Peer to peer (P2P) systems have moved from application specific architectures to a generic service oriented design philosophy. This raised 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 problem consists of partitioning a P2P network into $k$ groups (slices) of a given portion of the network nodes that share similar resource values. As the network is large and dynamic this partitioning is continuously updated without any node knowing the network size.
In this paper, we propose the first algorithm to solve the slicing problem. We introduce the metric of slice disorder and show that the existing ordering algorithm cannot nullify this disorder. We propose a new algorithm that speeds up the existing ordering algorithm but that suffers from the same inaccuracy. Then, we propose another algorithm based on ranking that is provably convergent under reasonable assumptions. In particular, we notice experimentally that ordering algorithms suffer from resource-correlated churn while the ranking algorithm can cope with it. These algorithms are proved viable theoretically and experimentally.