Improved algorithms for largest cardinality 2-interval pattern problem

Authors:
Hao Yuan;Linji Yang;Erdong Chen
Affiliations:
Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, P.R. China;Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, P.R. China;Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, P.R. China
Venue:
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Year:
2005

Citing 7
Cited 1

Trapezoid graphs and generalizations, geometry and algorithms

Discrete Applied Mathematics
Scheduling split intervals

SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Finding Common Subsequences with Arcs and Pseudoknots

CPM '99 Proceedings of the 10th Annual Symposium on Combinatorial Pattern Matching
On the computational complexity of 2-interval pattern matching problems

Theoretical Computer Science
Computing the similarity of two sequences with nested arc annotations

Theoretical Computer Science
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs

SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Approximating the 2-interval pattern problem

ESA'05 Proceedings of the 13th annual European conference on Algorithms

A PTAS for the weighted 2-interval pattern problem over the preceding-and-crossing model

COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

The 2-Interval Pattern problem is to find the largest constrained pattern in a set of 2-intervals. The constrained pattern is a subset of the given 2-intervals such that any pair of them are R-comparable, where model $R \subseteq \{O(dn)=O(n2) is the total length of all 2-intervals (density d is the maximum number of 2-intervals over any point). This improves previous O(n2log n) algorithm. Secondly, we use dynamic programming techniques to obtain an O(n log n + dn) algorithm for the case $R = \{ O(n2) result. Finally, we present another $O(n {\rm log} n + \mathcal{L})$ algorithm for the case $R = \{\sqsubset, \between\}$ with disjoint support(interval ground set), which improves previous $O(n^{2}\sqrt{n})$ upper bound.