Designing Approximate Binary Trees for Trees

2026-04-22

AI Summary

This work addresses the demand-aware network design problem of constructing a binary tree \( H \) over the same vertex set as a given tree \( G \), such that the sum of distances in \( H \) between all pairs of adjacent vertices in \( G \) is minimized. The paper presents the first linear-time 4-approximation algorithm for this problem. By integrating graph-theoretic modeling, tree restructuring techniques, and a greedy strategy, the proposed method achieves a provable approximation ratio while drastically improving computational efficiency. This approach enables scalable solutions for large-scale instances, striking a breakthrough balance between approximation quality and time complexity.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• approximate binary trees
• demand-aware network design
• tree embedding
• distance minimization

Innovation

• approximation algorithm
• binary tree
• demand-aware network
• linear-time
• tree embedding