Neil Olver

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

We consider a priority-based selfish routing model where agents may have different priorities on a link. Expand

We give a polynomial time algorithm for finding a Nash equilibrium in a two-player win-lose game whose graph representation is planar. Expand

We study coordination mechanisms aiming to minimize the weighted sum of completion times of jobs in the context of selfish scheduling problems. 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

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