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Metric k-Median


Metric k-median is the problem of choosing at most k candidate facilities to minimize the sum of distances from clients to their nearest chosen facilities in a metric space. For finite client and candidate sets J and F, a metric d, and a positive integer k<=|F|, the optimum is

 OPT_k=min_(S subset= F,1<=|S|<=k)sum_(j in J)min_(i in S)d(j,i).

For clients 0, 1, and 2 and candidates 0 and 2 with distance d(x,y)=|x-y|, the optimum for k=1 is 3.


See also

Metric Space, NP-Hard Problem, Optimization Theory, P Versus NP Problem

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References

Jain, K. and Vazirani, V. V. "Approximation Algorithms for Metric Facility Location and k-Median Problems Using the Primal-Dual Schema and Lagrangian Relaxation." J. ACM 48, 274-296, 2001. https://doi.org/10.1145/375827.375845.

Cite this as:

Weisstein, Eric W. "Metric k-Median." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Metrick-Median.html

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