Benchmark Problems for Totally Unimodular Set System Auction

Abstract

We consider a generalization of the $k$-flow set system auction where the set to be procured by a customer corresponds to a feasible solution to a linear programming problem where the coefficient matrix and right-hand-side together constitute a totally unimodular matrix. Our results generalize and strengthen bounds identified for several benchmarks, which form a crucial component in the study of frugality ratios of truthful auction mechanisms.