APPROXIMATION ALGORITHMS FOR CLUSTERING TO MINIMIZE THE SUM OF DIAMETERS

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We consider the problem of partitioning the nodes of a complete edge weighted graph into {kappa} clusters so as to minimize the sum of the diameters of the clusters. Since the problem is NP-complete, our focus is on the development of good approximation algorithms. When edge weights satisfy the triangle inequality, we present the first approximation algorithm for the problem. The approximation algorithm yields a solution that has no more than 10k clusters such the total diameter of these clusters is within a factor O(log (n/{kappa})) of the optimal value fork clusters, where n is the number of nodes in ... continued below

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14 p.

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Kopp, S.; Mortveit, H.S. & Reidys, S.M. February 1, 2000.

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We consider the problem of partitioning the nodes of a complete edge weighted graph into {kappa} clusters so as to minimize the sum of the diameters of the clusters. Since the problem is NP-complete, our focus is on the development of good approximation algorithms. When edge weights satisfy the triangle inequality, we present the first approximation algorithm for the problem. The approximation algorithm yields a solution that has no more than 10k clusters such the total diameter of these clusters is within a factor O(log (n/{kappa})) of the optimal value fork clusters, where n is the number of nodes in the complete graph. For any fixed {kappa}, we present an approximation algorithm that produces {kappa} clusters whose total diameter is at most twice the optimal value. When the distances are not required to satisfy the triangle inequality, we show that, unless P = NP, for any {rho} {ge} 1, there is no polynomial time approximation algorithm that can provide a performance guarantee of {rho} even when the number of clusters is fixed at 3. Other results obtained include a polynomial time algorithm for the problem when the underlying graph is a tree with edge weights.

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14 p.

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OSTI as DE00763370

Medium: P; Size: 14 pages

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  • ALGORITHMIC THEORY, BERGEN (NO), 07/05/2000--07/07/2000

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  • Report No.: LA-UR-00-982
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 763370
  • Archival Resource Key: ark:/67531/metadc716977

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  • February 1, 2000

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  • Sept. 29, 2015, 5:31 a.m.

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  • April 7, 2017, 2:04 p.m.

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Kopp, S.; Mortveit, H.S. & Reidys, S.M. APPROXIMATION ALGORITHMS FOR CLUSTERING TO MINIMIZE THE SUM OF DIAMETERS, article, February 1, 2000; New Mexico. (digital.library.unt.edu/ark:/67531/metadc716977/: accessed November 17, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.