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Kirchhoff's Circuit Law Applications to Graph Simplification in Search Problems
arXiv - CS - Discrete Mathematics Pub Date : 2020-09-23 , DOI: arxiv-2009.11675
Jaeho Choi, Joongheon Kim

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.

中文翻译:

基尔霍夫电路定律在搜索问题中图简化的应用

本文利用电位的概念提出了一种新的图形分析方法,并在此基础上提出了一种图形化简方法。假设加权图中的每个节点都有其各自的潜在值。此外,假设图中的起始节点和终止节点分别具有最大和零电位。当我们让每个节点的级别定义为从起始节点到节点的最小边/跳数时,可以根据几何比例关系估计每个级别的适当潜力。基于对每一层的估计潜力,我们可以将寻路问题的图重新设计为电路,因此基尔霍夫电路定律可以直接适用于简化寻路问题的图。
更新日期:2020-09-25
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