Approximation algorithms for nonuniform buy-at-bulk network design

C. Chekuri, M. T. Hajiaghayi, G. Kortsarz, M. R. Salavatipour

Research output: Contribution to journalArticlepeer-review


Buy-at-bulk network design problems arise in settings where the costs for purchasing or installing equipment exhibit economies of scale. The objective is to build a network of cheapest cost to support a given multicommodity flow demand between node pairs. We present approximation algorithms for buy-at-bulk network design problems with costs on both edges and nodes of an undirected graph. Our main result is the first poly-logarithmic approximation ratio for the non-uniform problem that allows different cost functions on each edge and node; the ratio we achieve is O(log4 h), where h is the number of demand pairs. In addition we present an O(log h) approximation for the single sink problem. Poly-logarithmic ratios for some related problems are also obtained. Our algorithm for the multicommodity problem is obtained via a reduction to the single source problem using the notion of junction trees. We believe that this presents a simple yet useful general technique for network design problems.

Original languageEnglish (US)
Pages (from-to)1772-1798
Number of pages27
JournalSIAM Journal on Computing
Issue number5
StatePublished - 2010


  • Approximation algorithm
  • Concave cost
  • Economies of scale
  • Network design
  • Network flow
  • Nonuniform buy-at-bulk

ASJC Scopus subject areas

  • General Computer Science
  • General Mathematics


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