Trans-dichotomous algorithms for minimum spanning trees and shortest paths
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
New techniques for the union-find problem
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Applications of Path Compression on Balanced Trees
Journal of the ACM (JACM)
Improved Algorithms for Finding Level Ancestors in Dynamic Trees
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Space-time tradeoff for answering range queries (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Design of data structures for mergeable trees
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A scaling algorithm for weighted matching on general graphs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Data structures for mergeable trees
ACM Transactions on Algorithms (TALG)
Path minima queries in dynamic weighted trees
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
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Consider a dynamic forest of unrooted trees over a set of nvertices which we update by linkoperations: Each link operation adds a new edge adjacent to vertices in two different trees. Every edge in the forest has a weight associated with it, and at any time we want to be able to answer a path-minquery which returns that edge of minimum weight along the path between two given vertices.For the case where the weights are integers we give an algorithm that performs n茂戮驴 1 link operations and mpathmin queries in O(n+ m茂戮驴(m,n)) time. This extends well known results of Tarjan [11] and Yao [12] to a more general dynamic setting at the cost of restricting the weights to be integers. We also suggest a simpler data structures for the case where trees are rooted and the link operation always adds an edge between the root of one tree and an arbitrary vertex of another tree.