Online Network Design Algorithms via Hierarchical Decompositions
Seeun Umboh

TL;DR
This paper introduces a novel deterministic approach using hierarchical tree embeddings to improve online network design algorithms, achieving better competitive ratios and simplifying analysis compared to prior randomized and dual-fitting methods.
Contribution
The authors develop a unified deterministic framework leveraging HST embeddings for online network design, improving competitive ratios and simplifying proofs.
Findings
Achieved $O( ext{log }k)$-competitive algorithms for multiple problems.
Improved previous bounds from randomized $O( ext{log }n)$ to deterministic $O( ext{log }k)$.
Simplified analysis without dual-fitting techniques.
Abstract
We develop a new approach for online network design and obtain improved competitive ratios for several problems. Our approach gives natural deterministic algorithms and simple analyses. At the heart of our work is a novel application of embeddings into hierarchically well-separated trees (HSTs) to the analysis of online network design algorithms --- we charge the cost of the algorithm to the cost of the optimal solution on any HST embedding of the terminals. This analysis technique is widely applicable to many problems and gives a unified framework for online network design. In a sense, our work brings together two of the main approaches to online network design. The first uses greedy-like algorithms and analyzes them using dual-fitting. The second uses tree embeddings and results in randomized -competitive algorithms, where is the total number of vertices in the graph.…
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Taxonomy
TopicsOptimization and Search Problems · Complexity and Algorithms in Graphs · Advanced Graph Theory Research
