I have lat/lon coordinates in a 400 million rows partitioned mysql table.
The table grows # 2000 records a minute and old data is flushed every few weeks.
I am exploring ways to do spatial analysis of this data as it comes in.
Most of the analysis requires finding whether a point is in a particular lat/lon polygon or which polygons contain that point.
I see the following ways of tackling the point in polygon (PIP) problem:
Create a mysql function that takes a point and a Geometry and returns a boolean.
Simple but not sure how Geometry can be used to perform operations on lat/lon co-ordinates since Geometry assumes flat surfaces and not spheres.
Create a mysql function that takes a point and identifier of a custom data structure and returns a boolean.
The polygon vertices can be stored in a table and a function can compute PIP using spherical math. Large number of polygon points may lead to a huge table and slow queries.
Leave point data in mysql and store polygon data in PostGIS and use the app server to run PIP query in PostGIS by probviding point as a parameter.
Port the application from MySQL to Postgresql/PostGIS.
This will require a lot of effort in rewriting queries and procedures.
I can still do it but how good is Postgresql at handling 400 million rows.
A quick search on google for "mysql 1 billion rows" returns many results. same query for Postgres returns no relevant results.
Would like to hear some thoughts & suggestions.
A few thoughts.
First PostgreSQL and MySQL are completely different beasts when it comes to performance tuning. So if you go the porting route be prepared to rethink your indexing strategies. Not only does PostgreSQL have a far more flexible indexing than MySQL, but the table approaches are very different also, meaning the appropriate indexing strategies are as different as the tactics are. Unfortunately this means you can expect to struggle a bit. If i could give advice I would suggest dropping all non-key indexes at first and then adding them back sparingly as needed.
The second point is that nobody here can likely give you a huge amount of practical advice at this point because we don't know the internals of your program. In PostgreSQL, you are best off indexing only what you need, but you can index functions' outputs (which is really helpful in cases like this) and you can index only part of a table.
I am more a PostgreSQL guy than a MySQL guy so of course I think you should go with PostgreSQL. However rather than tell you why etc. and have you struggle at this scale, I will tell you a few things that I would look at using if I were trying to do this.
Functional indexes
Write my own functions for indexes for related analysis
PostGIS is pretty amazing and very flexible
In the end, switching db's at this volume is going to be a learning curve, and you need to be prepared for that. However, PostgreSQL can handle the volume just fine.
The number of rows is quite irrelevant here.
The question is how much of the point in polygon work that can be done by the index.
The answer to that depends on how big the polygons are.
PostGIS is very fast to find all points in the bounding box of a polygon. Then it takes more effort to find out if the point actually is inside the polygon.
If your polygons is small (small bounding boxes) the query will be efficient. If your polygons are big or have a shape that mekes the bounding box big then it will be less efficient.
If your polygons is more or less static there is work arounds. You can divide your polygons in smaller polygons and recreate the idnex. Then the index will be more efficient.
If your polygons is actually multipolygons the firs step is to split the multipolygons to polygons with ST_Dump and recreate and build an index on the result.
HTH
Nicklas
Imagines there's a 2D space and in this space there are circles that grow at different constant rates. What's an efficient data structure for storing theses circles, such that I can query "Which circles intersect point p at time t?".
EDIT: I do realize that I could store the initial state of the circles in a spatial data structure and do a query where I intersect a circle at point p with a radius of fastest_growth * t, but this isn't efficient when there are a few circles that grow extremely quickly whereas most grow slowly.
Additional Edit: I could further augment the above approach by splitting up the circles and grouping them by there growth rate, then applying the above approach to each group, but this requires a bounded time to be efficient.
Represent the circles as cones in 3d, where the third dimension is time. Then use a BSP tree to partition them the best you can.
In general, I think the worst-case for testing for intersection is always O(n), where n is the number of circles. Most spacial data structures work by partitioning the space cleverly so that a fraction of the objects (hopefully close to half) are in each half. However, if the objects overlap then the partitioning cannot be perfect; there will always be cases where more than one object is in a partition. If you just think about the case of two circles overlapping, there is no way to draw a line such that one circle is entirely on one side and the other circle is entirely on the other side. Taken to the logical extreme, assuming arbitrary positioning of the circles and arbitrary radiuses, there is no way to partition them such that testing for intersection takes O(log(n)).
This doesn't mean that, in practice, you won't get a big advantage from using a tree, but the advantage you get will depend on the configuration of the circles and the distribution of the queries.
This is a simplified version of another problem I have posted about a week ago:
How to find first intersection of a ray with moving circles
I still haven't had the time to describe the solution that was expected there, but I will try to outline it here(for this simplar case).
The approach to solve this problem is to use a kinetic KD-tree. If you are not familiar with KD trees it is better to first read about them. You also need to add the time as additional coordinate(you make the space 3d instead of 2d). I have not implemented this idea yet, but I believe this is the correct approach.
I'm sorry this is not completely thought through, but it seems like you might look into multiplicatively-weighted Voronoi Diagrams (MWVDs). It seems like an adversary could force you into computing one with a series of well-placed queries, so I have a feeling they provide a lower-bound to your problem.
Suppose you compute the MWVD on your input data. Then for a query, you would be returned the circle that is "closest" to your query point. You can then determine whether this circle actually contains the query point at the query time. If it doesn't, then you are done: no circle contains your point. If it does, then you should compute the MWVD without that generator and run the same query. You might be able to compute the new MWVD from the old one: the cell containing the generator that was removed must be filled in, and it seems (though I have not proved it) that the only generators that can fill it in are its neighbors.
Some sort of spatial index, such as an quadtree or BSP, will give you O(log(n)) access time.
For example, each node in the quadtree could contain a linked list of pointers to all those circles which intersect it.
How many circles, by the way? For small n, you may as well just iterate over them. If you constantly have to update your spatial index and jump all over cache lines, it may end up being faster to brute-force it.
How are the centres of your circles distributed? If they cover the plane fairly evenly you can discretise space and time, then do the following as a preprocessing step:
for (t=0; t < max_t; t++)
foreach circle c, with centre and radius (x,y,r) at time t
for (int X = x-r; X < x+r; x++)
for (int Y = x-r; Y < y+r; y++)
circles_at[X][Y][T].push_back (&c)
(assuming you discretise space and time along integer boundaries, scale and offset however you like of course, and you can add circles later on or amortise the cost by deferring calculation for distant values of t)
Then your query for point (x,y) at time (t) could do a brute-force linear check over circles_at[x][y][ceil(t)]
The trade-off is obvious, increasing the resolution of any of the three dimensions will increase preprocessing time but give you a smaller bucket in circles_at[x][y][t] to test.
People are going to make a lot of recommendations about types of spatial indices to use, but I would like to offer a bit of orthogonal advice.
I think you are best off building a few indices based on time, i.e. t_0 < t_1 < t_2 ...
If a point intersects a circle at t_i, it will also intersect it at t_{i+1}. If you know the point in advance, you can eliminate all circles that intersect the point at t_i for all computation at t_{i+1} and later.
If you don't know the point in advance, then you can keep these time-point trees (built based on the how big each circle would be at a given time). At query time (e.g. t_query), find i such that t_{i-1} < t_query <= t_i. If you check all the possible circles at t_i, you will not have any false negatives.
This is sort of a hack for a data structure that is "time dynamics aware", but I don't know of any. If you have a threaded environment, then you only need to maintain one spacial index and be working on the next one in the background. It will cost you a lot of computation for the benefit of being able to respond to queries with low latency. This solution should be compared at the very least to the O(n) solution (go through each point and check if dist(point, circle.center) < circle.radius).
Instead of considering the circles, you can test on their bounding boxes to filter out the ones which do not contain the point. If your bounding box sides are all sorted, this is essentially four binary searches.
The tricky part is reconstructing the sorted sides for any given time, t. To do that, you can start off with the original points: two lists for the left and right sides with the x coordinate, and two lists for top and bottom with the y coordinates. For any time greater than 0, all the left side points will move to left, etc. You only need to check each location to the one next to it to obtain a points where the element and the one next to it are are swapped. This should give you a list of time points to modify your ordered lists. If you now sort these modification records by time, for any given starting time and an ending time you can extract all the modification records between the two, and apply them to your four lists in order. I haven't completely figured out the algorithm, but I think there will be edge cases where three or more successive elements can cross over exactly at the same time point, so you may need to modify the algorithm to handle those edge cases as well. Perhaps a list modification record that contains the position in list, and the number of records to reorder would suffice.
I think it's possible to create a binary tree that solves this problem.
Each branch should contain a growing circle, a static circle for partitioning and the latest time at which the partitioning circle cleanly partitions. Further more the growing circle that is contained within a node should always have a faster growing rate than either of it's child nodes' growing circles.
To do a query, take the root node. First check it's growing circle, if it contains the query point at the query time, add it to the answer set. Then, if the time that you're querying is greater than the time at which the partition line is broken, query both children, otherwise if the point falls within the partitioning circle, query the left node, else query the right node.
I haven't quite completed the details of performing insertions, (the difficult part is updating the partition circle so that the number of nodes on the inside and outside is approximately equal and the time when the partition is broken is maximized).
To combat the few circles that grow quickly case, you could sort the circles in descending order by rate of growth and check each of the k fastest growers. To find the proper k given t, I think you can perform a binary search to find the index k such that k*m = (t * growth rate of k)^2 where m is a constant factor you'll need to find by experimentation. The will balance the part the grows linearly with k with the part that falls quadratically with the growth rate.
If you, as already suggested, represent growing circles by vertical cones in 3d, then you can partition the space as regular (may be hexagonal) grid of packed vertical cylinders. For each cylinder calculate minimal and maximal heights (times) of intersections with all cones. If circle center (vertex of cone) is placed inside the cylinder, then minimal time is zero. Then sort cones by minimal intersection time. As result of such indexing, for each cylinder you’ll have the ordered sequence of records with 3 values: minimal time, maximal time and circle number.
When you checking some point in 3d space, you take the cylinder it belongs to and iterate its sequence until stored minimal time exceeds the time of the given point. All obtained cones, which maximal time is less than given time as well, are guaranteed to contain given point. Only cones, where given time lies between minimal and maximal intersection times, are needed to recalculate.
There is a classical tradeoff between indexing and runtime costs – the less is the cylinder diameter, the less is the range of intersection times, therefore fewer cones need recalculation at each point, but more cylinders have to be indexed. If circle centers are distributed non-evenly, then it may be worth to search better cylinder placement configuration then regular grid.
P.S. My first answer here - just registered to post it. Hope it isn’t late.
I am trying to work out the most efficient query to get points within a radius of a given point. The results do not have to be very accurate so I would favor speed over accuracy.
We have tried using a where clause comparing distance of points using STDistance like this (where #point and v.GeoPoint are geography types):
WHERE v.GeoPoint.STDistance(#point) <= #radius
Also one using STIntersects similar to this:
WHERE #point.STBuffer(#radius).STIntersects(v.GeoPoint) = 1
Are either of these queries preferred or is there another function that I have missed?
If accuracy is not paramount then using the Filter function might be a good idea:
http://msdn.microsoft.com/en-us/library/cc627367.aspx
This can i many cases be orders of magnitude faster because it does not do the check to see if your match was exact.
In the index the data is stored in a grid pattern, so how viable this approach is probably depends on your spatial index options.
Also, if you don't have to many matches then doing a filter first, and then doing a full intersect might be viable.
Benefits of SPATIAL over BOUNDING
What are the benefits of using a SPATIAL query rather than a simple MySQL query that utilised a bounding box?
For example, if I wanted to find all locations that fall within a certain polygon:
Something like this:
Bounding Box Example
SELECT * FROM geoplaces
WHERE geolat BETWEEN ? AND ?
AND geolng BETWEEN ? AND ?
As I understand, the only real benefit is that spatial will also factor in the earth's curvature?
Which method is fastest also?
Advantages:
You can use shapes other than points
and rectangles, and operations other
than "is-in".
If you can use SPATIAL
indexes, performance is orders of
magnitude better (depending of
course on the size and nature of
your data).
Disadvantages:
Spatial objects are binary blobs - some care is needed handling them (e.g. you typically can't copy-paste a value).
Spatial indexes in mySQL are only available for MyISAM tables.
Support in mySQL is somewhat primitive; many operations are not implemented yet
If your database is large and you need searches like the one in your example to be fast, you should definitely go with SPATIAL indexes.
I have a x,y,z 3D points stored in MySQL,
I would like to ask the regions, slices or point neighbours.
Are there way to index the points using Peano-Hilbert curves to accelerate the queries?
Or are there more efficient way to store the 3D data in the MySQL?
thanks Arman.
I've personally never went this far, but I used a Z-curve to store 2D points. This worked quite well, and didn't feel the need to try to implement the hilbert curve for better results.
This should allow you to quickly filter out points that certainly are not close by. In an absolute worst case scenario you still need to scan more than 25% of your table to find points within an area.
The way to go about it is to split the x y z in binary and stitch them together into a single value using the curve. I wish I had a SQL script ready, but I just have one for the 2d z-curve which is a much much easier to do.
Edit:
Sorry you might already know all this already and really just looking for SQL samples, but I have some additions:
I'm not sure the 25% worst case scan is true as well for 3D planes. It might be higher, don't have the brainpower right now to tell you ;).
This type of Curve will help you find ranges of where you need to search. If you have 2 coordinates, you can convert these to the hilbert-curve number to find out which section of your table you need to look for items that do exactly match your query.
You might be able to extend this concept to find neighbours, but in order to use the curve you are still 'stuck' to look in ranges.
You can probably take the algorithm to create a geohash, and extend it to 3 coordinates. Basically, you define would have a world cube of possible 3d points, and then as you add more bits, you narrow down the cube. You then consistently define it so that the lower left hand corner has the smallest value, and you can perform range checks like:
XXXXa < the_hash < XXXXz