TY - GEN

T1 - On the price of stability for undirected network design

AU - Christodoulou, George

AU - Chung, Christine

AU - Ligett, Katrina

AU - Pyrga, Evangelia

AU - Van Stee, Rob

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78651226976&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-12450-1_8

DO - 10.1007/978-3-642-12450-1_8

M3 - Conference contribution

AN - SCOPUS:78651226976

SN - 3642124496

SN - 9783642124495

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 86

EP - 97

BT - Approximation and Online Algorithms - 7th International Workshop, WAOA 2009, Revised Papers

T2 - 7th Workshop on Approximation and Online Algorithms, WAOA 2009

Y2 - 10 September 2009 through 11 September 2009

ER -