Pattern Matching for Separable Permutations

Abstract : Given a permutation π (called the text) of size n and another permutation σ (called the pattern) of size k, the NP-complete permutation pattern matching problem asks whether σ occurs in π as an order-isomorphic subsequence. In this paper, we focus on separable permutations (those permutations that avoid both 2413 and 3142, or, equivalently, that admit a separating tree). The main contributions presented in this paper are as follows. We simplify the algorithm of Ibarra (Finding pattern matchings for permutations, Information Processing Letters 61 (1997), no. 6) to detect an occurrence of a separable permutation in a permutation and show how to reduce the space complexity from O(n3k) to O(n3logk) . In case both the text and the pattern are separable permutations, we give a more practicable O(n2k) time and O(nk) space algorithm. Furthermore, we show how to use this approach to decide in O(nk32) time whether a separable permutation of size n is a disjoint union of two given permutations of size k and ℓ . Given a permutation of size n and a separable permutation of size k, we propose an O(n6k) time and O(n4log k) space algorithm to compute the largest common separable permutation that occurs in the two input permutations. This improves upon the existing O(n8) time algorithm by Rossin and Bouvel (The longest common pattern problem for two permutations, Pure Mathematics and Applications 17 (2006)). Finally, we give a O(n6k) time and space algorithm to detect an occurrence of a bivincular separable permutation in a permutation. (Bivincular patterns generalize classical permutations by requiring that positions and values involved in an occurrence may be forced to be adjacent).
Document type :
Conference papers
Complete list of metadatas

Cited literature [14 references]  Display  Hide  Download

https://hal-upec-upem.archives-ouvertes.fr/hal-01798554
Contributor : Admin Upem <>
Submitted on : Wednesday, May 23, 2018 - 4:15:06 PM
Last modification on : Thursday, July 5, 2018 - 2:45:47 PM
Long-term archiving on : Friday, August 24, 2018 - 9:22:34 PM

File

Spire-2016.pdf
Files produced by the author(s)

Identifiers

Citation

Both Neou, Romeo Rizzi, Stéphane Vialette. Pattern Matching for Separable Permutations. SPIRE 2016, Oct 2016, Beppu, Japan. pp.260-272, ⟨10.1007/978-3-319-46049-9_25⟩. ⟨hal-01798554⟩

Share

Metrics

Record views

106

Files downloads

191