Online primal-dual algorithms for covering and packing

Niv Buchbinder*, Joseph Naor

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study a wide range of online covering and packing optimization problems. In an online covering problem, a linear cost function is known in advance, but the linear constraints that define the feasible solution space are given one by one, in rounds. In an online packing problem, the profit function as well as the packing constraints are not known in advance. In each round additional information (i.e., a new variable) about the profit function and the constraints is revealed. An online algorithm needs to maintain a feasible solution in each round; in addition, the solutions generated over the different rounds need to satisfy a monotonicity property. We provide general deterministic primal-dual algorithms for online fractional covering and packing problems. We also provide deterministic algorithms for several integral online covering and packing problems. Our algorithms are designed via a novel online primal-dual technique and are evaluated via competitive analysis.

Original languageEnglish
Pages (from-to)270-286
Number of pages17
JournalMathematics of Operations Research
Issue number2
StatePublished - May 2009
Externally publishedYes


  • Competitive analysis
  • Covering and packing
  • Derandomization
  • Duality
  • Linear programming
  • Online algorithms


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