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Approximation Algorithms for Directed Weighted Spanners by Grigorescu, Elena; Kumar, Nithish; Lin, Young-San is a scholarly article available to read on EtoBox.

What is Approximation Algorithms for Directed Weighted Spanners about?

In the pairwise weighted spanner problem, the input consists of an $n$-vertex-directed graph, where each edge is assigned a cost and a length. Given $k$ vertex pairs and a distance constraint for each pair, the goal is to find a minimum-cost subgraph in which the distance constraints are satisfied. This formulation captures many well-studied connectivity problems, including spanners, distance preservers, and Steiner forests. In the offline setting, we show: 1. An $\tilde{O}(n^{4/5 + \epsilon})$-approximation algorithm for pairwise weighted spanners. When the edges have unit costs and lengths, the best previous algorithm gives an $\tilde{O}(n^{3/5 + \epsilon})$-approximation, due to Chlamt\'a\v{c}, Dinitz, Kortsarz, and Laekhanukit (TALG, 2020). 2. An $\tilde{O}(n^{1/2+\epsilon})$-approximation algorithm for all-pair weighted distance preservers. When the edges have unit costs and arbitrary lengths, the best previous algorithm gives an $\tilde{O}(n^{1/2})$-approximation for all-pair spanners, due to Berman, Bhattacharyya, Makarychev, Raskhodnikova, and Yaroslavtsev (Information and Computation, 2013). In the online setting, we show: 1. An $\tilde{O}(k^{1/2 + \epsilon})$-competitive

Author

Grigorescu, Elena; Kumar, Nithish; Lin, Young-San

Published

2023

Language

EN