Better Approximation Algorithms for Technology Diffusion

  • Jochen Könemann
  • Sina Sadeghian
  • Laura Sanità
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8125)

Abstract

Motivated by cascade effects arising in network technology upgrade processes in the Internet, Goldberg and Liu [SODA, 2013] recently introduced the following natural technology diffusion problem. Given a graph G = (V,E), and thresholds θ(v), for all v ∈ V. A vertex uactivates if it is adjacent to a connected component of active nodes of size at least θ(v). The goal is to find a seed set \(\mathcal{A}\) whose initial activation would trigger a cascade activating the entire graph.

Goldberg and Liu presented an algorithm for this problem that returns a seed set of size O(rl log(n)) times that of an optimum seed set, where r is the diameter of the given graph, and l is the number of distinct thresholds used in the instance. We improve upon this result by presenting an O( min {r,l} log(n))-approximation algorithm. Our algorithm is simple and combinatorial, in contrast with the previous approach that is based on randomized rounding applied to the solution of a linear program.

Keywords

Approximation Algorithms Technology Diffusion Combinatorial Optimization 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jochen Könemann
    • 1
  • Sina Sadeghian
    • 1
  • Laura Sanità
    • 1
  1. 1.Faculty of Mathematics, Department of Combinatorics & OptimizationUniversity of WaterlooWaterlooCanada

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