## A new result on the complexity of the p-center problem.(Spanish. English summary)Zbl 0692.90042

Summary: Let G be an undirected graph with n vertices and m edges. A p-center of G is a set of p points that minimizes the distance to the farthest vertex. This minimum is the p-radius. A local center is a point c at the same distance (the range of the local center) to the vertices of a nonempty set which are not all optimally reachable from c through the same adjacent vertex. Every p-radius is the range of a local center so that we only need to find the least range r such that there is a set of p points that covers all the vertices within a distance r. This value of r is the p-radius and the corresponding set is a p-center. By considering the r- extremes (the points that are at distance r from any vertex) it is enough to find these sets. By using r-extremes we give an $$O(m^ p\cdot n^{p+1}\cdot \log n)$$ simple algorithm that is experimentally compared with the Handler relaxation algorithm.

### MSC:

 90B05 Inventory, storage, reservoirs 90C35 Programming involving graphs or networks 68Q25 Analysis of algorithms and problem complexity

### Keywords:

facility location; undirected graph; p-center; p-radius; local center
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### References:

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