Parallel Write-Efficient Algorithms and Data Structures for Computational Geometry

TL;DR

This paper introduces parallel algorithms for computational geometry that minimize costly memory writes, leveraging a new model to address emerging non-volatile memory technologies.

Contribution

It presents novel parallel write-efficient algorithms for geometric problems using techniques like DAG tracing and prefix doubling within the Asymmetric Nested-Parallel Model.

Findings

Algorithms perform fewer writes than traditional methods.

Techniques like DAG tracing improve write-efficiency.

Applicable to various geometric data structures.

Abstract

In this paper, we design parallel write-efficient geometric algorithms that perform asymptotically fewer writes than standard algorithms for the same problem. This is motivated by emerging non-volatile memory technologies with read performance being close to that of random access memory but writes being significantly more expensive in terms of energy and latency. We design algorithms for planar Delaunay triangulation, $k$-d trees, and static and dynamic augmented trees. Our algorithms are designed in the recently introduced Asymmetric Nested-Parallel Model, which captures the parallel setting in which there is a small symmetric memory where reads and writes are unit cost as well as a large asymmetric memory where writes are $\omega$ times more expensive than reads. In designing these algorithms, we introduce several techniques for obtaining write-efficiency, including DAG tracing, prefix doubling, reconstruction-based rebalancing and $\alpha$-labeling, which we believe will be useful for designing other parallel write-efficient algorithms.