Approximation Algorithms for Disjoint Paths and Related Routing and Packing Problems

Approximation Algorithms for Disjoint Paths and Related Routing and Packing Problems

Given a network and a set of connection requests on it, we consider the maximum edge-disjoint paths and related generalizations and routing problems that arise in assigning paths for these requests. We present improved approximation algorithms and/or integrality gaps for all problems considered; the central theme of this work is the underlying multi-commodity flow relaxation. Applications of th...

Approximation Algorithms for Disjoint Paths

Approximation Algorithms for Covering and Packing Problems on Paths

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 f...

Approximation Algorithms for 2-dimensional Packing and Related Scheduling Problems

Main subject of this thesis are approximation algorithms for scheduling and packing, two classical geometrical problems in combinatorial optimization. It is divided into three parts. In the first part we consider a generalization of the strip packing problem or geometrical cutting stock problem. In strip packing a given set of rectangles has to be placed into a strip of fixed width and infinite...

Approximation Algorithms for Edge-Disjoint Paths and Unsplittable Flow

In the maximum edge-disjoint paths problem (MEDP) the input consists of a graph and a set of requests (pairs of vertices), and the goal is to connect as many requests as possible along edge-disjoint paths. We give a survey of known results about the complexity and approximability of MEDP and sketch some of the main ideas that have been used to obtain approximation algorithms for the problem. We...