Dynamic Capacitated Minimum Spanning Trees

Given a set of terminals, each associated with a positive number denoting the traffic to be routed to a central terminal (root), the Capacitated Minimum Spanning Tree (CMST) problem asks for a minimum spanning tree, spanning all terminals, such that the amount of traffic routed from a subtree, linked to the root by an edge, does not exceed the given capacity constraint . The CMST problem is NP-complete and has been extensively studied for the past 40 years. Current best heuristics, in terms of cost and computation time ( ), are due to Esau and Williams [1], and Jothi and Raghavachari [2]. In this paper, we consider the Dynamic Capacitated Minimum Spanning Tree (DCMST) problem in which a CMST , spanning nodes and rooted at a central node , with capacity constraint is given as part of the input. Requests, from new nodes, for joining arrive dynamically (online), one at a time. Under this setting, we want to add the new node to the existing CMST without having to recompute the entire CMST, which would take time. To our knowledge, the DCMST problem has not been studied before. For the DCMST problem, we propose three methods (COD, CFOD and BSA) to add the new nodes to the existing CMST. All our heuristics run in linear time. We compare the performance of our heuristics with a CMST algorithm that recomputes the solution every time a new node arrives. Keywords—Capacitated Minimum Spanning Trees, Network Design, Dynamic Graph Algorithms.