Abstract: "In this paper we consider the problem of finding a core of limited length in a tree. A core is a path, which minimizes the sum of the distances to all nodes in the tree. This problem has been examined under different constraints on the tree and on the set of paths, from which the cor...

Ausführliche Beschreibung

Bibliographische Detailangaben

Format:	Buch
Sprache:	English
Veröffentlicht:	København 1997
Schriftenreihe:	Datalogisk Institut <København>: DIKU-Rapport 1997,3
Schlagworte:	Combinatorial optimization Paths and cycles (Graph theory) Trees (Graph theory)
Zusammenfassung:	Abstract: "In this paper we consider the problem of finding a core of limited length in a tree. A core is a path, which minimizes the sum of the distances to all nodes in the tree. This problem has been examined under different constraints on the tree and on the set of paths, from which the core can be chosen. For all cases, we present linear or almost linear time algorithms, which improves the previous results. As Minieka and Patel observes [sic] (J. Algorithms, Vol. 4, 1983), the problem of finding a core of limited length would be simplified, if the core always contained the median, m. They conclude their paper by writing 'we do not know if a core of length l will contain m. Unfortunately, this situation remains unexplored and as this question remains open, the development of an efficient algorithm for locating a core of a specified length remains a difficult problem.' We show that the median is not necessarily included in the core and give an O(n min [log n[alpha](n, n), l]) algorithm for the problem, which improves the former best result O(n min [n², l log n])(Lo and Peng, J. Algorithms Vol. 20, 1996 and Minieka, Networks Vol, 15, 1985)."
Beschreibung:	10 S.