![10
Unified Sparse Storage
Rank 1 Rank 2
key CSR CSC DCSR DCSC COO
double- fiber_ind0
compressed fiber_ptr0
compressed indptr
sparse coord0
coord1
metadata fiber_axes [0] [0]
compressed_axes [0] [0]
coord_axes [0] [1] [1] [1] [1] [0, 1]
axis_order [0] [0, 1] [1, 0] [0, 1] [1, 0] [0,1], [1,0]
optional num_sorted_coords 0 or 1 0 or 1 0 or 1 0 or 1 0 or 1 0, 1, or 2
optional has_duplicates
Minimal, cohesive set of metadata and storage keys](https://image.slidesharecdn.com/hpec2021sparsebinaryformat-210921213317/85/HPEC-2021-sparse-binary-format-10-320.jpg)
![11
Unified Sparse Storage: Rank 3
key CSF CSF (alt) CSR+extra COO DCSR+extra
double- fiber_ind0
compressed fiber_ptr0
fiber_ind1
fiber_ptr1
compressed indptr
sparse coord0
coord1
coord2
metadata fiber_axes [0, 1] [1] [0]
compressed_axes [0] [0]
coord_axes [2] [2] [1, 2] [0, 1, 2] [1, 2]
axis_order
optional num_sorted_coords 0 or 1 0 or 1 0 - 2 0 - 3 0 - 2
optional has_duplicates](https://image.slidesharecdn.com/hpec2021sparsebinaryformat-210921213317/85/HPEC-2021-sparse-binary-format-11-320.jpg)
![12
Unified Sparse Storage: Rank 2 combinations
Rank 2 Combos
key
CSR
/COO
DCSR
/CSR
DCSR
/COO
DCSR/CSR
/COO
CSC
/COO
DCSC
/CSC
DCSC
/COO
DCSC/CSC
/COO
double- fiber_ind0
compressed fiber_ptr0
compressed indptr
sparse coord0
coord1
metadata fiber_axes [0] [0] [0] [0] [0] [0]
compressed_axes [0] [0] [0] [0] [0] [0]
coord_axes [0, 1] [1] [0, 1] [0, 1] [0, 1] [1] [0, 1] [0, 1]
axis_order [0, 1] [0, 1] [0, 1] [0, 1] [1, 0] [1, 0] [1, 0] [1, 0]
optional num_sorted_coords 0 or 1 0 or 1 0 or 1 0 or 1 0 or 1 0 or 1 0 or 1 0 or 1
optional has_duplicates](https://image.slidesharecdn.com/hpec2021sparsebinaryformat-210921213317/85/HPEC-2021-sparse-binary-format-12-320.jpg)
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HPEC 2021 sparse binary format
- 1. 1 Binary Storage Formats for Sparse Erik Welch [email protected] September 21, 2021
- 2. 2 ● To try to improve the status quo ○ Matrix Market, FROSTT, and other text-based formats ○ COO: coordinate triples of rows, columns, and values ■ Columnar storage technology is really good! ○ Bespoke, library-specific binary formats ○ TileDB ○ Domain-specific solutions (genomics, bioimaging, neuroscience, etc.) ● To discuss and create a vision for new binary storage formats for sparse ○ “Open standard” formats that are broadly useful and widely accessible ● To determine what is most important to the people here ○ Which languages, libraries, formats, features, technologies, etc. ○ And what do you wish for? Dream big! ● To find partners and team up for the next steps ○ Prototype, analyze, communicate results, and iterate ○ Goals for 3-6 months and beyond Why are we here?
- 3. 3 ● Library developers and users ● Anybody with large sparse data or graphs ● Hardware creators and vendors ○ For example, to better optimize running workloads on GPUs or other accelerators ● Researchers ● Companies with graph workloads ● Benchmark organizers ● Maintainers of repositories of sparse data ● Virtually anybody who needs to work with sparse data or graphs Who is this for?
- 4. 4 ● Data written to long term storage ○ Any technically competent person who discovers the file 10 years later should be able to figure out how to load and use it (even if they don’t recognize the format) ● The logical model of a file format ○ Metadata about metadata ■ File extension (such as .zip or .pdf) ■ “Magic number” at beginning of file (NumPy’s .npy is x93NUMPY) ■ Version number of format ■ Any additional extensions needed to understand the metadata or data ○ Metadata ■ Data type, endianness of data, shape of sparse array, etc. ■ Info about compression ○ Data ■ Contiguous arrays of raw bytes ■ May be chunked or compressed What is a file format?
- 5. 5 An “open” file format is also about community ● More likely to succeed with more partners ● Right now, a small group (or just me) can make a lot of progress with prototyping and documenting to bootstrap the effort ○ Along with feedback from LAGraph group and others ● We’ll want more partners eventually ● Please think about how/when you can help ○ Student projects ○ Volunteer to be beta users, give feedback ○ Participate in this session ● We’ll need a governance model eventually ○ Hopefully! This is a good “problem” to have ○ We’re happy to have this discussion “If you want to go quickly, go alone. If you want to go far, go together.” African Proverb
- 6. 6 ● Fast enough ● Small enough ● Flexible enough ● Portable enough ● Future-proof enough ● Standardized enough ● “Cloud native” enough ● Simple enough to implement ● Easy enough to use ● Scalable enough ● Able to evolve ● And, of course, able to support whatever optimized format Tim Davis can dream up! What are our high level goals? “Pinky, are you pondering what I’m pondering?” Brain
- 7. 7 Essential sparse formats to support: rank 1 and 2 Sparse vector indices values COO (ijv triples) rows columns values CSR indptr col_indices values CSC indptr row_indices values DCSR (HyperCSR) rows indptr col_indices values DCSC (HyperCSC) columns indptr row_indices values Let’s start designing! Many others: BSR, BSRX, DIA, SCS, Skyline, ELL (ITPACK/ELLPACK), hash map, CSB, CSR5, extended row scheme, etc.
- 8. 8 Essential formats for rank N: COO and CSF http://shaden.io/pub-files/smith2017knl.pdf CSF is like DCSR/HyperCSR generalized to higher dimensions
- 9. 9 ● Metadata ○ Let’s use JSON ○ Versatile ○ Human-readable ○ No need to think about endianness of metadata values Logical model of a file ● Data ○ Like a key-value store with binary data ○ This is just a logical model ○ We are free to pack the data into bytes however we wish
- 10. 10 Unified Sparse Storage Rank 1 Rank 2 key CSR CSC DCSR DCSC COO double- fiber_ind0 compressed fiber_ptr0 compressed indptr sparse coord0 coord1 metadata fiber_axes [0] [0] compressed_axes [0] [0] coord_axes [0] [1] [1] [1] [1] [0, 1] axis_order [0] [0, 1] [1, 0] [0, 1] [1, 0] [0,1], [1,0] optional num_sorted_coords 0 or 1 0 or 1 0 or 1 0 or 1 0 or 1 0, 1, or 2 optional has_duplicates Minimal, cohesive set of metadata and storage keys
- 11. 11 Unified Sparse Storage: Rank 3 key CSF CSF (alt) CSR+extra COO DCSR+extra double- fiber_ind0 compressed fiber_ptr0 fiber_ind1 fiber_ptr1 compressed indptr sparse coord0 coord1 coord2 metadata fiber_axes [0, 1] [1] [0] compressed_axes [0] [0] coord_axes [2] [2] [1, 2] [0, 1, 2] [1, 2] axis_order optional num_sorted_coords 0 or 1 0 or 1 0 - 2 0 - 3 0 - 2 optional has_duplicates
- 12. 12 Unified Sparse Storage: Rank 2 combinations Rank 2 Combos key CSR /COO DCSR /CSR DCSR /COO DCSR/CSR /COO CSC /COO DCSC /CSC DCSC /COO DCSC/CSC /COO double- fiber_ind0 compressed fiber_ptr0 compressed indptr sparse coord0 coord1 metadata fiber_axes [0] [0] [0] [0] [0] [0] compressed_axes [0] [0] [0] [0] [0] [0] coord_axes [0, 1] [1] [0, 1] [0, 1] [0, 1] [1] [0, 1] [0, 1] axis_order [0, 1] [0, 1] [0, 1] [0, 1] [1, 0] [1, 0] [1, 0] [1, 0] optional num_sorted_coords 0 or 1 0 or 1 0 or 1 0 or 1 0 or 1 0 or 1 0 or 1 0 or 1 optional has_duplicates
- 13. 13 ● No values? ○ Index-only ● Single values array ○ Typical usage ● Multiple value arrays! ○ Different data types ○ Give them different names? ○ Allows bitmaps ○ Want ability to read only one values array ● Dense array (may be rank N) for each element ○ For example, from embeddings ● Can a fill value be given for the missing elements? Unified Sparse Storage: Values
- 14. 14 ● Straw man proposal: use asar! ○ “asar is a simple extensive archive format, it works like tar that concatenates all files together without compression, while having random access support” ● Support random access ● Use JSON to store files' information ● Very easy to write a parser How should we pack bytes into a file? Other options ● ZIP file ● LMDB ● HDF4, HDF5, CDF5, NetCDF ● Directory of files on file system ● Directory of files in cloud ○ S3, GCS, Azure, Ceph, etc. ● Zarr ● n5 ● ASDF | UInt32: header_size | String: header | Bytes: file1 | ... | Bytes: file42 |
- 15. 15 ● Arbitrary metadata via JSON ○ Able to evolve and support extensions ● Metadata scheme to specify CSR, DCSR, COO, CSF, etc. ○ Indicates what data is available and how to read it ● Single file archive that supports random access ○ Logically behaves like a key-value store ● Great, but what about extensions? ○ Support other sparse formats ○ Specify compression ○ Split single array into chunks ○ Additional data types (such as datetime) ○ Indicate variant of or option for existing format Quick recap: what do we have so far? Design goal: easily show via feature matrix which formats and extensions are supported by each language and library.
- 16. 16 ● CSR ○ “Padded” CSR: add indptr_end so column indices and values can have gaps ■ Cheaper to add or remove values ○ Column indices in a given row can be: ■ unsorted ■ sorted ■ binary tree as a binary heap ○ CSR5 ● COO ○ One array per coordinate ■ May have different data types (uint8, uint16, etc.) ○ One array for all coordinates (N x D) ○ Has duplicates or not ○ Lexicographic sort depth File format variations
- 18. 18 Graph properties ● directed / undirected ● weighted / unweighted ● is adjacency matrix ● is incidence matrix ● is bipartite graph ● is multigraph ● is hypergraph ● has self-edges ● has node attributes Matrix properties ● is upper triangular ● is lower triangular ● is diagonal ● is symmetric ● is symmetric (only upper triangle) ● is symmetric (only lower triangle) ● is iso-valued ● ndiag What about other properties? A graph is more than just a sparse matrix
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