Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
The spatial complexity of oblivious k-probe Hash functions
SIAM Journal on Computing
Order-preserving minimal perfect hash functions and information retrieval
ACM Transactions on Information Systems (TOIS) - Special issue on research and development in information retrieval
Journal of the ACM (JACM)
SIAM Journal on Computing
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Locality preserving dictionaries: theory & application to clustering in databases
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Efficient suffix trees on secondary storage
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
Cache oblivious search trees via binary trees of small height
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Low Redundancy in Static Dictionaries with Constant Query Time
SIAM Journal on Computing
Polynomial Hash Functions Are Reliable (Extended Abstract)
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Exact and approximate membership testers
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
A locality-preserving cache-oblivious dynamic dictionary
Journal of Algorithms
Compressed data structures: Dictionaries and data-aware measures
Theoretical Computer Science
On the program size of perfect and universal hash functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
The program complexity of searching a table
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Succinct Data Structures for Retrieval and Approximate Membership (Extended Abstract)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Distributed indexing for semantic search
Proceedings of the 3rd International Semantic Search Workshop
Optimal trade-offs for succinct string indexes
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Fast prefix search in little space, with applications
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Flash memory efficient LTL model checking
Science of Computer Programming
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Minimal perfect hashing: A competitive method for indexing internal memory
Information Sciences: an International Journal
Theory and practice of monotone minimal perfect hashing
Journal of Experimental Algorithmics (JEA)
Order-preserving encryption revisited: improved security analysis and alternative solutions
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Alphabet-independent compressed text indexing
ESA'11 Proceedings of the 19th European conference on Algorithms
SILT: a memory-efficient, high-performance key-value store
SOSP '11 Proceedings of the Twenty-Third ACM Symposium on Operating Systems Principles
Improved compressed indexes for full-text document retrieval
SPIRE'11 Proceedings of the 18th international conference on String processing and information retrieval
Secure and Fast Aggregation of Financial Data in Cloud-Based Expense Tracking Applications
Journal of Network and Systems Management
New lower and upper bounds for representing sequences
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Improved compressed indexes for full-text document retrieval
Journal of Discrete Algorithms
Spaces, Trees, and Colors: The algorithmic landscape of document retrieval on sequences
ACM Computing Surveys (CSUR)
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A minimal perfect hash function maps a set S of n keys into the set {0, 1,..., n -- 1} bijectively. Classical results state that minimal perfect hashing is possible in constant time using a structure occupying space close to the lower bound of log e bits per element. Here we consider the problem of monotone minimal perfect hashing, in which the bijection is required to preserve the lexicographical ordering of the keys. A monotone minimal perfect hash function can be seen as a very weak form of index that provides ranking just on the set S (and answers randomly outside of S). Our goal is to minimise the description size of the hash function: we show that, for a set S of n elements out of a universe of 2w elements, O(n log log w) bits are sufficient to hash monotonically with evaluation time O(log w). Alternatively, we can get space O(n log w) bits with O(1) query time. Both of these data structures improve a straightforward construction with O(n log w) space and O(log w) query time. As a consequence, it is possible to search a sorted table with O(1) accesses to the table (using additional O(n log log w) bits). Our results are based on a structure (of independent interest) that represents a trie in a very compact way, but admits errors. As a further application of the same structure, we show how to compute the predecessor (in the sorted order of S) of an arbitrary element, using O(1) accesses in expectation and an index of O(n log w) bits, improving the trivial result of O(n w) bits. This implies an efficient index for searching a blocked memory.