Years and Authors of Summarized Original Work
2012; Munro, Raman, Raman, Rao
2012; Barbay, Fischer, Navarro
2013; Barbay, Navarro
2013; Barbay
Problem Definition
A basic building block for compressed data structures for texts and functions is the representation of a permutation of the integers {1, …, n}, denoted by [1… n]. A permutation π is trivially representable in \(n\lceil \lg n\rceil \) bits which is within O(n) bits of the information theoretic bound of \(\lg (n!)\), but instances from restricted classes of permutations can be represented using much less space.
We are interested in encodings of permutations that can efficiently access them. Given a permutation π over [1… n], an integer k and an integer i ∈ [1… n], data structures on permutations aim to support the following operators as fast as possible, using as little additional space as possible:
π(i): application of the permutation to i,
π−1(i): application of the inverse permutation to i,
π(k)(i): π() iteratively applied k...
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Ian Munro J, Raman R, Raman V, Srinivasa Rao S (2012) Succinct representations of permutations and functions. Theorical Computer Science (TCS) 438:74–88
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Barbay, J. (2016). Succinct and Compressed Data Structures for Permutations and Integer Functions. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_411
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