Linearizing Peer-to-Peer Systems with Oracles

We study distributed linearization or topological sorting in peer-to-peer networks. We define strict and eventual versions of the problem and consider these problems with and without input identifiers that do not exist in the system. None of these problems are solvable in the asynchronous messagepassing systems. We define a collection of oracles and prove which oracle combination is necessary to enable a solution in the message-passing systems for each variant of the linearization problem. We then present a linearization algorithm. We prove that this algorithm and a specific combination of oracles solves each stated variant of the linearization problem. Corresponding author: Mikhail Nesterenko, Department of Computer Science, Kent State University, Kent, OH, 44242, USA, fax: +1 (330) 672-0737, email: [email protected]