Peer to peer (P2P) systems are moving from application specific architectures to a generic service oriented design philosophy. This raises interesting problems in connection with providing useful P2P middleware services capable of dealing with resource assignment and management in a large-scale, heterogeneous and unreliable environment. The slicing service, has been proposed to allow for an automatic partitioning of P2P networks into groups (slices) that represent a controllable amount of some resource and that are also relatively homogeneous with respect to that resource. In this paper we propose two gossip-based algorithms to solve the distributed slicing problem. The first algorithm speeds up an existing algorithm sorting a set of uniform random numbers. The second algorithm statistically approximates the rank of nodes in the ordering. The scalability, efficiency and resilience to dynamics of both algorithms rely on their gossip-based models. These algorithms are proved viable theoretically and experimentally.
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