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

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 central… Expand

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 a… Expand

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

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>. A… Expand

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

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