We prove that, if a graph with e edges contains m vertex-disjoint edges, then m/e complete bipartite subgraphs are necessary to cover all its edges. Similar lower bounds are also proved for fractional covers. For sparse graphs, this improves the well-known fooling set lower bound in communication complexity. We also formulate several open problems about covering problems for graphs whose soluti...

This paper studies a covering problem on graph which is a variant of facility location problem. In this research, constraints are considered to improve the previous model. These constraints have not considered previously. The first constraint limits the capacity of the facilities and the other one considers different coverage distances. The objective is to determine the optimal subset of candid...

The Maximal Covering Location Problem (MCLP) maximizes the population that has a facility within a maximum travel distance or time. Numerous extensions have been proposed to enhance its applicability, like the probabilistic model for the maximum covering location-allocation with constraint in waiting time or queue length for congested systems, with one or more servers per service center. In thi...

Abstract One of the basic assumptions in hub covering problems is considering the covering radius as an exogenous parameter which cannot be controlled by the decision maker. Practically and in many real world cases with a negligible increase in costs, to increase the covering radii, it is possible to save the costs of establishing additional hub nodes. Change in problem parameters during the pl...