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DOI: 10.14569/IJACSA.2020.0110403
PDF

Conceptual Framework for Finding Approximations to Minimum Weight Triangulation and Traveling Salesman Problem of Planar Point Sets

Author 1: Marko Dodig
Author 2: Milton Smith

International Journal of Advanced Computer Science and Applications(IJACSA), Volume 11 Issue 4, 2020.

  • Abstract and Keywords
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Abstract: We introduce a novel Conceptual Framework for finding approximations to both Minimum Weight Triangulation (MWT) and optimal Traveling Salesman Problem (TSP) of planar point sets. MWT is a classical problem of Computational Geometry with various applications, whereas TSP is perhaps the most researched problem in Combinatorial Optimization. We provide motivation for our research and introduce the fields of triangulation and polygonization of planar point sets as theoretical bases of our approach, namely, we present the Isoperimetric Inequality principle, measured via Compactness Index, as a key link between our two stated problems. Our experiments show that the proposed framework yields tight approximations for both problems.

Keywords: Computational geometry; minimum weight triangu-lation; combinatorial optimization; traveling salesman problem

Marko Dodig and Milton Smith, “Conceptual Framework for Finding Approximations to Minimum Weight Triangulation and Traveling Salesman Problem of Planar Point Sets” International Journal of Advanced Computer Science and Applications(IJACSA), 11(4), 2020. http://dx.doi.org/10.14569/IJACSA.2020.0110403

@article{Dodig2020,
title = {Conceptual Framework for Finding Approximations to Minimum Weight Triangulation and Traveling Salesman Problem of Planar Point Sets},
journal = {International Journal of Advanced Computer Science and Applications},
doi = {10.14569/IJACSA.2020.0110403},
url = {http://dx.doi.org/10.14569/IJACSA.2020.0110403},
year = {2020},
publisher = {The Science and Information Organization},
volume = {11},
number = {4},
author = {Marko Dodig and Milton Smith}
}



Copyright Statement: This is an open access article licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, even commercially as long as the original work is properly cited.

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