Designing Approximate Binary Trees for Trees

TL;DR

This paper introduces a linear-time algorithm that approximates the optimal binary tree structure to minimize distances between adjacent vertices in a given tree, relevant for demand-aware network design.

Contribution

It provides the first linear-time factor-4 approximation algorithm for constructing binary trees that approximate the original tree's adjacency distances.

Findings

The algorithm runs in linear time.

It guarantees a solution within four times the optimal.

Applicable to demand-aware network design.

Abstract

We study the following problem that is motivated by demand-aware network design: Given a tree~$G$, the task is to find a binary tree~$H$ on the same vertex set. The objective is to minimize the sum of distances in~$H$ between vertex pairs that are adjacent in~$G$. We present a linear-time factor-4 approximation for this problem.