




















Abstract:The Connectivity Augmentation Problem (CAP) is a fundamental problem in fault-tolerant network design and has been extensively studied in the context of approximation algorithms. In this work, we consider CAP in the online setting: given a $k$-edge-connected graph $G$ and a set $L$ of additional edges over the vertices of $G$, called links, online requests arrive one by one, each specifying two vertices that need to be $(k+1)$-edge-connected. We start with the graph $G$ and progressively add links to serve these requests. More specifically, upon the arrival of a request $\{u,v\}$, we must immediately and irrevocably add zero or more links from $L$ to the graph so that $u$ and $v$ are $(k+1)$-edge-connected in the resulting augmented graph. The goal is to minimize the total number of links added, and we evaluate an algorithm's performance by its competitive ratio relative to an optimal offline solution. In this work, improving upon previous bounds, we obtain a tight competitive ratio for online CAP, along with other related results.
From: Aditya Subramanian [view email]
[v1]
Tue, 16 Jun 2026 16:59:40 UTC (131 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。