Online Buy-at-Bulk Network Design

TL;DR

This paper introduces the first non-trivial online algorithms for the multicommodity buy-at-bulk network design problem, achieving competitive ratios comparable to offline solutions by reducing complex instances to simpler single-sink problems.

Contribution

It presents an online reduction theorem from multicommodity to single-sink buy-at-bulk problems and designs new online algorithms using junction-tree solutions.

Findings

Achieved competitive ratios matching offline approximation factors.

Developed the first online algorithms for node-weighted/directed single-sink buy-at-bulk.

Provided new proofs for online Steiner forest problems.

Abstract

We present the first non-trivial online algorithms for the non-uniform, multicommodity buy-at-bulk (MC-BB) network design problem in undirected and directed graphs. Our competitive ratios qualitatively match the best known approximation factors for the corresponding offline problems. The main engine for our results is an online reduction theorem of MC-BB problems to their single-sink (SS-BB) counterparts. We use the concept of junction-tree solutions (Chekuri et al., FOCS 2006) that play an important role in solving the offline versions of the problem via a greedy subroutine -- an inherently offline procedure. Our main technical contribution is in designing an online algorithm using only the existence of good junction-trees to reduce an MC-BB instance to multiple SS-BB sub-instances. Along the way, we also give the first non-trivial online node-weighted/directed single-sink buy-at-bulk algorithms. In addition to the new results, our generic reduction also yields new proofs of recent results for the online node-weighted Steiner forest and online group Steiner forest problems.