Self-stabilizing Philosophers with Generic Conflicts

Abstract

We generalize the classic dining philosophers problem to separate the conflict and communication neighbors of each process. Communication neighbors may directly exchange information while conflict neighbors compete for the access to the exclusive critical section of code. This generalization is motivated by a number of practical problems in distributed systems including problems in wireless sensor networks. We present a self-stabilizing deterministic algorithm — $\mathcal{KDP}$ that solves a restricted version of the generalized problem where the conflict set for each process is limited to its k-hop neighborhood. Our algorithm is terminating. We formally prove $\mathcal{KDP}$ correct and evaluate its performance. We then extend $\mathcal{KDP}$ to handle fully generalized problem. We further extend it to handle a similarly generalized drinking philosophers problem. We describe how $\mathcal{KDP}$ can be implemented in wireless sensor networks and demonstrate that this implementation does not jeopardize its correctness or termination properties.