I have a large database tables that contains grid references (X and Y) associated with various objects (each with a unique object identifier) as they move with time. The objects move at approximately constant speed but random directions.
The table looks something like this….
CREATE TABLE positions (
objectId INTEGER,
x_coord INTEGER,
y_coord INTEGER,
posTime TIMESTAMP);
I want to find which two objects got closest to each other and at what time.
Finding the distance between two fixes is relatively easy – simple Pythagoras for the differences between the X and Y values should do the trick.
The first problem seems to be one of volume. The grid itself is large, 100,000 possible X co-ordinates and a similar number of Y co-ordinates. For any given time period the table might contain 10,000 grid reference positions for 1000 different objects – 10 million rows in total.
That’s not in itself a large number, but I can’t think of a way of avoiding doing a ‘product query’ to compare every fix to every other fix. Doing this with 10 million rows will produce 100 million million results.
The next issue is that I’m not just interested in the closest two fixes to each other, I’m interested in the closest two fixes from different objects.
Another issue is that I need to match time as well as position – I’m not just interested in two objects that have visited the same grid square, they need to have done so at the same time.
The other point (may not be relevant) is that the items are unlikely to every occupy exactly the same location at the same time.
I’ve got as far as a simple product query with a few sample rows, but I’m not sure on my next steps. I’m beginning to think this isn’t going something I can pull off with a single SQL query (please prove me wrong) and I’m likely to have to extract the data and subject it to some procedural programming.
Any suggestions?
I’m not sure what SE forum this best suited for – database SQL? Programming? Maths?
UPDATE - Another issue to add to the complexity, the timestamping for each object and position is irregular, one item might have a position recorded at 14:10:00 and another at 14:10:01. If these two positions are right next to each other and one second apart then they may actually represent the closest position although the time don't match!
In order to reduce the number of tested combinations you should segregate them by postime using subqueries. Also, it's recommended you create an index by postime to increase performance.
create index ix1_time on positions (postime);
Since you didn't mention any specific database I assumed PostgreSQL since it's easy to use (for me). The solution should look like:
with t as (
select distinct(postime) as pt from positions
)
select *
from t,
(
select *
from (
select
a.objectid as aid, b.objectid as bid,
a.x_coord + a.y_coord + b.x_coord + b.y_coord as dist -- fix here!
from t
join positions a on a.postime = t.pt
join positions b on b.postime = t.pt
where a.objectid <> b.objectid
) x
order by dist desc
limit 1
) y;
This SQL should compare each 10000 objects against each other on by postime. It will test 10 million combinations for each different postime value, but not against other postime values.
Please note: I used a.x_coord + a.y_coord + b.x_coord + b.y_coord as the distance formula. I leave the correct one for you to implement here.
In total it will compute 10 million x 1000 time values: a total of 10 billion comparisons. It will return the closest two points for each timepos, that is a total of 1000 rows.
Related
I have the following MYSQL table:
measuredata:
- ID (bigint)
- timestamp
- entityid
- value (double)
The table contains >1 billion entries. I want to be able to visualize any time-window. The time window can be size of "one day" to "many years". There are measurement values round about every minute in DB.
So the number of entries for a time-window can be quite different. Say from few hundrets to several thousands or millions.
Those values are ment to be visualiuzed in a graphical chart-diagram on a webpage.
If the chart is - lets say - 800px wide, it does not make sense to get thousands of rows from database if time-window is quite big. I cannot show more than 800 values on this chart anyhow.
So, is there a way to reduce the resultset directly on DB-side?
I know "average" and "sum" etc. as aggregate function. But how can I i.e. aggregate 100k rows from a big time-window to lets say 800 final rows?
Just getting those 100k rows and let the chart do the magic is not the preferred option. Transfer-size is one reason why this is not an option.
Isn't there something on DB side I can use?
Something like avg() to shrink X rows to Y averaged rows?
Or a simple magic to just skip every #th row to shrink X to Y?
update:
Although I'm using MySQL right now, I'm not tied to this. If PostgreSQL f.i. provides a feature that could solve the issue, I'm willing to switch DB.
update2:
I maybe found a possible solution: https://mike.depalatis.net/blog/postgres-time-series-database.html
See section "Data aggregation".
The key is not to use a unixtimestamp but a date and "trunc" it, avergage the values and group by the trunc'ed date. Could work for me, but would require a rework of my table structure. Hmm... maybe there's more ... still researching ...
update3:
Inspired by update 2, I came up with this query:
SELECT (`timestamp` - (`timestamp` % 86400)) as aggtimestamp, `entity`, `value` FROM `measuredata` WHERE `entity` = 38 AND timestamp > UNIX_TIMESTAMP('2019-01-25') group by aggtimestamp
Works, but my DB/index/structue seems not really optimized for this: Query for last year took ~75sec (slow test machine) but finally got only a one value per day. This can be combined with avg(value), but this further increases query time... (~82sec). I will see if it's possible to further optimize this. But I now have an idea how "downsampling" data works, especially with aggregation in combination with "group by".
There is probably no efficient way to do this. But, if you want, you can break the rows into equal sized groups and then fetch, say, the first row from each group. Here is one method:
select md.*
from (select md.*,
row_number() over (partition by tile order by timestamp) as seqnum
from (select md.*, ntile(800) over (order by timestamp) as tile
from measuredata md
where . . . -- your filtering conditions here
) md
) md
where seqnum = 1;
The problem I have is simple:
I have a set of datasets. Each dataset has within it a set of points. Each set of points is an identical a 6km spaced grid (this grid never changes). Each point has an associated value.Each dataset is unrelated, so the problem can be seen as just a single set of points.
If the value of a point exceeds a predefined threshold value then the point has to be queried against an oracle spatial database to find all line segments within a certain distance of the point.
Which is a simple enough problem to solve.
The line segments have a non-unique ID, which allow them to be grouped together into features of size 1 to 700 segments (it's all predefined topology).
Ultimately I need to know which feature IDs match against which points as well as the number of line segments for each feature match against each point.
In terms of dataset sizes:
There are around 200 datasets.
There are 56,000 points per dataset.
There is a little over 180,000 line segments in the spatially indexed database.
The line segments can be grouped into a total of 1900 features.
Usually there aren't many more than in the order of 10^3 points that exceed the threshold per dataset.
I have created a solution and it works adequately,
however I'm unhappy with the overall run times - it takes around 3min per dataset.
Normally I wouldn't mind if a precomputation task takes that long, but due to constraints this task cannot take more than an hour to run, and ideally would only take 1/2 an hour.
Currently I use SDO_WITHIN_DISTANCE to do the query, and I run this query for each and every point that exceeds the threshold:
SELECT id, count(shape) AS segments, sum(length) AS length
FROM (
SELECT shape, id, length
FROM lines_1
UNION ALL
SELECT shape, id, length
FROM lines_2
)
WHERE SDO_WITHIN_DISTANCE(
shape,
sdo_geometry(
3001,
8307,
SDO_POINT_TYPE(:lng,:lat, 0),
null,
null
),
'distance=4 unit=km'
) = 'TRUE'
GROUP BY id
This query takes around 0.4s to execute, which isn't all that bad, but it adds up for a single dataset, and is compounded over all of the datasets.
I am not overly experienced with Oracle spatial databases, so I'm not sure how to improve the speed.
Note that I cannot change the format of the incoming set of points, nor can I change the format of the database.
The only way to speed it up that I can think of is by pre computing the query for each point and storing that in a separate table, but I'd rather not do that as it more or less creates another copy of the data.
So the question is - is there a better way to do query?
I ended up precomputing my query into the following table.
+---------+---------+
| LINE_ID | VARCHAR |
| LAT | FLOAT |
| LNG | FLOAT |
+---------+---------+
There were just too many multiline segments for it to be efficient.
By precomputing it I can just lookup in the table for the relevant IDs (which ultimately was all I cared about).
The query takes less than 1/10th of the time, so it works out a lot faster.
Ultimately the tradeoff of having to recompute the point to ID mapping every week (takes about 2 hours) was worth the speed up.
My database has a directory of about 2,000 locations scattered throughout the United States with zipcode information (which I have tied to lon/lat coordinates).
I also have a table function which takes two parameters (ZipCode & Miles) to return a list of neighboring zip codes (excluding the same zip code searched)
For each location I am trying to get the neighboring location ids. So if location #4 has three nearby locations, the output should look like:
4 5
4 24
4 137
That is, locations 5, 24, and 137 are within X miles of location 4.
I originally tried to use a cross apply with my function as follows:
SELECT A.SL_STORENUM,A.Sl_Zip,Q.SL_STORENUM FROM tbl_store_locations AS A
CROSS APPLY (SELECT SL_StoreNum FROM tbl_store_locations WHERE SL_Zip in (select zipnum from udf_GetLongLatDist(A.Sl_Zip,7))) AS Q
WHERE A.SL_StoreNum='04'
However that ran for over 20 minutes with no results so I canceled it. I did try hardcoding in the zipcode and it immediately returned a list
SELECT A.SL_STORENUM,A.Sl_Zip,Q.SL_STORENUM FROM tbl_store_locations AS A
CROSS APPLY (SELECT SL_StoreNum FROM tbl_store_locations WHERE SL_Zip in (select zipnum from udf_GetLongLatDist('12345',7))) AS Q
WHERE A.SL_StoreNum='04'
What is the most efficient way of accomplishing this listing of nearby locations? Keeping in mind while I used "04" as an example here, I want to run the analysis for 2,000 locations.
The "udf_GetLongLatDist" is a function which uses some math to calculate distance between two geographic coordinates and returns a list of zipcodes with a distance of > 0. Nothing fancy within it.
When you use the function you probably have to calculate every single possible distance for each row. That is why it takes so long. SInce teh actual physical locations don;t generally move, what we always did was precalculate the distance from each zipcode to every other zip code (and update only once a month or so when we added new possible zipcodes). Once the distances are precalculated, all you have to do is run a query like
select zip2 from zipprecalc where zip1 = '12345' and distance <=10
We have something similar and optimized it by only calculating the distance of other zipcodes whose latitude is within a bounded range. So if you want other zips within #miles, you use a
where latitude >= #targetLat - (#miles/69.2) and latitude <= #targetLat + (#miles/69.2)
Then you are only calculating the great circle distance of a much smaller subset of other zip code rows. We found this fast enough in our use to not require precalculating.
The same thing can't be done for longitude because of the variation between equator and pole of what distance a degree of longitude represents.
Other answers here involve re-working the algorithm. I personally advise the pre-calculated map of all zipcodes against each other. It should be possible to embed such optimisations in your existing udf, to minimise code-changes.
A refactoring of the query, however, could be as follows...
SELECT
A.SL_STORENUM, A.Sl_Zip, C.SL_STORENUM
FROM
tbl_store_locations AS A
CROSS APPLY
dbo.udf_GetLongLatDist(A.Sl_Zip,7) AS B
INNER JOIN
tbl_store_locations AS C
ON C.SL_Zip = B.zipnum
WHERE
A.SL_StoreNum='04'
Also, the performance of the CROSS APPLY will benefit greatly if you can ensure that the udf is INLINE rather than MULTI-STATEMENT. This allows the udf to be expanded inline (macro like) for a much cleaner execution plan.
Doing so would also allow you to return additional fields from the udf. The optimiser can then include or exclude those fields from the plan depending on whether you actually use them. Such an example would be to include the SL_StoreNum if it's easily accessible from the query in the udf, and so remove the need for the last join...
In my postgres database, I have the following relationships (simplified for the sake of this question):
Objects (currently has about 250,000 records)
-------
n_id
n_store_object_id (references store.n_id, 1-to-1 relationship, some objects don't have store records)
n_media_id (references media.n_id, 1-to-1 relationship, some objects don't have media records)
Store (currently has about 100,000 records)
-----
n_id
t_name,
t_description,
n_status,
t_tag
Media
-----
n_id
t_media_path
So far, so good. When I need to query the data, I run this (note the limit 2 at the end, as part of the requirement):
select
o.n_id,
s.t_name,
s.t_description,
me.t_media_path
from
objects o
join store s on (o.n_store_object_id = s.n_id and s.n_status > 0 and s.t_tag is not null)
join media me on o.n_media_id = me.n_id
limit
2
This works fine and gives me two entries back, as expected. The execution time on this is about 20 ms - just fine.
Now I need to get 2 random entries every time the query runs. I thought I'd add order by random(), like so:
select
o.n_id,
s.t_name,
s.t_description,
me.t_media_path
from
objects o
join store s on (o.n_store_object_id = s.n_id and s.n_status > 0 and s.t_tag is not null)
join media me on o.n_media_id = me.n_id
order by
random()
limit
2
While this gives the right results, the execution time is now about 2,500 ms (over 2 seconds). This is clearly not acceptable, as it's one of a number of queries to be run to get data for a page in a web app.
So, the question is: how can I get random entries, as above, but still keep the execution time within some reasonable amount of time (i.e. under 100 ms is acceptable for my purpose)?
Of course it needs to sort the whole thing according to random criteria before getting first rows. Maybe you can work around by using random() in offset instead?
Here's some previous work done on the topic which may prove helpful:
http://blog.rhodiumtoad.org.uk/2009/03/08/selecting-random-rows-from-a-table/
I'm thinking you'll be better off selecting random objects first, then performing the join to those objects after they're selected. I.e., query once to select random objects, then query again to join just those objects that were selected.
It seems like your problem is this: You have a table with 250,000 rows and need two random rows. Thus, you have to generate 250,000 random numbers and then sort the rows by their numbers. Two seconds to do this seems pretty fast to me.
The only real way to speed up the selection is not have to come up with 250,000 random numbers, but instead lookup rows through an index.
I think you'd have to change the table schema to optimize for this case. How about something like:
1) Create a new column with a sequence starting at 1.
2) Every row will then have a number.
3) Create an index on: number % 1000
4) Query for rows where number % 1000 is equal to a random number
between 0 and 999 (this should hit the index and load a random
portion of your database)
5) You can probably then add on RANDOM() to your ORDER BY clause and
it will then just sort that chunk of your database and be 1,000x
faster.
6) Then select the first two of those rows.
If this still isn't random enough (since rows will always be paired having the same "hash"), you could probably do a union of two random rows, or have an OR clause in the query and generate two random keys.
Hopefully something along these lines could be very fast and decently random.
I have some entries in my database, in my case Videos with a rating and popularity and other factors. Of all these factors I calculate a likelihood factor or more to say a boost factor.
So I essentially have the fields ID and BOOST.The boost is calculated in a way that it turns out as an integer that represents the percentage of how often this entry should be hit in in comparison.
ID Boost
1 1
2 2
3 7
So if I run my random function indefinitely I should end up with X hits on ID 1, twice as much on ID 2 and 7 times as much on ID 3.
So every hit should be random but with a probability of (boost / sum of boosts). So the probability for ID 3 in this example should be 0.7 (because the sum is 10. I choose those values for simplicity).
I thought about something like the following query:
SELECT id FROM table WHERE CEIL(RAND() * MAX(boost)) >= boost ORDER BY rand();
Unfortunately that doesn't work, after considering the following entries in the table:
ID Boost
1 1
2 2
It will, with a 50/50 chance, have only the 2nd or both elements to choose from randomly.
So 0.5 hit goes to the second element
And 0.5 hit goes to the (second and first) element which is chosen from randomly so so 0.25 each.
So we end up with a 0.25/0.75 ratio, but it should be 0.33/0.66
I need some modification or new a method to do this with good performance.
I also thought about storing the boost field cumulatively so I just do a range query from (0-sum()), but then I would have to re-index everything coming after one item if I change it or develop some swapping algorithm or something... but that's really not elegant and stuff.
Both inserting/updating and selecting should be fast!
Do you have any solutions to this problem?
The best use case to think of is probably advertisement delivery. "Please choose a random ad with given probability"... however i need it for another purpose but just to give you a last picture what it should do.
edit:
Thanks to kens answer i thought about the following approach:
calculate a random value from 0-sum(distinct boost)
SET #randval = (select ceil(rand() * sum(DISTINCT boost)) from test);
select the boost factor from all distinct boost factors which added up surpasses the random value
then we have in our 1st example 1 with a 0.1, 2 with a 0.2 and 7 with a 0.7 probability.
now select one random entry from all entries having this boost factor
PROBLEM: because the count of entries having one boost is always different. For example if there is only 1-boosted entry i get it in 1 of 10 calls, but if there are 1 million with 7, each of them is hardly ever returned...
so this doesnt work out :( trying to refine it.
I have to somehow include the count of entries with this boost factor ... but i am somehow stuck on that...
You need to generate a random number per row and weight it.
In this case, RAND(CHECKSUM(NEWID())) gets around the "per query" evaluation of RAND. Then simply multiply it by boost and ORDER BY the result DESC. The SUM..OVER gives you the total boost
DECLARE #sample TABLE (id int, boost int)
INSERT #sample VALUES (1, 1), (2, 2), (3, 7)
SELECT
RAND(CHECKSUM(NEWID())) * boost AS weighted,
SUM(boost) OVER () AS boostcount,
id
FROM
#sample
GROUP BY
id, boost
ORDER BY
weighted DESC
If you have wildly different boost values (which I think you mentioned), I'd also consider using LOG (which is base e) to smooth the distribution.
Finally, ORDER BY NEWID() is a randomness that would take no account of boost. It's useful to seed RAND but not by itself.
This sample was put together on SQL Server 2008, BTW
I dare to suggest straightforward solution with two queries, using cumulative boost calculation.
First, select sum of boosts, and generate some number between 0 and boost sum:
select ceil(rand() * sum(boost)) from table;
This value should be stored as a variable, let's call it {random_number}
Then, select table rows, calculating cumulative sum of boosts, and find the first row, which has cumulative boost greater than {random number}:
SET #cumulative_boost=0;
SELECT
id,
#cumulative_boost:=(#cumulative_boost + boost) AS cumulative_boost,
FROM
table
WHERE
cumulative_boost >= {random_number}
ORDER BY id
LIMIT 1;
My problem was similar: Every person had a calculated number of tickets in the final draw. If you had more tickets then you would have an higher chance to win "the lottery".
Since I didn't trust any of the found results rand() * multiplier or the one with -log(rand()) on the web I wanted to implement my own straightforward solution.
What I did and in your case would look a little bit like this:
(SELECT id, boost FROM foo) AS values
INNER JOIN (
SELECT id % 100 + 1 AS counter
FROM user
GROUP BY counter) AS numbers ON numbers.counter <= values.boost
ORDER BY RAND()
Since I don't have to run it often I don't really care about future performance and at the moment it was fast for me.
Before I used this query I checked two things:
The maximum number of boost is less than the maximum returned in the number query
That the inner query returns ALL numbers between 1..100. It might not depending on your table!
Since I have all distinct numbers between 1..100 then joining on numbers.counter <= values.boost would mean that if a row has a boost of 2 it would end up duplicated in the final result. If a row has a boost of 100 it would end up in the final set 100 times. Or in another words. If sum of boosts is 4212 which it was in my case you would have 4212 rows in the final set.
Finally I let MySql sort it randomly.
Edit: For the inner query to work properly make sure to use a large table, or make sure that the id's don't skip any numbers. Better yet and probably a bit faster you might even create a temporary table which would simply have all numbers between 1..n. Then you could simply use INNER JOIN numbers ON numbers.id <= values.boost