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.


Local Search Facility Location Facility Location Problem Local Search Heuristic Good Facility 
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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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