Years and Authors of Summarized Original Work
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2009; Belazzougui, Boldi, Pagh, Vigna
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2011; Belazzougui, Boldi, Pagh, Vigna
Problem Definition
A minimal perfect hash function is a (data structure providing a) bijective map from a set S of n keys to the set of the first n natural numbers. In the static case (i.e., when the set S is known in advance), there is a wide spectrum of solutions available, offering different trade-offs in terms of construction time, access time, and size of the data structure.
An important distinction is whether any bijection will be suitable or whether one wants it to respect some specific property. A monotone minimal perfect hash function (MMPHF) is one where the keys are bit vectors and the function is required to preserve their lexicographic order.
Sometimes in the literature, this situation is identified with the one in which the set Shas some predefined linear order and the bijection is required to respect the order: in this case, one should more...
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Recommended Reading
Belazzougui D, Boldi P, Pagh R, Vigna S (2009) Monotone minimal perfect hashing: searching a sorted table with O(1) accesses. In: Proceedings of the 20th annual ACM-SIAM symposium on discrete mathematics (SODA). ACM, New York, pp 785–794
Belazzougui D, Boldi P, Pagh R, Vigna S (2011) Theory and practice of monotone minimal perfect hashing. ACM J Exp Algorithmics 16(3):3.2:1–3.2:26
Charles DX, Chellapilla K (2008) Bloomier filters: a second look. In: Halperin D, Mehlhorn K (eds) Algorithms – ESA 2008, Proceedings of the 16th annual European symposium, Karlsruhe, 15–17 Sept 2008. Lecture notes in computer science, vol 5193. Springer, pp 259–270
Dietzfelbinger M, Pagh R (2008) Succinct data structures for retrieval and approximate membership (extended abstract). In: Aceto L, Damgård I, Goldberg LA, Halldórsson MM, Ingólfsdóttir A, Walukiewicz I (eds) Proceedings of the 35th international colloquium on automata, languages and programming, ICALP 2008, Part I: Track A: algorithms, automata, complexity, and games. Lecture notes in computer science, vol 5125. Springer, pp 385–396
Fredman ML, Komlós J (1984) On the size of separating systems and families of perfect hash functions. SIAM J Algebraic Discret Methods 5(1):61–68
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Knuth DE (1997) The art of computer programming. Sorting and searching, vol 3, 2nd edn. Addison-Wesley, Reading
Majewski BS, Wormald NC, Havas G, Czech ZJ (1996) A family of perfect hashing methods. Comput J 39(6):547–554
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Boldi, P., Vigna, S. (2016). Monotone Minimal Perfect Hash Functions. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_639
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