Worst-case and amortised optimality in union-find (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A cell probe lower bound for dynamic nearest-neighbor searching
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Meldable heaps and boolean union-find
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Optimal bounds for the predecessor problem and related problems
Journal of Computer and System Sciences - STOC 1999
On AC0 implementations of fusion trees and atomic heaps
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Time and Space Efficient Multi-method Dispatching
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Space efficient dynamic stabbing with fast queries
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Tight bounds for the partial-sums problem
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Information and Computation
Journal of Computer and System Sciences - Special issue: STOC 2003
Black box for constant-time insertion in priority queues (note)
ACM Transactions on Algorithms (TALG)
On dynamic bit-probe complexity
Theoretical Computer Science
Tight bounds for dynamic convex hull queries (again)
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Data Structures with Local Update Operations
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Orthogonal range searching in linear and almost-linear space
Computational Geometry: Theory and Applications
Data Structures for Range Median Queries
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Succinct Index for Dynamic Dictionary Matching
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
New common ancestor problems in trees and directed acyclic graphs
Information Processing Letters
On the cell probe complexity of dynamic membership
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Testing outerplanarity of bounded degree graphs
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Theoretical Computer Science
The tree inclusion problem: In linear space and faster
ACM Transactions on Algorithms (TALG)
Dynamic planar range maxima queries
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Lossless fault-tolerant data structures with additive overhead
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Path minima queries in dynamic weighted trees
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
A fast algorithm for three-dimensional layers of maxima problem
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Near real-time suffix tree construction via the fringe marked ancestor problem
SPIRE'11 Proceedings of the 18th international conference on String processing and information retrieval
Unifying the Landscape of Cell-Probe Lower Bounds
SIAM Journal on Computing
Efficient Stream Sampling for Variance-Optimal Estimation of Subset Sums
SIAM Journal on Computing
A little advice can be very helpful
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
On dynamic bit-probe complexity
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Random access to grammar-compressed strings
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Persistent predecessor search and orthogonal point location on the word RAM
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Dynamic range selection in linear space
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
A dynamic stabbing-max data structure with sub-logarithmic query time
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Research paper: The saga of minimum spanning trees
Computer Science Review
An Optimal Dynamic Data Structure for Stabbing-Semigroup Queries
SIAM Journal on Computing
String indexing for patterns with wildcards
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Connectivity oracles for planar graphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Near real-time suffix tree construction via the fringe marked ancestor problem
Journal of Discrete Algorithms
Persistent Predecessor Search and Orthogonal Point Location on the Word RAM
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
Dynamic planar point location with sub-logarithmic local updates
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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Consider a rooted tree whose nodes can be in two states: marked or unmarked. The marked ancestor problem is to maintain a data structure with the following operations: Mark(v) marks node v; unmark(v) removes any marks from node v; findfirst(v) returns the first marked node on the path from v to the root.We show tight upper and lower bounds for the marked ancestor problem. The lower bounds are proved in the cell probe model, the algorithms run on a unit-cost RAM.As easy corollaries we prove (often optimal) lower bounds on a number of problems. These include planar range searching, including the existential or emptiness problem, priority search trees, static tree union--find, and several problems from dynamic computational geometry, including segment intersection, interval maintenance, and ray shooting in the plane. Our upper bounds improve algorithms from various fields, including coloured ancestor problems and maintenance of balanced parentheses.