This repository attempts to compare the performance of an S2 based geospatial indexing strategy in CockroachDB to the PostGIS implementation in Postgres.
A spatial index is commonly used on top of objects existing in an infinite 2d plane (projected maps) or a sphere (the Earth). This index can be used to speed up queries of various types: contains (what indexed objects does this object contain), containing (what indexed objects contain this object), intersection (what indexes objects overlap this object), and nearest-neighbors (what are the K nearest objects in the index to this object).
Typically, geospatial indexes operate using approximations of the objects they contain. Example: PostGIS indexes consist of rectangular bounding boxes. This means the index will not give exact answers, it will give a list with false positives but no false negatives. A slower exact computation will then be run on the results from the index. (Note that from an index's perspective, "intersection" is simply the union of "contains" and "containing").
Implemented here is a possible mechanism for building geospatial indexes in CockroachDB using the S2 geometry library. Unlike the divide-the-objects approach used in PostGIS, S2's divide-the-space approach maps much better to CockroachDB's KV model. As explained in the SIFT paper, divide-the-space also maps much better to horizontal distribution.
A full exploration of how S2 works is out of scope of this README (the link has a lot of background), but at a high level, a sphere representing the Earth is divided into 6 30-level quadtrees of "cells". These cells are content-addressed, meaning it's possible to map the identifier of the cell to its position in the tree with no external information. To index an object, a "covering" of one or more cells is computed and saved in an inverted index of cell -> primary key. Queries of types "contains" and type "containing" then can be implemented using two key properties of S2 cell identifiers.
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There is a function that maps S2 cell identifers to strings (ditto for uint64s) such that every cell (of every size) contained by a cell is expressible as a range query (which returns no unrelated cells). This is how "contains" is implemented. Compute a covering of the query object and, for each cell in the covering, run a range query on the inverted index, union'ing and distinct'ing the results.
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This same mapping also allows computing the string (or uint64) for each "parent" (containing) of a given cell. A "containing" query is then the union+distinct of all parent cells of the cells in a covering. In the worst case, this is
O(cells in covering) * O(levels in tree = 31), but typical coverings will share most of their parent cells, making this much closer toO(cells in covering) + O(levels in tree = 31)in practice.
A real world dataset of roads was converted into CSV and imported into both CockroachDB and PostGIS. A second table representing the inverted index that CockroachDB would use was created and imported only into CockroachDB.
The index part of "contains", "containing", and "intersects" operations were benchmarked, skipping the followup exact match filter for now. "nearest-neighbor" is not implemented yet. The benchmarks come in three flavors of needle shape: cell (the exact bounds of an S2 cell - best case for S2), cap (everything within some distance of a point), and rect (a rectangular box). The query shapes were scaled from ~1 meter to ~6000 meters to see the effect of fetching more data.
In the following, meters is the approximate scaling, numQ is the number of
queries actually run, p* are latency percentiles, and count* are percentiles
for how many results were returned.
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Both index time and query time were run with 4-cell coverings here. Defaults for these are something to tune (and possibly will end up as an index option for advanced users).
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This corresponds to exactly one S2 cell, the best case for S2.
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Note that a very similar number of results are returned for both impls. This is good as they'd have to run the exact filtering computation on a similar number of things.
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For the most part, CockroachDB appears to be about half as fast. Unclear whether this is due to our geospatial indexing or due to more general performances differences between the two systems.
Note that CockroachDB has a baseline latency that is almost double that of postgres: 0.48ms vs 0.22 ms. However, each query was returning a count, so I assume this overhead disappears in the noise for larger query sizes.
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Key insight One big difference between PostGIS and our S2 impl is that each primary key is stored once per cell in the covering in CockroachDB but exactly once in Postgres. This means the Cockroach retrieval query had to
distinctbefore it counts but PostGIS doesn't. To attempt to measure this, I ran with 1 cell coverings in CockroachDB, which then means we can skip the distinct. This generates some absurd coverings, so it probably isn't viable, but it should give us an idea of the overhead.
S2 in CockroachDB (4 cell index/4 cell query)
level__meters_____numQ_pMin(ms)__p50(ms)__p95(ms)__p99(ms)_pMax(ms)__count50__count95__count99_countMax
8 39092 100 1.11 9.44 18.87 46.14 48.23 3711 6399 17407 17407
9 19546 100 0.92 3.15 6.55 8.91 10.49 863 2047 3199 3967
10 9773 100 0.72 1.31 3.41 5.24 6.03 255 895 1343 1727
11 4886 100 0.62 0.95 2.03 3.54 3.80 75 367 495 639
12 2443 100 0.51 0.75 1.18 2.62 3.80 22 123 159 247
13 1221 100 0.49 0.72 1.11 1.18 1.25 12 57 71 75
14 610 100 0.51 0.72 1.05 1.70 3.41 4 22 37 51
15 305 100 0.49 0.69 1.64 4.72 5.51 3 9 20 20
16 152 100 0.52 0.69 1.18 3.15 4.06 2 6 8 8
17 76 100 0.52 0.69 1.11 1.44 3.28 1 4 4 5
18 38 100 0.52 0.69 1.05 1.18 1.90 1 3 6 6
19 19 100 0.51 0.69 1.18 1.57 3.41 0 2 3 3
20 9 100 0.59 0.92 1.11 3.01 12.06 0 1 2 2
PostGIS
level__meters_____numQ_pMin(ms)__p50(ms)__p95(ms)__p99(ms)_pMax(ms)__count50__count95__count99_countMax
8 39092 100 0.59 2.49 14.68 20.97 31.46 3583 6399 17407 17407
9 19546 100 0.52 1.11 7.08 8.13 13.11 799 1983 3071 3967
10 9773 100 0.36 0.62 3.28 4.19 4.46 223 831 1279 1599
11 4886 100 0.33 0.49 3.01 3.28 4.98 57 303 463 575
12 2443 100 0.28 0.41 2.10 3.93 4.46 14 99 107 215
13 1221 100 0.23 0.39 1.64 3.15 3.28 6 37 41 43
14 610 100 0.22 0.39 1.18 3.01 3.67 2 12 17 22
15 305 100 0.25 0.36 1.57 2.23 5.51 1 4 6 14
16 152 100 0.26 0.36 0.82 1.57 1.77 0 2 4 5
17 76 100 0.26 0.36 0.85 2.88 19.92 0 1 2 3
18 38 100 0.28 0.36 0.56 3.01 3.41 0 1 2 4
19 19 100 0.25 0.36 0.72 3.15 3.28 0 0 0 3
20 9 100 0.28 0.39 0.62 1.97 26.21 0 0 0 0
S2 in CockroachDB (DISTINCT unnecessary/1 cell index/1 cell query)
level__meters_____numQ_pMin(ms)__p50(ms)__p95(ms)__p99(ms)_pMax(ms)__count50__count95__count99_countMax
8 39092 100 0.66 2.03 3.67 7.34 7.86 3455 6143 17407 17407
9 19546 100 0.59 1.05 1.64 2.10 2.23 767 1919 3071 3839
10 9773 100 0.56 0.79 1.18 2.23 4.98 223 799 1279 1535
11 4886 100 0.56 0.72 0.98 1.18 1.25 55 303 447 575
12 2443 100 0.56 0.69 0.98 1.11 1.18 14 99 107 215
13 1221 100 0.52 0.69 1.02 1.05 1.64 6 37 41 41
14 610 100 0.46 0.72 0.88 1.18 2.62 2 12 17 21
15 305 100 0.46 0.69 1.02 2.75 3.01 1 3 6 14
16 152 100 0.48 0.69 0.95 1.18 1.18 0 2 4 5
17 76 100 0.52 0.69 0.98 1.25 1.57 0 1 2 3
18 38 100 0.51 0.69 0.92 1.11 1.25 0 1 2 4
19 19 100 0.52 0.69 1.02 1.25 1.38 0 0 0 3
20 9 100 0.52 0.72 0.98 1.05 5.77 0 0 0 0
S2 in CockroachDB (DISTINCT unnecessary/1 cell index/4 cell query)
level__meters_____numQ_pMin(ms)__p50(ms)__p95(ms)__p99(ms)_pMax(ms)__count50__count95__count99_countMax
8 39092 100 0.82 3.54 5.77 15.20 15.73 3455 6143 17407 17407
9 19546 100 0.72 1.44 2.49 3.15 4.06 767 1919 3071 3839
10 9773 100 0.59 0.92 1.57 1.97 2.03 223 799 1279 1535
11 4886 100 0.59 0.82 1.18 1.31 1.38 55 303 447 575
12 2443 100 0.56 0.72 1.18 1.25 1.44 14 99 107 215
13 1221 100 0.52 0.72 1.02 1.25 1.25 6 37 41 41
14 610 100 0.52 0.72 1.11 1.25 3.28 2 12 17 21
15 305 100 0.52 0.72 1.02 1.25 1.51 1 3 6 14
16 152 100 0.51 0.72 0.95 1.18 1.25 0 2 4 5
17 76 100 0.52 0.69 0.98 1.25 1.38 0 1 2 3
18 38 100 0.52 0.72 1.05 1.25 1.51 0 1 2 4
19 19 100 0.56 0.75 1.05 1.25 1.25 0 0 0 3
20 9 100 0.59 0.82 1.11 3.15 11.01 0 0 0 0
S2 in CockroachDB (counts are wrong/4 cell index/1 cell query)
level__meters_____numQ_pMin(ms)__p50(ms)__p95(ms)__p99(ms)_pMax(ms)__count50__count95__count99_countMax
8 39092 100 1.05 6.03 12.06 27.26 27.26 14335 25599 69631 69631
9 19546 100 0.72 1.97 4.46 6.29 39.85 3199 7935 12799 15359
10 9773 100 0.56 0.98 2.03 2.62 3.01 959 3327 5375 6399
11 4886 100 0.49 0.75 1.25 1.38 1.90 271 1343 1919 2431
12 2443 100 0.44 0.66 0.98 1.05 1.25 71 447 511 927
13 1221 100 0.43 0.62 0.88 0.95 1.25 33 183 207 223
14 610 100 0.43 0.62 0.85 1.11 1.11 11 63 91 143
15 305 100 0.44 0.59 0.88 1.02 1.11 7 25 43 61
16 152 100 0.44 0.59 0.82 1.18 1.57 4 13 22 24
17 76 100 0.43 0.59 0.82 0.98 1.11 1 8 12 12
18 38 100 0.39 0.59 0.75 0.92 0.92 1 7 14 20
19 19 100 0.38 0.62 0.98 1.18 1.77 0 3 5 9
20 9 100 0.48 0.72 0.95 3.80 4.72 0 2 2 3
S2 in CockroachDB without DISTINCT (counts are wrong/4 cell index/4 cell query)
level__meters_____numQ_pMin(ms)__p50(ms)__p95(ms)__p99(ms)_pMax(ms)__count50__count95__count99_countMax
8 39092 100 1.02 7.86 14.68 37.75 37.75 14335 25599 69631 69631
9 19546 100 0.92 2.49 5.24 6.55 8.91 3199 7935 12799 15359
10 9773 100 0.59 1.11 2.62 3.41 3.93 959 3327 5375 6399
11 4886 100 0.52 0.85 1.51 1.64 1.84 271 1343 1919 2431
12 2443 100 0.51 0.72 1.11 1.25 1.31 71 447 511 927
13 1221 100 0.49 0.69 1.02 1.18 1.38 33 183 207 223
14 610 100 0.48 0.66 0.95 1.11 1.18 11 63 91 143
15 305 100 0.46 0.62 0.95 1.11 1.25 7 25 43 61
16 152 100 0.48 0.62 0.88 0.98 1.02 4 13 22 24
17 76 100 0.48 0.62 0.95 1.05 1.11 1 8 12 12
18 38 100 0.48 0.62 0.92 1.18 1.18 1 7 14 20
19 19 100 0.49 0.66 1.02 1.05 1.51 0 3 5 9
20 9 100 0.56 0.82 1.05 1.44 11.01 0 2 2 3
S2 in Postgres (4 cell index/4 cell query)
level__meters_____numQ_pMin(ms)__p50(ms)__p95(ms)__p99(ms)_pMax(ms)__count50__count95__count99_countMax
8 39092 100 2.49 33.55 88.08 130.02 184.55 3711 6399 17407 17407
9 19546 100 2.10 8.91 24.12 29.36 30.41 863 2047 3199 3967
10 9773 100 0.75 2.75 7.34 11.53 13.11 255 895 1343 1727
11 4886 100 0.39 1.18 4.98 5.77 6.03 75 367 495 639
12 2443 100 0.29 0.62 2.23 4.19 4.72 22 123 159 247
13 1221 100 0.24 0.56 2.49 2.88 3.41 12 57 71 75
14 610 100 0.21 0.39 0.88 2.62 2.75 4 22 37 51
15 305 100 0.25 0.34 1.05 2.88 16.25 3 9 20 20
16 152 100 0.21 0.33 0.72 0.98 2.62 2 6 8 8
17 76 100 0.22 0.33 0.88 2.36 3.01 1 4 4 5
18 38 100 0.23 0.33 0.72 2.49 2.49 1 3 6 6
19 19 100 0.25 0.34 2.36 2.62 2.62 0 2 3 3
20 9 100 0.28 0.41 0.79 2.49 9.44 0 1 2 2
S2 in CockroachDB (4 cell index/4 cell query)
level__meters_____numQ_pMin(ms)__p50(ms)__p95(ms)__p99(ms)_pMax(ms)__count50__count95__count99_countMax
8 39092 100 0.52 0.82 1.18 1.31 1.31 1 4 8 8
9 19546 100 0.52 0.85 1.18 1.64 1.90 3 6 8 11
10 9773 100 0.56 0.85 1.25 1.38 1.38 4 8 9 11
11 4886 100 0.69 0.88 1.31 1.44 1.51 5 10 13 19
12 2443 100 0.69 0.88 1.38 1.44 1.97 5 13 15 15
13 1221 100 0.69 0.95 1.44 1.77 3.15 7 12 16 19
14 610 100 0.75 0.95 1.51 5.24 5.51 7 13 17 20
15 305 100 0.75 0.98 1.44 1.90 31.46 8 14 20 24
16 152 100 0.75 0.98 1.31 6.03 8.91 8 14 17 28
17 76 100 0.75 0.98 1.38 1.51 1.90 9 14 21 33
18 38 100 0.79 1.02 1.38 3.28 3.41 9 17 20 22
19 19 100 0.85 1.05 1.64 3.41 3.67 8 16 21 23
20 9 100 0.82 1.11 1.51 1.70 1.77 9 18 22 24
PostGIS
level__meters_____numQ_pMin(ms)__p50(ms)__p95(ms)__p99(ms)_pMax(ms)__count50__count95__count99_countMax
8 39092 100 0.23 0.31 0.51 0.56 0.59 0 0 0 0
9 19546 100 0.25 0.31 0.51 0.66 0.82 0 4 4 6
10 9773 100 0.25 0.31 0.39 0.51 0.52 0 4 5 5
11 4886 100 0.25 0.33 0.48 0.56 0.56 0 4 5 6
12 2443 100 0.25 0.34 0.59 0.59 1.25 1 5 6 6
13 1221 100 0.26 0.34 0.49 0.56 0.62 2 6 7 9
14 610 100 0.26 0.36 0.46 0.51 0.59 2 6 8 9
15 305 100 0.28 0.36 0.48 0.59 0.59 3 7 9 12
16 152 100 0.28 0.36 0.46 0.59 0.69 3 8 12 14
17 76 100 0.26 0.36 0.51 0.59 0.62 3 7 9 10
18 38 100 0.26 0.36 0.48 0.62 0.69 3 8 9 12
19 19 100 0.28 0.38 0.56 0.59 0.59 3 9 13 13
20 9 100 0.28 0.38 0.51 0.62 0.88 4 9 10 11
S2 in CockroachDB (4 cell index/4 cell query)
level__meters_____numQ_pMin(ms)__p50(ms)__p95(ms)__p99(ms)_pMax(ms)__count50__count95__count99_countMax
8 39092 100 2.23 17.83 32.51 83.89 83.89 3711 6399 17407 17407
9 19546 100 1.70 5.24 10.49 16.25 19.92 863 2047 3327 3967
10 9773 100 1.25 2.36 6.55 7.60 8.91 271 895 1343 1727
11 4886 100 1.11 1.64 3.01 3.67 3.80 87 367 511 639
12 2443 100 1.05 1.44 2.75 4.06 6.82 26 135 167 255
13 1221 100 1.05 1.38 1.70 1.90 4.19 19 67 83 83
14 610 100 1.02 1.38 1.77 2.10 3.67 11 30 45 55
15 305 100 1.11 1.38 1.77 4.46 5.51 11 22 30 33
16 152 100 1.11 1.38 1.90 2.23 4.46 10 17 22 28
17 76 100 1.05 1.38 1.84 3.15 5.77 9 16 23 35
18 38 100 1.11 1.38 1.77 2.23 2.23 9 18 21 23
19 19 100 1.11 1.44 1.97 2.10 2.36 9 17 21 26
20 9 100 1.25 1.70 2.36 4.46 8.13 9 18 22 24
PostGIS
level__meters_____numQ_pMin(ms)__p50(ms)__p95(ms)__p99(ms)_pMax(ms)__count50__count95__count99_countMax
8 39092 100 0.69 1.97 5.24 6.03 6.55 3711 6655 17407 17407
9 19546 100 0.56 0.92 1.57 1.90 2.23 863 2175 3327 4095
10 9773 100 0.41 0.66 0.98 1.25 1.51 271 895 1407 1727
11 4886 100 0.38 0.56 0.75 0.82 0.82 87 367 511 639
12 2443 100 0.38 0.49 0.69 0.79 0.85 26 135 167 255
13 1221 100 0.36 0.48 0.62 0.75 0.75 17 67 75 87
14 610 100 0.36 0.46 0.62 0.72 0.75 9 28 37 57
15 305 100 0.36 0.46 0.62 0.72 0.75 9 18 26 30
16 152 100 0.38 0.44 0.56 0.59 0.59 7 13 15 16
17 76 100 0.34 0.44 0.56 0.69 0.72 7 13 14 16
18 38 100 0.36 0.44 0.56 0.72 0.72 6 11 14 15
19 19 100 0.34 0.46 0.66 0.69 0.72 6 13 17 21
20 9 100 0.38 0.46 0.62 0.72 0.98 6 11 12 14
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Download the sample dataset of roads courtesy of University of Minnesota.
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Run
go run *.go convert roads.csv.bz2 table.csv index.csvto convert the raw data into CSVs suitable for importing into CockroachDB and Postgres. -
Start CockroachDB with
--external-io-dirpointing at the directory with table.csv and index.csv. -
To create the necessary tables and fill them in CockroachDB, run:
go run *.go crdbload 'postgresql://[email protected]:26257?sslmode=disable' 'nodelocal:///table.csv' 'nodelocal:///index.csv' -
To run tests against S2 in CockroachDB, run:
go run *.go s2latencies 'postgresql://root@localhost:26257?sslmode=disable' roads.csv.bz2 -
Start Postgres and load the PostGIS extension.
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To create the necessary tables and fill them in Postgres, run:
`go run *.go pgload 'postgresql://[email protected]:5432/postgres?sslmode=disable' path/to/table.csv path/to/index.csv
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To run tests against PostGIS, run:
go run *.go pqlatencies 'postgresql://[email protected]:5432/postgres?sslmode=disable' roads.csv.bz2 -
To run tests against S2 in Postgres, run:
go run *.go s2latencies 'postgresql://[email protected]:5432/postgres?sslmode=disable' roads.csv.bz2
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