A “maximum node clustering” problem

Giuliana Carello (), Federico Della Croce (), Andrea Grosso () and Marco Locatelli ()
Additional contact information
Giuliana Carello: Politecnico di Milano
Federico Della Croce: Politecnico di Torino
Andrea Grosso: Università di Torino
Marco Locatelli: Università di Torino

Journal of Combinatorial Optimization, 2006, vol. 11, issue 4, No 2, 373-385

Abstract: 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.

Keywords: Maximum Node Clustering; Knapsack; Complexity; Approximation (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-006-8210-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:11:y:2006:i:4:d:10.1007_s10878-006-8210-x

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-006-8210-x

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().