MRSweep: Distributed In-Memory Sweep-line for Scalable Object Intersection Problems
Bibliographic record
Abstract
Several data mining and machine learning problems can be reduced to the computational geometry problem of finding intersections of a set of geometric objects, such as intersections of line segments or rectangles/boxes. Currently, the state-of-the-art approach for addressing such intersection problems in Euclidean space is collectively known as the sweep-line or plane sweep algorithm, and has been utilized in a variety of application domains, including databases, gaming and transportation, to name a few. The idea behind sweep line is to employ a conceptual line that is swept or moved across the plane, stopping at intersection points. However, to report all K intersections among any N objects, the standard sweep line algorithm (based on the Bentley-Ottmann algorithm) has a time complexity of O((N + K)logN), therefore cannot scale to very large number of objects and cases where there are many intersections. In this paper, we propose MRSWEEP and MRSWEEP-D, two sophisticated and highly scalable algorithms for the parallelization of sweep-line and its variants. We provide algorithmic details of fully distributed in-memory versions of the proposed algorithms using the MapReduce programming paradigm in the Apache Spark cluster environment. A theoretical analysis of the proposed algorithms is presented, as well as a thorough experimental evaluation that provides evidence of the algorithms' scalability in varying levels of problem complexity. We make source code and datasets available to support the reproducibility of the results.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".