Journal of the ACM (JACM)
Linear-time computability of combinatorial problems on series-parallel graphs
Journal of the ACM (JACM)
Graph theory: An algorithmic approach (Computer science and applied mathematics)
Graph theory: An algorithmic approach (Computer science and applied mathematics)
Maintaining Center and Median in Dynamic Trees
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Centrality measures based on current flow
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
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A general framework is presented for rapidly analyzing tree networks to compute a measure of the centrality or eccentricity of all vertices in the tree. Several problems, which have been previously described in the literature, fit this framework. Some of these problems have no published solution better than performing a separate traversal for each vertex whose eccentricity is calculated. The method presented in this paper performs just two traversals and yields the eccentricities of all vertices in the tree. Natural sufficient conditions for the algorithm to work in linear time on any given problem are stated.