Binary Interval Search: a scalable algorithm for counting interval intersections

Binary Interval Search: a scalable algorithm for counting interval intersections

MOTIVATION The comparison of diverse genomic datasets is fundamental to understand genome biology. Researchers must explore many large datasets of genome intervals (e.g. genes, sequence alignments) to place their experimental results in a broader context and to make new discoveries. Relationships between genomic datasets are typically measured by identifying intervals that intersect, that is, t...

Binary Interval Search (BITS): A Scalable Algorithm for Counting Interval Intersections

Motivation: The comparison of diverse genomic datasets is fundamental to understanding genome biology. Researchers must explore many large datasets of genome intervals (e.g., genes, sequence alignments) to place their experimental results in a broader context and to make new discoveries. Relationships between genomic datasets are typically measured by identifying intervals that intersect: that ...

A Novel Search Interval Forecasting Optimization Algorithm

In this paper, we propose a novel search interval forecasting (SIF) optimization algorithm for global numerical optimization. In the SIF algorithm, the information accumulated in the previous iteration of the evolution is utilized to forecast area where better optimization value can be located with the highest probability for the next searching operation. Five types of searching strategies are ...

Gauss elimination algorithm for interval matrix

Counting Stabilized-Interval-Free Permutations

A stabilized-interval-free (SIF) permutation on [n] = {1, 2, ..., n} is one that does not stabilize any proper subinterval of [n]. By presenting a decomposition of an arbitrary permutation into a list of SIF permutations, we show that the generating function A(x) for SIF permutations satisfies the defining property: [xn−1]A(x)n = n! . We also give an efficient recurrence for counting SIF permut...