A novel critical node in generalized networking

Abstract

Critical Nodes problem is an important problem in networking. There are several types of critical nodes which having been defined. In this paper, we propose a novel type of critical nodes based on two important parameters: range and support. How to find the critical nodes to make the networking stable is the key problem. We prove that the decision form of this problem (the total cost is no more than a given threshold) is NP-complete and the optimization form of this problem (to obtain the minimum total cost) is NP-hard. Then we bring out a heuristic algorithm to solve this problem and apply this problem to banking ATM placement problem. Finally, we analyse the advantages of our heuristic algorithm.