Kirchhoff's Circuit Law Applications to Graph Simplification in Search Problems

TL;DR

This paper introduces a novel graph analysis method using electric potential concepts and Kirchhoff's Law to simplify graphs for search problems, enhancing path-finding efficiency.

Contribution

It presents a new graph simplification technique based on electrical potential analysis and Kirchhoff's Law, enabling more efficient path-finding in weighted graphs.

Findings

Potential-based graph estimation improves search efficiency

Graph simplification reduces computational complexity

Electrical circuit analogy enhances path-finding algorithms

Abstract

This paper proposes a new analysis of graph using the concept of electric potential, and also proposes a graph simplification method based on this analysis. Suppose that each node in the weighted-graph has its respective potential value. Furthermore, suppose that the start and terminal nodes in graphs have maximum and zero potentials, respectively. When we let the level of each node be defined as the minimum number of edges/hops from the start node to the node, the proper potential of each level can be estimated based on geometric proportionality relationship. Based on the estimated potential for each level, we can re-design the graph for path-finding problems to be the electrical circuits, thus Kirchhoff's Circuit Law can be directed applicable for simplifying the graph for path-finding problems.