NDLI: Online Buy-at-Bulk Network Design

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Online Buy-at-Bulk Network Design

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Chakrabarty, Deeparnab Panigrahi, Debmalya Ene, Alina Krishnaswamy, Ravishankar
Copyright Year	2018
Abstract	We present the first online algorithms for the nonuniform, multicommodity buy-at-bulk (MC-BB) network design problem. Our competitive ratios qualitatively match the best known approximation factors for the corresponding offline problems. In particular, we show (a) a polynomial time online algorithm with a polylogarithmic competitive ratio for the MC-BB problem in undirected edge-weighted graphs, (b) a quasi-polynomial time online algorithm with a polylogarithmic competitive ratio for the MC-BB problem in undirected node-weighted graphs, (c) for any fixed $\epsilon > 0$, a polynomial time online algorithm with a competitive ratio of $\tilde{O}\big(k^{\frac{1}{2}+\epsilon})$ (where $k$ is the number of demands, and the tilde hides polylog factors) for MC-BB in directed graphs, and (d) algorithms with matching competitive ratios for the prize-collecting variant of all the preceding problems. Prior to our work, a logarithmic competitive ratio was known for undirected, edge-weighted graphs only for the special case of uniform costs [B. Awerbuch and Y. Azar, FOCS, 1997, pp. 542--547], and a polylogarithmic-competitive algorithm was known for the edge-weighted single-sink problem [A. Meyerson, Procedings of SPAA, 2004, pp. 275--280]. We believe no online algorithm was known in the node-weighted and directed settings, even for uniform costs. Our main technical contribution is an online reduction theorem of MC-BB problems to their single-sink counterparts. We use the concept of junction-tree solutions from [C. Chekuri, M. T. Hajiaghayi, G. Kortsarz, and M. R. Salavatipour, Proceedings of FOCS, 2006, pp. 677--686], which play an important role in solving the offline versions of the problem via a greedy subroutine---an inherently offline procedure. We use just the existence of good junction-trees for our reduction.
Sponsorship	Google. Duke University
Starting Page	1505
Ending Page	1528
Page Count	24
File Format	PDF
ISSN	00975397
DOI	10.1137/16M1117317
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	4
Volume Number	47
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2018-07-26
Access Restriction	Subscribed
Subject Keyword	algorithms Online algorithms Approximation methods and heuristics Approximation algorithms approximation algorithms network design online algorithms
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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