APPROXIMATION ALGORITHMS FOR THE BANDWIDTH MINIMIZATION PROBLEM FOR A LARGE CLASS OF TREES

We present approximation algorithms for the Bandwidth Minimization Problem (BMP) for cases of special trees. The BMP has many different applications and has been studied for both graphs and matrices. The problem has important applications in large distributed processing systems and databases as well as communication theory. The technique presented here is used to provide a communication protocol for maximum throughput and concurrency control. We study the problem on a tree network model having the following property: For any node of the tree, if more than one subtree is present, then the difference of the depths of the subtrees is bounded. We call these trees special height balanced trees. If this difference is a constant on the size of the depth d of the tree, then an O(log d) algorithm is presented. For any depth difference F(d), where F(d) << d, the approximation factor becomes O(F(d)log d).