A reversing traversal algorithm to predict deleting node for the optimal k-node set reliability with capacity constraint of distributed systems

Abstract

A k-node set reliability with capacity constraint is defined as the probability that a set, K, of nodes is connected in a distributed system and the total capacity of the nodes in K is sufficient under a given capacity. This is generally an NP-hard problem. For reducing computational time, a reasonable k-node set within a given capacity constraint must be determined by an efficient algorithm. In this work, we propose a reversing traversal method to derive a k-node set under capacity constraint having an approximate solution. Initially, the set K is assigned to all the nodes in a system. The proposed algorithm uses an objective function to evaluate the fitness value of each node in K and predict a deleting node, which is not a critical node, in K with minimal fitness value. After deleting the node, the fitness value of each node that is adjacent to the deleted node is tuned. The above two processes are repeated until the total capacity of the nodes in each subset of the set K does not satisfy the capacity constraint. In our simulation, the proposed method can obtain an exact solution above 90%. When a sub-optimal solution is obtained, the average deviation from an exact solution is under 0.0033. Computational results demonstrate that the proposed algorithm is efficient in execution time and effective for obtaining an optimal k-node set with capacity constraint. (C) 2001 Elsevier Science B.V. All rights reserved.