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A “maximum node clustering” problem

Author

Listed:
  • Giuliana Carello

    (Politecnico di Milano)

  • Federico Della Croce

    (Politecnico di Torino)

  • Andrea Grosso

    (Università di Torino)

  • Marco Locatelli

    (Università di Torino)

Abstract

In this note we introduce a graph problem, called Maximum Node Clustering (MNC). We prove that the problem (which is easily shown to be strongly NP-complete) can be approximated in polynomial time within a ratio arbitrarily close to 2. For the special case where the graph is a tree, the problem is NP-complete in the ordinary sense; for this case we present a pseudopolynomial algorithm based on dynamic programming, and a related Fully Polynomial Time Approximation Scheme (FPTAS). Also, the tree case is shown to be exactly solvable in $${\mathcal O}(2^{{\frac{2}{3}}n}{\rm poly}(n))$$ time, where n is the number of nodes.

Suggested Citation

  • Giuliana Carello & Federico Della Croce & Andrea Grosso & Marco Locatelli, 2006. "A “maximum node clustering” problem," Journal of Combinatorial Optimization, Springer, vol. 11(4), pages 373-385, June.
    • Handle: RePEc:spr:jcomop:v:11:y:2006:i:4:d:10.1007_s10878-006-8210-x
    DOI: 10.1007/s10878-006-8210-x
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