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Clustering With Center Constraints

Authors Parinya Chalermsook, Suresh Venkatasubramanian



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Parinya Chalermsook
Suresh Venkatasubramanian

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Parinya Chalermsook and Suresh Venkatasubramanian. Clustering With Center Constraints. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 401-412, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)
https://doi.org/10.4230/LIPIcs.FSTTCS.2013.401

Abstract

In the classical maximum independent set problem, we are given a graph G of "conflicts" and are asked to find a maximum conflict-free subset. If we think of the remaining nodes as being "assigned" (at unit cost each) to one of these independent vertices and ask for an assignment of minimum cost, this yields the vertex cover problem. In this paper, we consider a more general scenario where the assignment costs might be given by a distance metric d (which can be unrelated to G) on the underlying set of vertices. This problem, in addition to being a natural generalization of vertex cover and an interesting variant of the k-median problem, also has connection to constrained clustering and database repair. Understanding the relation between the conflict structure (the graph) and the distance structure (the metric) for this problem turns out to be the key to isolating its complexity. We show that when the two structures are unrelated, the problem inherits a trivial upper bound from vertex cover and provide an almost matching lower bound on hardness of approximation. We then prove a number of lower and upper bounds that depend on the relationship between the two structures, including polynomial time algorithms for special graphs.
Keywords
  • Clustering
  • vertex cover
  • approximation algorithms

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