Tight Bounds for Online Weighted Tree Augmentation
| العنوان: | Tight Bounds for Online Weighted Tree Augmentation |
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| المؤلفون: | David P. Williamson, Joseph (Seffi) Naor, Seeun William Umboh |
| المصدر: | Algorithmica. 84:304-324 |
| بيانات النشر: | Springer Science and Business Media LLC, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Combinatorics, Tree (data structure), 000 Computer science, knowledge, general works, General Computer Science, Applied Mathematics, Computer Science, Computer Science Applications, Mathematics |
| الوصف: | 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. |
| تدمد: | 1432-0541 0178-4617 |
| DOI: | 10.1007/s00453-021-00888-7 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5ec6d02b7b837c7b370537090dd1e205 https://doi.org/10.1007/s00453-021-00888-7 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....5ec6d02b7b837c7b370537090dd1e205 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 14320541 01784617 |
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| DOI: | 10.1007/s00453-021-00888-7 |