  The analysis of high-dimensional sparse data is becoming increasingly popular
in many important domains. However, real-world sparse tensors are challenging
to process due to their irregular shapes and data distributions. We propose the
Adaptive Linearized Tensor Order (ALTO) format, a novel mode-agnostic (general)
representation that keeps neighboring nonzero elements in the multi-dimensional
space close to each other in memory. To generate the indexing metadata, ALTO
uses an adaptive bit encoding scheme that trades off index computations for
lower memory usage and more effective use of memory bandwidth. Moreover, by
decoupling its sparse representation from the irregular spatial distribution of
nonzero elements, ALTO eliminates the workload imbalance and greatly reduces
the synchronization overhead of tensor computations. As a result, the parallel
performance of ALTO-based tensor operations becomes a function of their
inherent data reuse. On a gamut of tensor datasets, ALTO outperforms an oracle
that selects the best state-of-the-art format for each dataset, when used in
key tensor decomposition operations. Specifically, ALTO achieves a geometric
mean speedup of 8X over the best mode-agnostic (coordinate and hierarchical
coordinate) formats, while delivering a geometric mean compression ratio of
4.3X relative to the best mode-specific (compressed sparse fiber) formats.
