NDLI: Online and Stochastic Survivable Network Design

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Gupta, Anupam Ravi, R. Krishnaswamy, Ravishankar
Copyright Year	2012
Abstract	Consider the edge-connectivity survivable network design problem (SNDP): given a graph $G = (V,E)$ with edge-costs, and edge-connectivity requirements $r_{ij} \in \mathbb{Z}_{\geq 0}$ for every pair of vertices $i, j \in V$, find an (approximately) minimum-cost network that provides the required connectivity. While this problem is known to admit good approximation algorithms in the offline case, no algorithms were known for this problem in the online setting. In this paper, we give a randomized $\tilde{O}(r_{\max} \log^3 n)$-competitive online algorithm for this edge-connectivity network design problem that runs in time $O(m^{r_{\max}})$, where $r_{\max} = \max_{ij} r_{ij}$. Our algorithms use the standard embeddings of graphs into random subtrees (i.e., into singly connected subgraphs) as an intermediate step to get algorithms for higher connectivity. As a consequence of using these random embeddings, our algorithms are competitive only against oblivious adversaries. Our results for the online problem give us approximation algorithms that admit strict cost-shares with the same strictness value. This, in turn, implies approximation algorithms for (a) the rent-or-buy version and (b) the (two-stage) stochastic version of the edge-connected network design problem with independent arrivals. If we are in the case when the underlying graph is complete and the edge-costs are metric (i.e., the triangle inequality is satisfied), we improve on our results to give an $O(\log n)$-competitive deterministic online algorithm for the rooted version of the problem, and constant-factor approximation algorithms for the rent-or-buy and stochastic variants of SNDP.
Starting Page	1649
Ending Page	1672
Page Count	24
File Format	PDF
ISSN	00975397
DOI	10.1137/09076725X
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	6 (Special Section on the Forty-First Annual ACM Symposium on Theory of Computing (STOC 2009))
Volume Number	41
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2012-12-18
Access Restriction	Subscribed
Subject Keyword	Online algorithms survivable network design Approximation algorithms approximation algorithms Graph algorithms online algorithms stochastic optimization
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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