The following game is played on a weighted graph: Alice selects a matching M and
Bob selects a number k. Alice’s payoff is the ratio of the weight of the k heaviest edges
of M to the maximum weight of a matching of size at most k. If M guarantees a payoff
of at least α then it is called α-robust. Hassin and Rubinstein [7] gave an algorithm
that returns a 1/
√
2-robust matching, which is best possible.
We show that Alice can improve her payoff to 1/ ln(4) by playing a randomized
strategy. This result extends to a very general class of independence systems that
includes matroid intersection, b-matchings, and strong 2-exchange systems. It also
implies an improved approximation factor for a stochastic optimization variant known
as the maximum priority matching problem and translates to an asymptotic robustness
guarantee for deterministic matchings, in which Bob can only select numbers larger than
a given constant. Moreover, we give a new LP-based proof of Hassin and Rubinstein’s
bound.
Lenguage
dc.language.iso
en
Publisher
dc.publisher
INFORMS Inst.for Operations Res.and the Management Sciences