Design of Dynamic Algorithms via Primal-Dual Method

  • Sayan BhattacharyaEmail author
  • Monika Henzinger
  • Giuseppe F. Italiano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9134)


In this paper, we develop a dynamic version of the primal-dual method for optimization problems, and apply it to obtain the following results. (1) For the dynamic set-cover problem, we maintain an \(O(f^2)\)-approximately optimal solution in \(O(f \cdot \log (m+n))\) amortized update time, where \(f\) is the maximum “frequency” of an element, \(n\) is the number of sets, and \(m\) is the maximum number of elements in the universe at any point in time. (2) For the dynamic \(b\)-matching problem, we maintain an \(O(1)\)-approximately optimal solution in \(O(\log ^3 n)\) amortized update time, where \(n\) is the number of nodes in the graph.


Online Algorithm Vertex Cover Input Graph Dynamic Version Dynamic Setting 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Sayan Bhattacharya
    • 1
    Email author
  • Monika Henzinger
    • 2
  • Giuseppe F. Italiano
    • 3
  1. 1.Institute of Mathematical SciencesChennaiIndia
  2. 2.University of ViennaViennaAustria
  3. 3.Università di Roma “Tor Vergata”RomeItaly

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