The parsimonious property of cut covering problems and its applications

The Parsimonious Property of Cut Covering Problems

We consider the analysis of linear programming relaxations of a large class of combinatorial problems that can be formulated as problems of covering cuts, including the Steiner tree, the traveling salesman, the vehicle routing, the matching, the T-join and the survivable network design problem, to name a few. We prove that all of the problems in the class satisfy a deep structural property, the...

Multigranulation single valued neutrosophic covering-based rough sets and their applications to multi-criteria group decision making

In this paper, three types of (philosophical, optimistic and pessimistic) multigranulation single valued neutrosophic (SVN) covering-based rough set models are presented, and these three models are applied to the problem of multi-criteria group decision making (MCGDM).Firstly, a type of SVN covering-based rough set model is proposed.Based on this rough set model, three types of mult...

The topological ordering of covering nodes

The topological ordering algorithm sorts nodes of a directed graph such that the order of the tail of each arc is lower than the order of its head. In this paper, we introduce the notion of covering between nodes of a directed graph. Then, we apply the topological orderingalgorithm on graphs containing the covering nodes. We show that there exists a cut set withforward arcs in these...

Presenting a three-objective model in location-allocation problems using combinational interval full-ranking and maximal covering with backup model

Covering models have found many applications in a wide variety of real-world problems; nevertheless, some assumptions of covering models are not realistic enough. Accordingly, a general approach would not be able to answer the needs of encountering varied aspects of real-world considerations. Assumptions like the unavailability of servers, uncertainty, and evaluating more factors at the same ti...

Schur-Pair Property and the Structure of Varietal Covering Groups