Speeding up isosurface extraction using interval trees

1997 ◽  
Vol 3 (2) ◽  
pp. 158-170 ◽  
Author(s):  
P. Cignoni ◽  
P. Marino ◽  
C. Montani ◽  
E. Puppo ◽  
R. Scopigno
Keyword(s):  
Isosurface Extraction ◽  
Interval Trees

scholarly journals Augmented Interval List: a novel data structure for efficient genomic interval search

2019 ◽  
Vol 35 (23) ◽  
pp. 4907-4911 ◽  
Author(s):  
Jianglin Feng ◽  
Aakrosh Ratan ◽  
Nathan C Sheffield
Keyword(s):  
Data Structure ◽  
High Performance ◽  
Genomic Analysis ◽  
Genomic Data ◽  
Interval Data ◽  
Supplementary Information ◽  
Genomic Interval ◽  
Interval Trees ◽  
Running Maximum ◽  
Scalable Methods

Abstract Motivation Genomic data is frequently stored as segments or intervals. Because this data type is so common, interval-based comparisons are fundamental to genomic analysis. As the volume of available genomic data grows, developing efficient and scalable methods for searching interval data is necessary. Results We present a new data structure, the Augmented Interval List (AIList), to enumerate intersections between a query interval q and an interval set R. An AIList is constructed by first sorting R as a list by the interval start coordinate, then decomposing it into a few approximately flattened components (sublists), and then augmenting each sublist with the running maximum interval end. The query time for AIList is O(log2N+n+m), where n is the number of overlaps between R and q, N is the number of intervals in the set R and m is the average number of extra comparisons required to find the n overlaps. Tested on real genomic interval datasets, AIList code runs 5–18 times faster than standard high-performance code based on augmented interval-trees, nested containment lists or R-trees (BEDTools). For large datasets, the memory-usage for AIList is 4–60% of other methods. The AIList data structure, therefore, provides a significantly improved fundamental operation for highly scalable genomic data analysis. Availability and implementation An implementation of the AIList data structure with both construction and search algorithms is available at http://ailist.databio.org. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Paths in m-ary interval trees

2004 ◽  
Vol 287 (1-3) ◽  
pp. 45-53 ◽  
Author(s):  
Mehri Javanian ◽  
Hosam Mahmoud ◽  
Mohammad Vahidi-Asl
Keyword(s):  
Interval Trees

scholarly journals Multiresolution Isosurface Extraction with Adaptive Skeleton Climbing

1998 ◽  
Vol 17 (3) ◽  
pp. 137-147 ◽  
Author(s):  
Tim Poston ◽  
Tien-Tsin Wong ◽  
Pheng-Ann Heng
Keyword(s):  
Isosurface Extraction

scholarly journals AVERAGE-CASE ANALYSIS OF PERFECT SORTING BY REVERSALS

2011 ◽  
Vol 03 (03) ◽  
pp. 369-392 ◽  
Author(s):  
MATHILDE BOUVEL ◽  
CEDRIC CHAUVE ◽  
MARNI MISHNA ◽  
DOMINIQUE ROSSIN
Keyword(s):  
Average Length ◽  
Algorithm Analysis ◽  
Sorting Algorithm ◽  
Average Case Analysis ◽  
Signed Permutation ◽  
Average Case ◽  
Combinatorial Properties ◽  
Sorting By Reversals ◽  
Identity Permutation ◽  
Interval Trees

Perfect sorting by reversals, a problem originating in computational genomics, is the process of sorting a signed permutation to either the identity or to the reversed identity permutation, by a sequence of reversals that do not break any common interval. Bérard et al. (2007) make use of strong interval trees to describe an algorithm for sorting signed permutations by reversals. Combinatorial properties of this family of trees are essential to the algorithm analysis. Here, we use the expected value of certain tree parameters to prove that the average run-time of the algorithm is at worst, polynomial, and additionally, for sufficiently long permutations, the sorting algorithm runs in polynomial time with probability one. Furthermore, our analysis of the subclass of commuting scenarios yields precise results on the average length of a reversal, and the average number of reversals.

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