An Optimal Truthful Mechanism for the Online Weighted Bipartite Matching Problem

Data dell'evento: 
Venerdì, 12 Ottobre, 2018 - 14:00
Luogo: 
Aula Magna DIAG, via Ariosto 25
Speaker: 
Rebecca Reiffenhauser (RWTH Aachen)
Abstract

We present an optimal, e-competitive truthful mechanism for the weighted bipartite matching problem.  We consider its online version where the  first vertex set is known beforehand, but vertices of the second set appear one after another in random order (secretary model). Vertices of the first set are interpreted as items, and those of the second set as bidders. On arrival, each bidder vertex reveals the weights of all adjacent edges and the algorithm has to decide which of those to add to the matching.

It has been shown that the upper and lower bound of e for the original secretary problem extends to various other problems even with rich combinatorial structure, one of them being weighted bipartite matching. But truthful mechanisms so far fall short of reasonable competitive ratios once respective algorithms deviate from the original, simple threshold form. The best known mechanism for weighted bipartite matching offers only a ratio logarithmic in the number of online vertices. We close this gap, showing that truthfulness does not impose any additional bounds.

 

Contatto: 
Stefano Leonardi (leonardi@diag.uniroma1.it)