The Use of Probability and Edge Analysis to Solve the Multi-Period Degree Constrained Minimum Spanning Tree Problem

Abstract

The goal of the Multiperiod Degree Constrained Minimum Spanning Tree (MPDCMST) problem is to determine the smallest weight-spanning tree that satisfies the vertex installation criterion for each period and maintains the degree requirement in each vertex. This issue emerges as a network connection problem. The degree requirement indicates the reliability of each vertex, and the vertex connection/installation requirement denotes the priority vertices that must be inserted in the network within a specific time frame. The installation is split up into multiple phases/stages. This is because of various considerations such as severe weather, budgetary limitations, etc. In this research, two algorithms for solving the MPDCMST using probability hybridized with Prim’s modification, and edge analysis are proposed. The algorithms are implemented on the undirected complete graph of orders 10 to 100. The solutions are compared with some heuristics which are already in the literature. The results show that the proposed algorithms perform better.