New Results for the 2-Interval Pattern Problem - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2004

New Results for the 2-Interval Pattern Problem

Résumé

We present new results concerning the problem of finding a constrained pattern in a set of 2-intervals. Given a set of n 2-intervals D and a model R describing if two disjoint 2-intervals can be in precedence order ($<$), be allowed to nest ($\sqsubset$) and/or be allowed to cross $(\between$), we consider the problem of finding a maximum cardinality subset $\D' \subseteq \D$ of disjoint $2$-intervals such that any two $2$-intervals in $\D'$ agree with $R$. We improve the time complexity of the best known algorithm for $R = \{\sqsubset\}$ by giving an optimal O(n log n) time algorithm. Also, we give a graph-like relaxation for $R = \{\sqsubset,\between\}$ that is solvable in $O(n^2 \sqrt{n})$ time. Finally, we prove that the problem is NP-complete for $R = \{<,\between\}$ and in addition to that, we give a fixed-parameter tractability result based on the crossing structure of D.
Fichier principal
Vignette du fichier
hal.pdf (319.36 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00620366 , version 1 (30-09-2011)

Identifiants

  • HAL Id : hal-00620366 , version 1

Citer

Guillaume Blin, Guillaume Fertin, Stéphane Vialette. New Results for the 2-Interval Pattern Problem. 15th Symposium on Combinatorial Pattern Matching (CPM'04), Jul 2004, Istanbul, Turkey, Turkey. pp.311-322. ⟨hal-00620366⟩
197 Consultations
203 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More