APPROX 2009, RANDOM 2009: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques pp 272-285 | Cite as
Minimizing Average Shortest Path Distances via Shortcut Edge Addition
Conference paper
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
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