Download the full-sized PDF of Approximation techniques for unsplittable flow and traveling salesmen problemsDownload the full-sized PDF



Permanent link (DOI):


Export to: EndNote  |  Zotero  |  Mendeley


This file is in the following communities:

Graduate Studies and Research, Faculty of


This file is in the following collections:

Theses and Dissertations

Approximation techniques for unsplittable flow and traveling salesmen problems Open Access


Other title
Combinatorial Optimization
Approximation Algorithms
Type of item
Degree grantor
University of Alberta
Author or creator
Friggstad, Zachary
Supervisor and department
Salavatipour, Mohammad (Computing Science)
Examining committee member and department
Shirvani, Mazi (Mathematics)
Gupta, Anupam (Computer Science)
Hayward, Ryan (Computing Science)
Hoover, Jim (Computing Science)
Department of Computing Science

Date accepted
Graduation date
Doctor of Philosophy
Degree level
In this thesis, we present a variety of approximation algorithms for the Unsplittable Flow on Paths problem and some Traveling Salesman problems. The main contribution to the Unsplittable Flow on Paths problem is a logarithmic approximation algorithm which is the first non-trivial approximation for general instances of the problem. The algorithm works by using dynamic programming to approximate solutions on instances that cannot be approximated well through linear programming techniques. A generalization of this algorithm provides a constant-factor approximation in sub-exponential time. We also demonstrate that certain sparse instances can be approximated within a constant factor. The Traveling Salesman problems we consider mostly deal with finding paths in asymmetric metrics, though we do consider others. First, we demonstrate that the integrality gap of a natural linear programming relaxation for the Asymmetric Traveling Salesman Path problem is O(log n) where n is the number of nodes in the metric. We then further generalize the problem and study the problem of finding up to k paths with minimum total distance in an asymmetric metric such that the union of these paths spans all nodes. In the case that all paths are required to share a common start and end node, we demonstrate a family of bicriteria approximation algorithms that find a little more than k paths whose total cost is within some bounded ratio of the optimum value of a linear programming relaxation. These results are extended to many other variants of finding multiple paths in metrics whose union spans all nodes. However, we show that the most general case when each path has its own start and end location specified in advance cannot be approximated within any bounded ratio unless P = NP. Finally, we formulate a linear programming relaxation for the Minimum Latency problem in asymmetric metrics and prove that the integrality gap of this relaxation is O(log n). This critically relies on the fact that the integrality gap of a natural linear programming relaxation for the Asymmetric Traveling Salesman Path problem is O(log n). This is the first sub-polynomial approximation algorithm for the problem.
License granted by Zachary Friggstad ( on 2011-08-26T14:41:55Z (GMT): Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of the above terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication

File Details

Date Uploaded
Date Modified
Audit Status
Audits have not yet been run on this file.
File format: pdf (Portable Document Format)
Mime type: application/pdf
File size: 1130785
Last modified: 2015:10:12 11:38:12-06:00
Filename: phd.pdf
Original checksum: acfd66623f3777f51c1c07058effbfbc
Well formed: true
Valid: true
Status message: Too many fonts to report; some fonts omitted. Total fonts = 1324
File title: phd.dvi
Page count: 131
Activity of users you follow
User Activity Date