Why Unit Two-Variable-Per-Inequality (UTVPI) Constraints Are So Efficient to Handle: Intuitive Explanation

Authors

Saeid Tizpaz-Niari, The University of Texas at El PasoFollow
Martine Ceberio, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

8-1-2023

Comments

Technical Report: UTEP-CS-23-45

Abstract

In general, integer linear programming is NP-hard. However, there exists a class of integer linear programming problems for which an efficient algorithm is possible: the class of so-called unit two-variable-per-inequality (UTVPI) constraints. In this paper, we provide an intuitive explanation for why an efficient algorithm turned out to be possible for this class. Namely, the smaller the class, the more probable it is that a feasible algorithm is possible for this class, and the UTVPI class is indeed the smallest -- in some reasonable sense described in this paper.