficiently

Improved approximation ratios for key problems

Applicable to large-scale routing and scheduling instances

Abstract

Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances, which are fast and yet come close to the optimal value. In this thesis, we study the design and analysis of approximation algorithms for such problems. We focus on two important class of problems. The first is the Unsplittable Flow Problem and some of its variants and the second is the Resource Allocation for Job Scheduling Problem and some of its variants. The first is a packing problem, whereas the second is a covering problem.