Minimum Average Delay of Routing Trees

TL;DR

This paper investigates the problem of minimizing the average delay in routing trees, showing that finding such an optimal tree is NP-hard, thus highlighting computational complexity challenges in network design.

Contribution

The paper introduces the concept of tree length as a measure for average delay and proves that computing the optimal routing tree with minimum tree length is NP-hard.

Findings

Minimum tree length is a valid measure for average delay.

Finding optimal routing trees with minimum tree length is NP-hard.

The study extends understanding of complexity in communication tree optimization.

Abstract

The general communication tree embedding problem is the problem of mapping a set of communicating terminals, represented by a graph G, into the set of vertices of some physical network represented by a tree T. In the case where the vertices of G are mapped into the leaves of the host tree T the underlying tree is called a routing tree and if the internal vertices of T are forced to have degree 3, the host tree is known as layout tree. Different optimization problems have been studied in the class of communication tree problems such as well-known minimum edge dilation and minimum edge congestion problems. In this report we study the less investigate measure i.e. tree length, which is a representative for average edge dilation (communication delay) measure and also for average edge congestion measure. We show that finding a routing tree T for an arbitrary graph G with minimum tree length is an NP-Hard problem.