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
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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 -