BLMA: A Blind Matching Algorithm With Application to Cognitive Radio Networks

Abstract

We consider a two-sided matching problem with a defined notion of pairwise stability. We propose a distributed blind matching algorithm (BLMA) to solve the problem. We prove the solution produced by BLMA will converge to an -pairwise stable outcome with probability one. We then consider a matching problem in cognitive radio networks. Secondary users (SUs) are allowed access time to the spectrum belonging to the primary users (PUs) provided that they relay primary messages. We propose a realization of the BLMA to produce an -pairwise stable solution assuming quasi-convex and quasiconcave utilities. In the case of more general utility forms, we show another BLMA realization to provide a stable solution. Furthermore, we propose negotiation mechanism to bias the algorithm towards one side of the market. We use this mechanism to protect the exclusive rights of the PUs to the spectrum. In all such implementations of the BLMA, we impose a limited information exchange in the network so that agents can only calculate their own utilities, but no information is available about the utilities of any other users in the network.

Many-to-one blind matching for device-to-device communications

“…3 The new aspiration levels a k (t+1) and b kℓ (t+1), as well as the matching, µ t+1 , are updated accordingly.…”

“…However, we proceed as follows: First, we make an analogy between the current many-to-one problem and the one-to-one matching problem in [3]. Once we establish this analogy, we proceed by summarizing the claims that were used to establish convergence in the one-to-one case.…”

“…Once we establish this analogy, we proceed by summarizing the claims that were used to establish convergence in the one-to-one case. The full proof for the one-to-one case can be found in [3].…”

“…Several works in the literature, e.g. [2] and our recent work [3], take important steps towards eliminating the need for a coordinator in a matching market. The algorithms in these works are characterized by a simple learning process and random encounters between agents on the two sides of the market.…”

“…In this paper, we extend the model of [3] to the many-to-one case. The extension is not trivial since ‡ The research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST).…”