Accueil

Graph Coalition Structure Generation.

Thu, 02/10/2011 - 16:01 — SomNambul
Authors: Thomas D. Voice, Maria Polukarov, Nicholas R. Jennings
Subjects: Data Structures and Algorithms
link: http://arxiv.org/abs/1102.1747
Abstract

We give the first analysis of the computational complexity of {\it coalition
structure generation over graphs}. Given an undirected graph $G=(N,E)$ and a
valuation function $v:2^N\rightarrow\RR$ over the subsets of nodes, the problem
is to find a partition of $N$ into connected subsets, that maximises the sum of
the components' values. This problem is generally NP--complete; in particular,
it is hard for a defined class of valuation functions which are {\it
independent of disconnected members}---that is, two nodes have no effect on
each other's marginal contribution to their vertex separator. Nonetheless, for
all such functions we provide bounds on the complexity of coalition structure
generation over general and minor free graphs. Our proof is constructive and
yields algorithms for solving corresponding instances of the problem.
Furthermore, we derive polynomial time bounds for acyclic, $K_{2,3}$ and $K_4$
minor free graphs. However, as we show, the problem remains NP--complete for
planar graphs, and hence, for any $K_k$ minor free graphs where $k\geq 5$.
Moreover, our hardness result holds for a particular subclass of valuation
functions, termed {\it edge sum}, where the value of each subset of nodes is
simply determined by the sum of given weights of the edges in the induced
subgraph.

official bruins jerseys shop

Tue, 07/05/2011 - 07:12 — sa

Tim Thomas Jersey

Milan Lucic Jersey

Bobby Orr Jersey

Marc Savard Jersey

Zdeno Chara Jersey

Blake Wheeler Stanley Cup Jersey
Bobby Orr Stanley Cup Jersey
Cam Neely Stanley Cup Jersey
David Krejci Stanley Cup Jersey
Dennis Wideman Stanley Cup Jersey
Marc Savard Stanley Cup Jersey
Marco Sturm Stanley Cup Jersey
Milan Lucic Stanley Cup Jersey
Horton Nathan Stanley Cup Jersey
Patrice Bergeron Stanley Cup Jersey
Phil Esposito Stanley Cup Jersey
Phil Kessel Stanley Cup Jersey
Ray Bourque Stanley Cup Jersey
Tim Thomas Stanley Cup Jersey
Tyler Seguin Stanley Cup Jersey
Zdeno Chara Stanley Cup Jersey

Blake Wheeler Jersey
Cam Neely Jersey
David Krejci Jersey
Dennis Wideman Jersey
Horton Nathan Jersey
Marco Sturm Jersey
Nathan Horton Jersey
Patrice Bergeron Jersey
Phil Esposito Jersey
Phil Kessel Jersey
Ray Bourque Jersey
Tyler Seguin Jersey

NFL Super Bowl Authentic Jerseys
Clay Matthews Super Bowl Jersey

Aaron Rodgers Super Bowl Jersey

Charles Woodson Super Bowl Jersey

Donald Driver Super Bowl Jersey

Jermichael Finley Super Bowl Jersey

A.j.hawk Jersey
Aaron Kampman Jersey
Aaron Rodgerrs Jersey
Al Harris Jersey
B.j. Rajii Jersey
Brett Favre Jersey
Charles Woodsons Jersey
Clay Matthew Jersey
Donald Driver Jersey
Greg Jennings Jersey
Jermichael Finley Jersey
Michael Crabtree Jersey
Paul Hornung Jersey
Reggie White Jersey
Ryan Grant Jersey
William Henderson Jersey

NFL Bears Authentic Jerseys

Brian Urlacher Jersey

Dick Butkus Jersey

Mike Ditka Jersey

Walter Payton Jersey

163

Sat, 04/28/2012 - 06:09 — lishaohong163

"My career was sac longchamp in the economy," Romney said. "I am convinced that to beat Barack Obama it's louis vuitton borseto take someone sac longchamp pas cher understands the economy in his bones. And I do and borse louis vuitton will beat him with Sac Longchamp Lady understanding."He told those gathered that of thesupport epublicans if they have Sacs Lancel Gland plan to create jobs and improve economy sacs longchamp pliage candidates, he has "the best chance and perhaps Longchamp Classic chance at actually replacing Barack Obama as president of the United States.HAHA "My was sac louis vuitton in the economy," Romney said. "I am convinced that to beat Barack louis vuitton pas cher it's going to take someone who understands the economy in Louis Vuitton Sac Toile bones. vuitton pas cher do and I will Lancel Portefeuille him with that understanding."Romney's Illinois sac louis vuitton chairman summed up what's on he line come Election Day."This is all Louis Vuitton Autre 1,144 people in standing up and saying we want Mitt Romney to be our nominee," said Illinois Treasurer Dan Rutherford."For Mitt gucci borse to say he's the borse gucci heavyweight — gucci sito ufficiale is a man who doesn't understand conservative principles. Conservatives louis vuitton borse
go out there and say, 'I'm going to create jobs and I'm going to gucci outlet the economy, I'm going to manage the economy. Just the opposite. What we believe in is hogan scarpe government out of the way, creating opportunity and let the private sector do these things,"said Santorum, who was campaigning Sunday in gucci borse 2012 which holds its primary Saturday.