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          Institute: MPI für Informatik     Collection: Algorithms and Complexity Group     Display Documents



ID: 536743.0, MPI für Informatik / Algorithms and Complexity Group
On the price of stability for undirected network design
Authors:Christodoulou, George; Chung, Christine; Ligett, Katrina; Pyrga, Evangelia; van Stee, Rob
Language:English
Publisher:Springer
Place of Publication:Berlin
Date of Publication (YYYY-MM-DD):2010
Title of Proceedings:Approximation and Online Algorithms : 7th International Workshop, WAOA 2009
Start Page:86
End Page:97
Title of Series:Lecture Notes in Computer Science
Place of Conference/Meeting:Copenhagen, Denmark
(Start) Date of Conference/Meeting
 (YYYY-MM-DD):
2009-09-10
End Date of Conference/Meeting 
 (YYYY-MM-DD):
2009-09-11
Audience:Experts Only
Intended Educational Use:No
Abstract / Description: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 $12/7\approx1.778$.

We present a nontrivial lower bound of $42/23\approx1.8261$.
Furthermore,
we show that for two players, the price of stability is exactly $4/3$, while for
three players it is at least $74/48\approx 1.542$ and at most $1.65$.
These are the first improvements on the bound of $H_n$ for general networks.
In particular, this demonstrates a separation between the price of
stability on undirected graphs and that on directed graphs,
Previously, such a gap was only known for the cases where all players
have a shared source, and for weighted players.
Last Change of the Resource (YYYY-MM-DD):2010-12-17
External Publication Status:published
Document Type:Conference-Paper
Communicated by:Kurt Mehlhorn
Affiliations:MPI für Informatik/Algorithms and Complexity Group
Identifiers:LOCALID:C1256428004B93B8-15740B661D36E848C12577F40050BB78-...
DOI:10.1007/978-3-642-12450-1_8
ISBN:9-783642-12449-5
Full Text:
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