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Matroids and integrality gaps for hypergraphic steiner tree relaxations
TLDR
We take a fresh look at hypergraphic LP relaxations for the Steiner tree problem---one that heavily exploits methods and results from the theory of matroids and submodular functions---which leads to stronger integrality gaps, faster algorithms, and a variety of structural insights of independent interest. Expand
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A Priority-Based Model of Routing
TLDR
We consider a priority-based selfish routing model where agents may have different priorities on a link. Expand
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A Polynomial Time Algorithm for Finding Nash Equilibria in Planar Win-Lose Games
TLDR
We give a polynomial time algorithm for finding a Nash equilibrium in a two-player win-lose game whose graph representation is planar. Expand
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The Price of Anarchy and a Priority-Based Model of Routing
The price of anarchy, a concept introduced by Koutsoupias and Papadimitriou [9], is the main topic of this thesis. It is a measure of the loss of efficiency that occurs when there is no centralExpand
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On explosions in heavy-tailed branching random walks
Consider a branching random walk on R, with offspring distribution Z and nonnegative displacement distribution W. We say that explosion occurs if an infinite number of particles may be found within aExpand
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Inner product spaces for MinSum coordination mechanisms
TLDR
We study coordination mechanisms aiming to minimize the weighted sum of completion times of jobs in the context of selfish scheduling problems. Expand
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Long Term Behavior of Dynamic Equilibria in Fluid Queuing Networks
TLDR
We show that, under a natural condition on the queuing capacity, a dynamic equilibrium reaches a steady state (after which queue lengths remain constant) in finite time. Expand
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The VPN Conjecture Is True
We consider the following network design problem. We are given an undirected graph <i>G</i> = (<i>V</i>,<i>E</i>) with edge costs <i>c</i>(<i>e</i>) and a set of terminal nodes <i>W</i> ⊆ <i>V</i>. AExpand
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On the equivalence of the bidirected and hypergraphic relaxations for Steiner tree
TLDR
The bottleneck of the currently best $$(\ln (4)+{\varepsilon })$$(ln(4)+ε)-approximation algorithm for the NP-hard Steiner tree problem is the solution of its large, so called hypergraphic, linear programming relaxation (HYP). Expand
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Pipage Rounding, Pessimistic Estimators and Matrix Concentration
TLDR
We introduce a simple but useful technique called concavity of pessimistic estimators that allows us to show concentration of submodular functions and concentration of matrix sums under pipage rounding. Expand
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