Overlays with preferences: Approximation algorithms for matching with preference lists

Rapport, 2009

In envisioning the future of networking, a key relevant goal is overlays where peers establish connections with other peers based on some suitability metric related to e.g. the node’s distance, interests, recommendations, transaction history or available resources. Each node may choose individually an appropriate metric and try to connect or be matched with the available peers that considers best. We present a distributed algorithm for matching peers with preferences that enables peers to coordinate while forming mutually beneficial connections according to their individual preferences. We show that peers following our method can collectively achieve a guaranteed level of quality for their requested connections. Our approach suggests an optimization version of the generalized stable roommates problem, aiming at maximizing the satisfaction in the network; we then show a solution with guaranteed approximation, via many-to-many maximum weighted matchings. As such, the algorithm can be of independent interest as well, outside the context of overlays with preferences.