On the price of stability for undirected network design

George Christodoulou*, Christine Chung, Katrina Ligett, Evangelia Pyrga, Rob Van Stee

*Corresponding author for this work

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

26 Scopus citations


We continue the study of the effects of selfish behavior in the network design problem. We provide new bounds for the price of stability for network design with fair cost allocation for undirected graphs. We consider the most general case, for which the best known upper bound is the Harmonic number H n, where n is the number of agents, and the best previously known lower bound is 12/7 ≈ 1.778. We present a nontrivial lower bound of 42/23 ≈ 1.8261. Furthermore, we show that for two players, the price of stability is exactly 4/3, while for three players it is at least 74/48 ≈ 1.542 and at most 1.65. These are the first improvements on the bound of Hn for general networks. In particular, this demonstrates a separation between the price of stability on undirected graphs and that on directed graphs, where Hn is tight. Previously, such a gap was only known for the cases where all players have a shared source, and for weighted players.

Original languageAmerican English
Title of host publicationApproximation and Online Algorithms - 7th International Workshop, WAOA 2009, Revised Papers
Number of pages12
StatePublished - 2009
Externally publishedYes
Event7th Workshop on Approximation and Online Algorithms, WAOA 2009 - Copenhagen, Denmark
Duration: 10 Sep 200911 Sep 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5893 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference7th Workshop on Approximation and Online Algorithms, WAOA 2009


Dive into the research topics of 'On the price of stability for undirected network design'. Together they form a unique fingerprint.

Cite this