Dynamic Reconfiguration of Complete Binary Trees in Faulty Hypercubes

Abstract

In this paper we present how to reconfigure dynamically a complete binary tree in faulty hypercubes. First, we use a dynamic algorithm to reconfigure a complete binary tree of height h (h≥0) in an (h+1)-dimensional faulty hypercube. If there is a faulty node in the hypercube, both the dilation and congestion are 2 after reconfiguration. If there are two faulty nodes in the hypercube, both the dilation and congestion are 3 after reconfiguration. If there are more than two faulty nodes in the hypercube, we impose a constraint on the type of the faulty nodes, both the dilation and congestion are 3 after reconfiguration. Then we reconfigure a complete binary tree of height h in an (h+2)-dimensional hypercube with at most 2h+1-1 nodes, and the dilation and congestion are, respectively, 2 and 1 after reconfiguration. The number of the affected nodes are minimized after reconfiguration.