Network improvement for equilibrium routing

Umang Bhaskar, Katrina Ligett, Leonard J. Schulman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations


In routing games, agents pick routes through a network to minimize their own delay. A primary concern for the network designer in routing games is the average agent delay at equilibrium. A number of methods to control this average delay have received substantial attention, including network tolls, Stackelberg routing, and edge removal. A related approach with arguably greater practical relevance is that of making investments in improvements to the edges of the network, so that, for a given investment budget, the average delay at equilibrium in the improved network is minimized. This problem has received considerable attention in the literature on transportation research. We study a model for this problem introduced in transportation research literature, and present both hardness results and algorithms that obtain tight performance guarantees. In general graphs, we show that a simple algorithm obtains a 4/3-approximation for affine delay functions and an O(p/logp)-approximation for polynomial delay functions of degree p. For affine delays, we show that it is NP-hard to improve upon the 4/3 approximation. Motivated by the practical relevance of the problem, we consider restricted topologies to obtain better bounds. In series-parallel graphs, we show that the problem is still NP-hard. However, we show that there is an FPTAS in this case. Finally, for graphs consisting of parallel paths, we show that an optimal allocation can be obtained in polynomial time.

Original languageAmerican English
Title of host publicationInteger Programming and Combinatorial Optimization - 17th International Conference, IPCO 2014, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783319075563
StatePublished - 2014
Externally publishedYes
Event17th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2014 - Bonn, Germany
Duration: 23 Jun 201425 Jun 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8494 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference17th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2014

Bibliographical note

Funding Information:
Supported in part by NSF Awards 1038578 and 1319745, an NSF CAREER Award (1254169), the Charles Lee Powell Foundation, and a Microsoft Research Faculty Fellowship.


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