[Paper Review] Binary Interval Search (BITS): A Scalable Algorithm for Counting Interval Intersections

Ryan M. Layer, Kevin Skadron+3 more|arXiv (Cornell University)|Aug 16, 2012

Software Testing and Debugging Techniques7 references4 citations

TL;DR

BITS is a novel, scalable algorithm for counting genomic interval intersections using two binary searches to efficiently compute overlap counts in Θ(N log N) time, outperforming existing tools. It is inherently parallelizable, enabling highly efficient GPU-accelerated Monte Carlo simulations for statistical significance testing across large-scale genomics datasets.

ABSTRACT

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 is, they overlap and thus share a common genome interval. Given the continued advances in DNA sequencing technologies, efficient methods for measuring statistically significant relationships between many sets of genomic features is crucial for future discovery. Results: We introduce the Binary Interval Search (BITS) algorithm, a novel and scalable approach to interval set intersection. We demonstrate that BITS outperforms existing methods at counting interval intersections. Moreover, we show that BITS is intrinsically suited to parallel computing architectures such as Graphics Processing Units (GPUs) by illustrating its utility for efficient Monte-Carlo simulations measuring the significance of relationships between sets of genomic intervals.

Motivation & Objective

• Address the growing computational challenge of analyzing billions of genomic intervals from high-throughput sequencing.
• Develop a scalable algorithm for counting interval intersections that outperforms existing methods in both sequential and parallel execution.
• Enable efficient statistical significance testing of interval relationships using Monte Carlo simulations on large genomic datasets.
• Design an algorithm inherently suited for parallel architectures like GPUs to accelerate large-scale genomics workloads.
• Facilitate unbiased, high-throughput screening of functional relationships among diverse genomics features (e.g., transcription factors, epigenetic marks).

Proposed method

• Apply two binary searches—one on interval start and one on end coordinates—to directly compute the number of intersections without enumerating all pairs.
• Use a divide-and-conquer strategy based on sorting intervals and leveraging binary search to exclude non-overlapping intervals efficiently.
• Achieve Θ(N log N) time complexity by reducing the problem to a series of binary searches, proven optimal via reduction to element uniqueness.
• Design the algorithm to be work-efficient and load-balanced, minimizing thread divergence for high-performance execution on GPUs.
• Implement a GPU-optimized version (BITS-CUDA) that leverages parallel threads to perform independent binary searches across interval sets.
• Integrate BITS into Monte Carlo simulations to compare observed interval intersections against randomized null distributions for statistical significance.

Experimental results

Research questions

• RQ1 Can a binary search-based approach outperform existing enumeration-based methods in counting interval intersections for large-scale genomics datasets?
• RQ2 To what extent is the BITS algorithm parallelizable and efficient on GPU architectures for large-scale genomics workloads?
• RQ3 How does the performance of BITS compare to established tools like BEDTools and UCSC tools in terms of speed and scalability?
• RQ4 Can BITS enable feasible large-scale, unbiased screening of functional relationships among diverse genomic features across multiple cell types?
• RQ5 What insights into genome biology can be uncovered through high-throughput, statistically rigorous analysis of interval intersections using BITS?

Key findings

• The sequential version of BITS outperforms existing tools such as BEDTools and UCSC tools in counting interval intersections across large datasets.
• BITS achieves Θ(N log N) time complexity, which is optimal for the interval intersection counting problem, as proven by reduction to element uniqueness.
• The algorithm is intrinsically suited for GPU parallelization, with minimal thread divergence and no performance overhead, enabling efficient execution on highly parallel architectures.
• A single GPU running BITS-CUDA completed a 10,000-iteration Monte Carlo simulation involving 4 billion intervals and over 44 trillion comparisons in just under 6 days (9,069 minutes).
• The same analysis would require at least 112 traditional CPUs using conventional tools, demonstrating a 100x+ performance gain with BITS-CUDA.
• Application of BITS to ENCODE data revealed biologically meaningful patterns, including widespread enrichment of transcription factor binding sites and unexpected associations with segmental duplications, highlighting its utility in uncovering novel genomic relationships.