Uniquely Represented Data Structures for Computational Geometry
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
History-Independent Cuckoo Hashing
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
B-Treaps: A Uniquely Represented Alternative to B-Trees
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Linear Probing with 5-wise Independence
SIAM Review
Internally deterministic parallel algorithms can be fast
Proceedings of the 17th ACM SIGPLAN symposium on Principles and Practice of Parallel Programming
History-independence: a fresh look at the case of R-trees
Proceedings of the 27th Annual ACM Symposium on Applied Computing
Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming
HIFS: history independence for file systems
Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security
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We present a strongly history independent (SHI) hash table that supports search in O(1) worst-case time, and insert and delete in O(1) expected time using O(n) data space. This matches the bounds for dynamic perfect hashing, and improves on the best previous results by Naor and Teague on history independent hashing, which were either weakly history independent, or only supported insertion and search (no delete) each in O(1) expected time. The results can be used to construct many other SHI data structures. We show straightforward constructions for SHI ordered dictionaries: for n keys from {1, . . . , n^k} searches take O(log log n) worst-case time and updates (insertions and deletions) O(log log n) expected time, and for keys in the comparison model searches take O(log n) worst-case time and updates O(log n) expected time. We also describe a SHI data structure for the order-maintenance problem. It supports comparisons in O(1) worst-case time, and updates in O(1) expected time. All structures use O(n) data space.