Sharing Supermodular Costs

We study cooperative games with supermodular costs. We show that supermodular costs arise in a variety of situations: in particular, we show that the problem of minimizing a linear function over a supermodular polyhedron–a problem that often arises in combinatorial optimization–has supermodular optimal costs. In addition, we examine the computational complexity of the least core … Read more

Revisiting the Greedy Approach to Submodular Set Function Maximization

We consider the problem of maximizing a nondecreasing submodular set function over various constraint structures. Specifically, we explore the performance of the greedy algorithm, and a related variant, the locally greedy algorithm in solving submodular function maximization problems. Most classic results on the greedy algorithm and its variant assume the existence of an optimal polynomial-time … Read more

Efficiency and Fairness of System-Optimal Routing with User Constraints

We study the route-guidance system proposed by Jahn, Möhring, Schulz and Stier-Moses (2004) from a theoretical perspective. This approach computes a traffic pattern that minimizes the total travel time subject to user constraints, which ensure that routes suggested to users are not much longer than shortest paths. We show that when distances are measured with … Read more

On-Line Scheduling to Minimize Average Completion Time Revisited

We consider the scheduling problem of minimizing the average weighted completion time on identical parallel machines when jobs are arriving over time. For both the preemptive and the nonpreemptive setting, we show that straightforward extensions of Smith’s ratio rule yield smaller competitive ratios than the previously best-known deterministic on-line algorithms. Citation Working Paper 4435-03, Sloan … Read more