This paper concerns the optimal partition of a graph into p connected clusters of vertices, with various constraints on their topology and weight. We consider different objectives, depending on the cost of the trees spanning the clusters. This rich family of problems mainly applies to telecommunication network design, but it can be useful in other fields. We achieve a complete characterization of its computational complexity, previously studied only for special cases: a polynomial algorithm based on a new matroid solves the easy cases; the others are strongly NP-hard by direct reduction from SAT. Finally, we give results on special graphs.
|Titolo:||On the complexity of graph tree partition problems|
CORDONE, ROBERTO (Primo)
|Parole Chiave:||computational complexity; greedy algorithm; tree partition|
|Settore Scientifico Disciplinare:||Settore INF/01 - Informatica|
|Data di pubblicazione:||gen-2004|
|Digital Object Identifier (DOI):||10.1016/S0166-218X(03)00340-8|
|Appare nelle tipologie:||01 - Articolo su periodico|