Work

An Integer Linear Programming Model for Partially Ordered Sets

Year: 2022

Type: article

Abstract: Linear programming is an important approach that is used to represent a large class of combinatorial optimization problems. The simplex algorithm is one of the algorithms for solving linear programming problems with exponential time complexity. Fortunately, this algorithm solves real‐world problems with polynomial time complexity. In particular, a new Integer Linear Programming model (ILPM) is proposed for partially ordered sets. Robert Dilworth’s Decomposition theorem is formulated by ILPM and proves its correctness using the paradigm of strong duality in linear programming. Finally, ILPM is run on fifteen benchmark partially ordered sets for finding their width. The computational experiments show the validity of the proposed model.

Source: Journal of Mathematics

DOI: 10.1155/2022/7660174

Authors: Elsayed Badr, I.M. Selim, Hoda Mostafa, Hala Attiya

Institutions: Benha University, University of Sadat City, Menoufia University, Beni-Suef University

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,160

OpenAlex ID: W4295120695