A linear algorithm for finding dominators in flow graphs and related problems
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
A data structure for dynamic trees
Journal of Computer and System Sciences
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
Optimal on-line decremental connectivity in trees
Information Processing Letters
Applications of Path Compression on Balanced Trees
Journal of the ACM (JACM)
A unifying look at data structures
Communications of the ACM
Meldable heaps and boolean union-find
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Improved Algorithms for Finding Level Ancestors in Dynamic Trees
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
The randomized complexity of maintaining the minimum
Nordic Journal of Computing
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Space-time tradeoff for answering range queries (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Efficient cluster compensation for lin-kernighan heuristics
Efficient cluster compensation for lin-kernighan heuristics
Approximating geometric bottleneck shortest paths
Computational Geometry: Theory and Applications
SIAM Journal on Computing
Logarithmic Lower Bounds in the Cell-Probe Model
SIAM Journal on Computing
Path Minima in Incremental Unrooted Trees
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
On Cartesian Trees and Range Minimum Queries
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
On space efficient two dimensional range minimum data structures
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
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In the path minima problem on trees each tree edge is assigned a weight and a query asks for the edge with minimum weight on a path between two nodes. For the dynamic version of the problem on a tree, where the edge-weights can be updated, we give comparison-based and RAM data structures that achieve optimal query time. These structures support inserting a node on an edge, inserting a leaf, and contracting edges. When only insertion and deletion of leaves in a tree are needed, we give two data structures that achieve optimal and significantly lower query times than when updating the edge-weights is allowed. One is a semigroup structure for which the edge-weights are from an arbitrary semigroup and queries ask for the semigroup-sum of the edge-weights on a given path. For the other structure the edge-weights are given in the word RAM. We complement these upper bounds with lower bounds for different variants of the problem.