Extended TANYAKUMU Labelling Method to Compute Shortest Paths in Directed Networks

Author:

Tawanda Trust1,Munapo Elias2,Kumar Santosh3,Nyamugure Philimon1

Affiliation:

1. Department of Statistics and Operations Research, National University of Science and Technology, Bulawayo, Zimbabwe.

2. School of Economics and Decision Sciences, North West University, Mafikeng Campus Mafikeng, South Africa.

3. School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Australia.

Abstract

Shortest path problem (SPP) has various applications in areas such as telecommunications, transportation and emergency services, and postal services among others. As a result, several algorithms have been developed to solve the SPP and related problems. The current paper extends the TANYAKUMU labelling method for solving the Travelling salesman problem (TSP) to solve SPP in directed transportation networks. Numerical illustrations are used to prove the validity of the proposed method. The main contributions of this paper are as follows: (i) modification of TSP algorithm to solve single source SPP, (ii) the developed method numerically evaluated on four increasingly complex problems of sizes 11×11, 21×21, 23×23 and 26×26 and lastly (iii) the solutions obtained from solving these four problems are compared with those obtained by Minimum incoming weight label (MIWL) algorithm. The proposed algorithm computed the same shortest paths as the MIWL algorithm on all four problems.

Publisher

Ram Arti Publishers

Subject

General Engineering,General Business, Management and Accounting,General Mathematics,General Computer Science

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