Edge- and Node-Disjoint Paths in P Systems

TL;DR

This paper develops distributed P system algorithms for discovering maximum edge- and node-disjoint paths in networks, starting from no initial structural information and incorporating node capacity constraints.

Contribution

It introduces native P system implementations of fundamental graph problems, extending standard algorithms to a fully distributed setting with capacity constraints.

Findings

Successfully implemented distributed algorithms for maximum disjoint paths

Extended P system rules to enforce node capacity constraints

Demonstrated applicability to topological network discovery

Abstract

In this paper, we continue our development of algorithms used for topological network discovery. We present native P system versions of two fundamental problems in graph theory: finding the maximum number of edge- and node-disjoint paths between a source node and target node. We start from the standard depth-first-search maximum flow algorithms, but our approach is totally distributed, when initially no structural information is available and each P system cell has to even learn its immediate neighbors. For the node-disjoint version, our P system rules are designed to enforce node weight capacities (of one), in addition to edge capacities (of one), which are not readily available in the standard network flow algorithms.