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.
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Meyerson, A., Tagiku, B. (2009). Minimizing Average Shortest Path Distances via Shortcut Edge Addition. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2009 2009. Lecture Notes in Computer Science, vol 5687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03685-9_21
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DOI: https://doi.org/10.1007/978-3-642-03685-9_21
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