Graph Theoretic Approach

Next: Probabilistic Approach Up: The Model of the Previous: The Model of the

Graph Theoretic Approach

This model for the clustering problem can be reduced to a clique graph editing problem, stated as follows.

$\begin{problem}{\em clique graph editing problem} \\ {\bf INPUT:} $G(V,E)$\spa... ...al difference between the two edge sets: $\vert E \Delta F\vert$ . \end{problem}$
Clique graph editing problem is NP-hard [5].

$\begin{problem}{\em clique graph completion problem} \\ {\bf INPUT:} $G(V,E)$\... ...th $E \subseteq F$\space which minimizes $\vert E \Delta F\vert$ . \end{problem}$

The clique graph completion problem can be solved by finding all connected components of the input graph and adding all missing edges in each component. Thus the clique graph completion problem is polynomial.

$\begin{problem}{\em clique graph deletion problem} \\ {\bf INPUT:} $G(V,E)$\sp... ...h $F \subseteq E$\space which minimizes $\vert E \Delta F\vert$ . \end{problem}$

The clique graph deletion problem is NP-hard [3]. Moreover, any constant factor approximation to the clique graph deletion problem is NP-hard as well [5].

Peer Itsik
2001-02-01