Local Pruning for Information Dissemination for the Idempotent Semiring Algebraic Path Problem

The advent of pervasive mobile devices has created the need for new algorithm design mechanisms for mobile computing platforms. The limited capabilities of these mobile devices have created several interesting problems that do not exist in traditional networks. These limitations have made communication an expensive commodity for distributed algorithms. In this paper, we consider the communicationintensive information broadcast problem for distributed computation. In distributed computing, several different computations can be viewed from a common viewpoint as instances of the Semiring Algebraic Path Problem (SAPP) on graphs. We first show that many algorithms broadcast information to enable recomputation of the SAPP on a dynamic graph. We then develop a general theory of local pruning for the SAPP problem for idempotent semirings. We motivate the pruning problem as a multi-agent optimization problem, where the agents try to limit the amount of information they broadcast while ensuring that the broadcast is sufficient to recompute the SAPP. The main contribution of this paper is establishing that this local pruning scheme chooses sufficient information to compute the original SAPP. For the dynamic SAPP, the information broadcast required to recompute the SAPP is reduced by the pruning. We also show that our solution corresponds to a local Gauss elimination solution over an extended semiring.