Problem Definition
A permutation on \( { \{1,\ldots,8\} } \), with two cycles and three back pointers. The full black lines correspond to the permutation, the dashed lines to the back pointers and the gray lines to the edges traversed to compute \( { \pi^{-1}(3) } \)
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All logarithms are taken to the base 2. By convention, the iterated logarithm is denoted by \( { \lg^{(i)} n } \); hence, \( { \lg\lg\lg x } \) is \( { \lg^{(3)} x } \).
Recommended Reading
Barbay, J., Golynski, A., Munro, J.I., Rao, S.S.: Adaptive searching in succinctly encoded binary relations and tree‐structured documents. In: Proceedings of the 17th Annual Symposium on Combinatorial Pattern Matching (CPM). Lecture Notes in Computer Science (LNCS), vol. 4009, pp. 24–35. Springer, Berlin (2006)
Barbay, J., He, M., Munro, J.I., Rao, S.S.: Succinct indexes for strings, binary relations and multi-labeled trees. In: Proceedings of the 18th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 680–689. ACM, SIAM (2007)
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Golynski, A., Munro, J.I., Rao, S.S.: Rank/select operations on large alphabets: a tool for text indexing. In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 368–373. ACM, SIAM (2006)
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Munro, J.I., Raman, R., Raman, V., Rao, S.S.: Succinct representations of permutations. In: Proceedings of the 30th International Colloquium on Automata, Languages and Programming (ICALP). Lecture Notes in Computer Science (LNCS), vol. 2719, pp. 345–356. Springer, Berlin (2003)
Munro, J.I., Raman, V.: Succinct representation of balanced parentheses and static trees. SIAM J. Comput. 31, 762–776 (2001)
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Barbay, J., Munro, J. (2008). Succinct Encoding of Permutations: Applications to Text Indexing. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_411
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DOI: https://doi.org/10.1007/978-0-387-30162-4_411
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