eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-07-04
88:1
88:14
10.4230/LIPIcs.ICALP.2019.88
article
Tight Bounds for Online Weighted Tree Augmentation
Naor, Joseph (Seffi)
1
Umboh, Seeun William
2
https://orcid.org/0000-0001-6984-4007
Williamson, David P.
3
https://orcid.org/0000-0002-2884-0058
Technion, Haifa, Israel
The University of Sydney, Australia
Cornell University, Ithaca, NY, USA
The Weighted Tree Augmentation problem (WTAP) is a fundamental problem in network design. In this paper, we consider this problem in the online setting. We are given an n-vertex spanning tree T and an additional set L of edges (called links) with costs. Then, terminal pairs arrive one-by-one and our task is to maintain a low-cost subset of links F such that every terminal pair that has arrived so far is 2-edge-connected in T cup F. This online problem was first studied by Gupta, Krishnaswamy and Ravi (SICOMP 2012) who used it as a subroutine for the online survivable network design problem. They gave a deterministic O(log^2 n)-competitive algorithm and showed an Omega(log n) lower bound on the competitive ratio of randomized algorithms. The case when T is a path is also interesting: it is exactly the online interval set cover problem, which also captures as a special case the parking permit problem studied by Meyerson (FOCS 2005). The contribution of this paper is to give tight results for online weighted tree and path augmentation problems. The main result of this work is a deterministic O(log n)-competitive algorithm for online WTAP, which is tight up to constant factors.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol132-icalp2019/LIPIcs.ICALP.2019.88/LIPIcs.ICALP.2019.88.pdf
Online algorithms
competitive analysis
tree augmentation
network design