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The design of scalable and robust overlay topologies has been a main researchsubject since the very origins of peer-to-peer (p2p) computing. Today, thecorresponding optimization tradeoffs are fairly well-understood, at least inthe static case and from a worst-case perspective.  This paper revisits the peer-to-peer topology design problem from aself-organization perspective. We initiate the study of topologies which areoptimized to serve the communication demand, or even self-adjusting as demandchanges. The appeal of this new paradigm lies in the opportunity to be able togo beyond the lower bounds and limitations imposed by a static,communication-oblivious, topology. For example, the goal of having shortrouting paths (in terms of hop count) does no longer conflict with therequirement of having low peer degrees.  We propose a simple overlay topology Obst(k) which is composed of k (rootedand directed) Binary Search Trees (BSTs), where k is a parameter. We firstprove some fundamental bounds on what can and cannot be achieved optimizing atopology towards a static communication pattern (a static Obst(k)). Inparticular, we show that the number of BSTs that constitute the overlay canhave a large impact on the routing costs, and that a single additional BST mayreduce the amortized communication costs from Omega(log(n)) to O(1), where n isthe number of peers. Subsequently, we discuss a natural self-adjustingextension of Obst(k), in which frequently communicating partners are "splayedtogether".

OBST: A Self-Adjusting Peer-to-Peer Overlay Based on Multiple BSTs