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We study coordination mechanisms aiming to minimize the weighted sum of completion times of jobs in the context of selfish scheduling problems. Our goal is to design local policies that achieve a good price of anarchy in the resulting equilibria for unrelated machine scheduling. To obtain these approximation bounds, we introduce a new technique that while… (More)

We consider a priority-based selfish routing model, where agents may have different priorities on a link. An agent with a higher priority on a link can traverse it with a smaller delay or cost than an agent with lower priority. This general framework can be used to model a number of different problems. The structural properties that lead to inefficiencies… (More)

We consider the following network design problem. We are given an undirected graph G=(V,E) with edges costs c(e) and a set of terminal nodes W. A <i>hose</i> demand matrix for W is any symmetric matrix [D<sub>ij</sub>] such that for each i, ∑ j ≠ i D<sub>ij</sub> ≤ 1. We must compute the minimum cost edge capacities that are able to… (More)

Until recently, LP relaxations have only played a very limited role in the design of approximation algorithms for the Steiner tree problem. In particular, no (efficiently solvable) Steiner tree relaxation was known to have an integrality gap bounded away from 2, before Byrka et al. [3] showed an upper bound of ~1.55 of a hypergraphic LP relaxation and… (More)

Two-player win-lose games have a simple directed graph representation. Exploiting this, we develop graph theoretic techniques for finding Nash equilibria in such games. In particular, we give a polynomial time algorithm for finding a Nash equilibrium in a two-player win-lose game whose graph representation is planar.

Consider the robust network design problem of finding a minimum cost network with enough capacity to route all traffic demand matrices in a given polytope. We investigate the impact of different routing models in this robust setting: in particular, we compare oblivious routing, where the routing between each terminal pair must be fixed in advance, to… (More)

Pipage rounding is a dependent random sampling technique that has several interesting properties and diverse applications. One property that has been particularly useful is negative correlation of the resulting vector. Unfortunately negative correlation has its limitations, and there are some further desirable properties that do not seem to follow from… (More)

We consider robust network design problems where the set of feasible demands may be given by an arbitrary polytope or convex body more generally. This model, introduced by Ben-Ameur and Kerivin [2], generalizes the well studied virtual private network (VPN) problem. Most research in this area has focused on finding constant factor approximations for… (More)