I have formulated a solution to a problem where I am storing parameters in a set of tables, and I want to be able to look up the parameters based on multiple criteria.
For example, if criteria 1 and criteria 2 can each be either A or B, then I'd have four potential parameters - one for each combination A&A, A&B, B&A and B&B. For these sort of criteria I could concatenate the fields or something similar and create a unique key to look up each value quickly.
Unfortunately not all of my criteria are like this. Some of the criteria are numerical and I only care about whether or not a result sits above or below a boundary. That also wouldn't be a problem on its own - I could maybe use a binary search or something relatively quick to find the nearest key above or below my value.
My problem is I need to include a number of each in the same table. In other words, I could have three criteria - two with A/B entries, and one with less-than-x/greater-than-x type entries, where x is in no way fixed. So in this example I would have a table with 8 entries. I can't just do a binary search for the boundary because the closest boundary won't necessarily be applicable due to the other criteria. For example, if the first two criteria are A&B, then the closest boundary might be 100, but if the if first two criteria are A&A, the closest boundary might be 50. If I want to look up A, A, 101, then I want it to recognise that 50 is the closest boundary that applies - not 100.
I have a procedure to do the lookup but it gets very slow as the tables get bigger - it basically goes through each criteria, checks if a match is still possible, and if so it looks at more criteria - if not, it moves on to check the next entry in the table. So in other words, my procedure requires cycling through the table entries one by one and checking for a match. I have tried to optimise that by ensuring the tables that are input to the procedure are as small as possible and by making sure it looks at the criteria that are least likely to match first (so that it checks each entry as quickly as possible) but it is still very slow.
The biggest tables are maybe 200 rows with about 10 criteria to check, but many are much smaller (maybe 10x5). The issue is that I need to call the procedure many times during my application, so algorithms with some initial overhead don't necessarily make things better. I do have some scope to change the format of the tables before runtime but I would like to keep away from that as much as possible (while recognising it may be the only way forward).
I've done quite a bit of research but I haven't had any luck. Does anyone know of any algorithms that have been designed to tackle this kind of problem? I was really hoping that there would be some clever hash function or something that means I won't have to cycle through the tables, but from my limited knowledge something like that would struggle here. I feel confident that I understand the problem well enough to gradually optimise the solution I have at the moment, but I want to be sure I've not missed a much better solution.
Apologies for the very long and abstract description of the problem - hopefully it's clear what I'm trying to do. I'll amend my question if it's unclear.
Thanks for any help.
this is basically what a query optimizer does in SQL land. There are fast, free, in memory databases for exactly this purpose. Checkout sqlite https://www.sqlite.org/inmemorydb.html.
It sounds like you are doing what is called a 'full table scan' for each query, which is like the last resort for a query optimizer.
As I've understood, you want to select entries by criteria like
A& not B & x1 >= lower_x1 & x1 < upper_x1 & x2 >= lower_x2 & x2 < lower_x2 & ...
The easiest way is to have them sorted by all possible xi, where i=1,2.. in separate sets, and have separated 'words' for various combination of A,B,..
The search will works as follows:
Select a proper world by Boolean criteria combination
For each i, find the population of lower_xi..upper_xi range in corresponding set (this operation is O(log(N))
Select i where the population is the lowest
While iterating instances through lower_xi..upper_xi range, filter the results by checking other upper/lower bound criteria (for all xj where j!=i)
Note that this s a general solution. Of course if you know some relation between your bound(s), you may use a list sorted by respective combination(s) of item values.
Related
Below is my problem definition:
Given a database D, each row has m categorical attributes. Given a query which is a vector of m categorical attributes and the number of matching, k. How to find all the row ids such that the number of matching attributes to the query is greater than or equal to k efficiently?
The easier version (I think) is that given a vector of <=m-categorical attributes, how to find ids of all the rows that match those <=m-categorical attributes.
In some of the question (e.g. this), they need to scan the whole database every time the query comes in. I think this is not fast enough. I am not sure about the complexity on this actually.
If it is possible, I want to avoid scanning all the rows in the database. Therefore, I am thinking of building some kinds of index but I am wondering if there is any existing work for these?
In addition, is there a problem similar to this and what is it called? I want to take a look.
Thank you very much for your help.
(Regarding the coding, I mainly code in Python 2.7 for this.)
There is a particular class of algorithm coding problems which require us to evaluate multiple queries which can be of two kind :
Perform search over a range of data
Update the data over a given range
One example which I've been recently working on is this(though not the only one) : Quadrant Queries
Now, to optimize my algorithm, I have had one idea :
I can use dynamic programming to keep the search results for a particular range, and generate data for other ranges as required.
For example, if I have to calculate sum of numbers in an array from index 4 to 7, I can already keep sum of elements upto 4 and sum of elements upto 7 which is easy and then I'll just need the difference of the two + 4th element which is O(1). But this raises another problem : During the update operation, I'll have to update my stored search data for all the elements following the updated element. This seems to be inefficient, though I did not try it practically.
Someone suggested me that I can combine subsequent update operations using some special data structure.(Actually read it on some forum).
Question: Is there a known way to optimize these kind of problems? Is there a special data structure that does it? The idea I mentioned;Is it possible that it might be more efficient than direct approach? Should I try it out?
It might help:
Segment Trees (Range-Range part)
I have two databases that are differently formatted. Each database contains person data such as name, date of birth and address. They are both fairly large, one is ~50,000 entries the other ~1.5 million.
My problem is to compare the entries and find possible matches. Ideally generating some sort of percentage representing how close the data matches. I have considered solutions involving generating multiple indexes or searching based on Levenshtein distance but these both seem sub-optimal. Indexes could easily miss close matches and Levenshtein distance seems too expensive for this amount of data.
Let's try to put a few ideas together. The general situation is too broad, and these will be just guidelines/tips/whatever.
Usually what you'll want is not a true/false match relationship, but a scoring for each candidate match. That is because you never can't be completely sure if candidate is really a match.
The score is a relation one to many. You should be prepared to rank each record of your small DB against several records of the master DB.
Each kind of match should have assigned a weight and a score, to be added up for the general score of that pair.
You should try to compare fragments as small as possible in order to detect partial matches. Instead of comparing [address], try to compare [city] [state] [street] [number] [apt].
Some fields require special treatment, but this issue is too broad for this answer. Just a few tips. Middle initial in names and prefixes could add some score, but should be kept at a minimum (as they are many times skipped). Phone numbers may have variable prefixes and suffixes, so sometimes a substring matching is needed. Depending on the data quality, names and surnames must be converted to soundex or similar. Streets names are usually normalized, but they may lack prefixes or suffixes.
Be prepared for long runtimes if you need a high quality output.
A porcentual threshold is usually set, so that if after processing a partially a pair, and obtaining a score of less than x out of a max of y, the pair is discarded.
If you KNOW that some field MUST match in order to consider a pair as a candidate, that usually speeds the whole thing a lot.
The data structures for comparing are critical, but I don't feel my particular experience will serve well you, as I always did this kind of thing in a mainframe: very high speed disks, a lot of memory, and massive parallelisms. I could think what is relevant for the general situation, if you feel some help about it may be useful.
HTH!
PS: Almost a joke: In a big project I managed quite a few years ago we had the mother maiden surname in both databases, and we assigned a heavy score to the fact that = both surnames matched (the individual's and his mother's). Morale: All Smith->Smith are the same person :)
You could try using Full text search feature maybe, if your DBMS supports it? Full text search builds its indices, and can find similar word.
Would that work for you?
I've be told and read it everywhere (but no one dared to explain why) that when composing an index on multiple columns I should put the most selective column first, for performance reasons.
Why is that?
Is it a myth?
I should put the most selective column first
According to Tom, column selectivity has no performance impact for queries that use all the columns in the index (it does affect Oracle's ability to compress the index).
it is not the first thing, it is not the most important thing. sure, it is something to consider but it is relatively far down there in the grand scheme of things.
In certain strange, very peculiar and abnormal cases (like the above with really utterly skewed data), the selectivity could easily matter HOWEVER, they are
a) pretty rare
b) truly dependent on the values used at runtime, as all skewed queries are
so in general, look at the questions you have, try to minimize the indexes you need based on that.
The number of distinct values in a column in a concatenated index is not relevant when considering
the position in the index.
However, these considerations should come second when deciding on index column order. More importantly is to ensure that the index can be useful to many queries, so the column order has to reflect the use of those columns (or the lack thereof) in the where clauses of your queries (for the reason illustrated by AndreKR).
HOW YOU USE the index -- that is what is relevant when deciding.
All other things being equal, I would still put the most selective column first. It just feels right...
Update: Another quote from Tom (thanks to milan for finding it).
In Oracle 5 (yes, version 5!), there was an argument for placing the most selective columns first
in an index.
Since then, it is not true that putting the most discriminating entries first in the index
will make the index smaller or more efficient. It seems like it will, but it will not.
With index
key compression, there is a compelling argument to go the other way since it can make the index
smaller. However, it should be driven by how you use the index, as previously stated.
You can omit columns from right to left when using an index, i.e. when you have an index on col_a, col_b you can use it in WHERE col_a = x but you can not use it in WHERE col_b = x.
Imagine to have a telephone book that is sorted by the first names and then by the last names.
At least in Europe and US first names have a much lower selectivity than last names, so looking up the first name wouldn't narrow the result set much, so there would still be many pages to check for the correct last name.
The ordering of the columns in the index should be determined by your queries and not be any selectivity considerations. If you have an index on (a,b,c), and most of your single column queries are against column c, followed by a, then put them in the order of c,a,b in the index definition for the best efficiency. Oracle prefers to use the leading edge of the index for the query, but can use other columns in the index in a less efficient access path known as skip-scan.
The more selective is your index, the fastest is the research.
Simply imagine a phonebook: you can find someone mostly fast by lastname. But if you have a lot of people with the same lastname, you will last more time on looking for the person by looking at the firstname everytime.
So you have to give the most selective columns firstly to avoid as much as possible this problem.
Additionally, you should then make sure that your queries are using correctly these "selectivity criterias".
Currently I am loooking for a way to develop an algorithm which is supposed to analyse a large dataset (about 600M records). The records have parameters "calling party", "called party", "call duration" and I would like to create a graph of weighted connections among phone users.
The whole dataset consists of similar records - people mostly talk to their friends and don't dial random numbers but occasionaly a person calls "random" numbers as well. For analysing the records I was thinking about the following logic:
create an array of numbers to indicate the which records (row number) have already been scanned.
start scanning from the first line and for the first line combination "calling party", "called party" check for the same combinations in the database
sum the call durations and divide the result by the sum of all call durations
add the numbers of summed lines into the array created at the beginning
check the array if the next record number has already been summed
if it has already been summed then skip the record, else perform step 2
I would appreciate if anyone of you suggested any improvement of the logic described above.
p.s. the edges are directed therefore the (calling party, called party) is not equal to (called party, calling party)
Although the fact is not programming related I would like to emphasize that due to law and respect for user privacy all the informations that could possibly reveal the user identity have been hashed before the analysis.
As always with large datasets the more information you have about the distribution of values in them the better you can tailor an algorithm. For example, if you knew that there were only, say, 1000 different telephone numbers to consider you could create a 1000x1000 array into which to write your statistics.
Your first step should be to analyse the distribution(s) of data in your dataset.
In the absence of any further information about your data I'm inclined to suggest that you create a hash table. Read each record in your 600M dataset and calculate a hash address from the concatenation of calling and called numbers. Into the table at that address write the calling and called numbers (you'll need them later, and bear in mind that the hash is probably irreversible), add 1 to the number of calls and add the duration to the total duration. Repeat 600M times.
Now you have a hash table which contains the data you want.
Since there are 600 M records, it seems to be large enough to leverage a database (and not too large to require a distributed Database). So, you could simply load this into a DB (MySQL, SQLServer, Oracle, etc) and run the following queries:
select calling_party, called_party, sum(call_duration), avg(call_duration), min(call_duration), max (call_duration), count(*) from call_log group by calling_party, called_party order by 7 desc
That would be a start.
Next, you would want to run some Association analysis (possibly using Weka), or perhaps you would want to analyze this information as cubes (possibly using Mondrian/OLAP). If you tell us more, we can help you more.
Algorithmically, what the DB is doing internally is similar to what you would do yourself programmatically:
Scan each record
Find the record for each (calling_party, called_party) combination, and update its stats.
A good way to store and find records for (calling_party, called_party) would be to use a hashfunction and to find the matching record from the bucket.
Althought it may be tempting to create a two dimensional array for (calling_party, called_party), that will he a very sparse array (very wasteful).
How often will you need to perform this analysis? If this is a large, unique dataset and thus only once or twice - don't worry too much about the performance, just get it done, e.g. as Amrinder Arora says by using simple, existing tooling you happen to know.
You really want more information about the distribution as High Performance Mark says. For starters, it's be nice to know the count of unique phone numbers, the count of unique phone number pairs, and, the mean, variance and maximum of the count of calling/called phone numbers per unique phone number.
You really want more information about the analysis you want to perform on the result. For instance, are you more interested in holistic statistics or identifying individual clusters? Do you care more about following the links forward (determining who X frequently called) or following the links backward (determining who X was frequently called by)? Do you want to project overviews of this graph into low-dimensional spaces, i.e. 2d? Should be easy to indentify indirect links - e.g. X is near {A, B, C} all of whom are near Y so X is sorta near Y?
If you want fast and frequently adapted results, then be aware that a dense representation with good memory & temporal locality can easily make a huge difference in performance. In particular, that can easily outweigh a factor ln N in big-O notation; you may benefit from a dense, sorted representation over a hashtable. And databases? Those are really slow. Don't touch those if you can avoid it at all; they are likely to be a factor 10000 slower - or more, the more complex the queries are you want to perform on the result.
Just sort records by "calling party" and then by "called party". That way each unique pair will have all its occurrences in consecutive positions. Hence, you can calculate the weight of each pair (calling party, called party) in one pass with little extra memory.
For sorting, you can sort small chunks separately, and then do a N-way merge sort. That's memory efficient and can be easily parallelized.