Finding Cores of Limited Length

In this paper we consider the problem of nding 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 di erent 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 (J. Algorithms, Vol. 4, 1983), the problem of nding a core of limited length would be simpli ed, 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 e cient algorithm for locating a core of a speci ed length remains a di cult problem." We show that the median is not necessarily included in the core and give an O(nminflogn (n;n);lg) algorithm for the problem, which i...

• Type: Conference
• Year: 1997
• Where: WADS
• Authors: Stephen Alstrup, Peter W. Lauridsen, Peer Sommerlund, Mikkel Thorup
• Keywords: Algorithms, Di Erent Constraints, Limited Length, Linear Time Algorithms, WADS 1997