Counting all possible simple paths using Artificial Cell division mechanism for directed acyclic graphs

Abstract

Counting all possible paths between two nodes is always a challenging job. The work present a multi-agent counting model based upon the concept of biological cell division method. Artificial Cells, which are inspired by biological living cells works as the key feature in counting process, are governed by artificial rules and abilities. In the proposed work a novel algorithm is used to find the number of simple paths between two nodes of a directed acyclic graph. The algorithm is built upon the proposed model of multiple agents which works simultaneously instead of single agent to find the solution by discarding unsuccessful and repetitive traverses. A detail theoretical and experimental analysis is provided in evidence of ingenuity of the proposed algorithm.