A streaming, certificate-based reduction for convex hull preservation in planar point sets.

Abstract

Convex hull computation on large planar point sets is commonly preceded by geometric filtering to reduce input size. Motivated by invariants used in incremental convex hull maintenance, we derive a streaming, certificate-based reduction that discards only points certified interior to the hull. We show that the reduction preserves the exact convex hull and operates in a single streaming pass with only local geometric operations. Experiments on synthetic and real-world datasets demonstrate substantial reduction, retaining between 5% and 11% of input points on average for synthetic distributions and below 1% on large real-world data under typical arrival order.