Sparse Tensor Transpositions

TL;DR

The paper introduces Quesadilla, a new algorithm for transposing sparse tensors efficiently by minimizing sorting passes, with demonstrated improvements over existing methods in serial and parallel settings.

Contribution

It presents a novel sparse tensor transposition algorithm that exploits coordinate ordering and transposition knowledge to optimize sorting, outperforming prior approaches.

Findings

Quesadilla outperforms SPLATT in 60% of cases in serial tests.

Quesadilla and Top-2-sadilla are best in 52% of cases in parallel tests.

The algorithm reduces sorting passes, improving efficiency for scientific and data analytic tensors.

Abstract

We present a new algorithm for transposing sparse tensors called Quesadilla. The algorithm converts the sparse tensor data structure to a list of coordinates and sorts it with a fast multi-pass radix algorithm that exploits knowledge of the requested transposition and the tensors input partial coordinate ordering to provably minimize the number of parallel partial sorting passes. We evaluate both a serial and a parallel implementation of Quesadilla on a set of 19 tensors from the FROSTT collection, a set of tensors taken from scientific and data analytic applications. We compare Quesadilla and a generalization, Top-2-sadilla to several state of the art approaches, including the tensor transposition routine used in the SPLATT tensor factorization library. In serial tests, Quesadilla was the best strategy for 60% of all tensor and transposition combinations and improved over SPLATT by at least 19% in half of the combinations. In parallel tests, at least one of Quesadilla or Top-2-sadilla was the best strategy for 52% of all tensor and transposition combinations.