Distributed multiple relay selection by an auction mechanism

In this article, we study distributed relay selection methods assuming a dual-hop Decode-and-Forward (DF) relaying protocol. We assume Uplink (UL) phase in a cellular network where multiple source nodes seek the assistance of candidate relay nodes for message delivery. Due to complexity considerations, we consider that each relay node belongs to the relay set of at most one source node. Through local information exchanges, source nodes and relay nodes can learn the existence of nodes and related Channel State Information (CSI) in their neighborhood. We formalize a relay subset selection problem (RSSP) in which each source node that wishes to transmit determines a ranking of different subsets of relays and the problem is to decide how best to assign relays to source nodes in order to maximize the total transmission capacity of all sources. We first reduce the relay subset selection problem to the well known weighted independent set problem, which is NP-hard. This reduction enables a greedy centralized approximation algorithm. We also present a distributed auctioning algorithm which only requires direct communication between source nodes and those relays that are useful to the source nodes. No communication is required between the relay nodes. Numerical simulations were performed to compare the distributed auction method against the centralized greedy approximation algorithm.