Abstract
We present a branch and bound method which finds a maximum weight clique in an arbitrary weighted graph. The main ingredients are a weighted coloring heuristic which simultaneously produces lower and upper bounds and a branching rule that uses the information obtained in the coloring. The algorithm performs comparable to the fastest method known so far but is much easier to implement.
Zusammenfassung
Wir stellen eine Branch- and Bound-Methode zur Ermittlung einer Clique größten Gewichts in einem beliebigen gewichteten Graph vor. Die Hauptbestandteile sind eine Färbungsheuristik, die gleichzeitig untere und obere Schranken liefert, sowie eine Verzweigungsregel, die die Informationen der Färbung verwendet. Der Algorithmus ist ähnlich leistungsfähig wie die schnellste bisher bekannte Methode, allerdings ist er sehr viel einfacher zu implementieren.
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Babel, L. A fast algorithm for the maximum weight clique problem. Computing 52, 31–38 (1994). https://doi.org/10.1007/BF02243394
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DOI: https://doi.org/10.1007/BF02243394