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Abstract

We consider adding k shortcut edges (i.e. edges of small fixed length δ ≥ 0) to a graph so as to minimize the weighted average shortest path distance over all pairs of vertices. We explore several variations of the problem and give O(1)-approximations for each. We also improve the best known approximation ratio for metric k-median with penalties, as many of our approximations depend upon this bound. We give a \((1+2\frac{(p+1)}{\beta(p+1)-1},\beta)\)-approximation with runtime exponential in p. If we set β = 1 (to be exact on the number of medians), this matches the best current k-median (without penalties) result.

Keywords

Local Search Facility Location Facility Location Problem Local Search Heuristic Good Facility 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Adam Meyerson
    • 1
  • Brian Tagiku
    • 1
  1. 1.University of CaliforniaLos AngelesUSA

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