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Search algorithm for partial words in C#

I'm currently looking for a way to realize a partial word pattern algorithm in C#. The situation I'm in looks like follows:
I got a textfield for the search pattern. Every time the user enters or deletes a char in this field, an event triggers which re-runs the search algorithm. So in case I want to search for the word "face" in strings like
"Facebook", "Facelifting", ""Faceless Face" (whatever that should be) or in generally ANY real life sentences as strings,
the algorithm would first start running when typing "f" in the field. It then show the most relevant String on top of a list the strings are in. The second time it runs when "fa" is typed, and the list is sorted again. This goes on until "face" is completely typed in the textfield and the list is sorted again.
However I don't know what algorithm could be used. I tried the answer from Alain (Getting the closest string match), a simple Levenshtein-Distance algorithm as well as an self-made algorithm, which calculates the priority via
priority = (length_of_typed_pattern) * (amount_of_substr_matches)
In C#, the latter looks like this:
count = Regex.Matches(Regex.Escape(title), pattern).Count;
priority = pattern.Length * count;
The pattern as well as the title are composed of only lowercase letters.
My conclusions so far:
Hamming distance won't make any sense since the strings are not the same length most of the time
The answer from Alain works fine, but only if at least one word completely matches (you only find a most relevant string/sentence when at least one word is equal with the pattern, so if you have "face" typed and there's a string containing the word "facebook", the string containing "facebook" is almost never a top priority
What other ideas could I try? The goal would be to sort the list of strings the best possible way in the earliest moment (with the fewest letters).
You can look at my implementations in the search-* branches of my repository on http://github.com/croemheld/sprung) in Sprung/WindowMatcher.cs and Sprung/Window.cs.
Thanks for your help.

First of all you need to store frequency related to a string(number of times a particular string is searched) in some place to show most relevant one when searched. If you need to show say k most relevant entries so a Min Heap of size 'k' can be implemented.
Case 1- If a letter is pressed for the first time:-
Step (a) Read all the string starting from a Data base or dictionary and store in some data structure(Say DS1) with a FLAG_VALID(set to 1 initially) which shows that it is valid string for the present search characters(for first letter all the strings will be valid).
As you read strings fill the Min Heap according to their Frequency and an element with certain frequency is inserted only when its frequency is greater than minimum one(i.e. the first element of min Heap).
Step (b) (This step is same for all case to show result) To show results you need to show elements in reverse order than Min Heap i.e. first element in Min Heap will have least priority, so basically we need to delete all elements one by one and show it from last to first.
NOTE:- Min Heap will contain reference to a particular string and so the string and its frequency can be accessed at the same time.
Case 2- Inserting next letters in search box:
Step (a) Search through DS1 in which all strings are present and check FLAG_VALID first. If it is a valid string than compare the string from search box and the string from DS1. Set the flag accordingly(if it is a match-1 or not-0) and fill k-Min Heap as it is empty from last search as in Case 1.
Step (b) is as usual.
Case 3- Deleting a letter in search box:
It is similar to above cases but this time we will need to search for those strings also whose FALG_VALID is 0(i.e string which are invalid).
This is a crude searching method and can be improved using certain Data structure and tweaking the algorithm.

Algorithm to identify similarity between text messages

I'm looking for an algorithm than can compare two text messages (let's say forum posts) and identify the similarity in percentage.
What would be the most efficient solution for this purpose?
The idea is to use this algorithm to identify users on a forum who have more than two nicknames, pretending to be different people.
I'm going to build a program that will read all their posts and compare each post from the first account to posts of the second account to find whether they are genuinely two different persons or just two registrations of a single user.

The first thing that came to my mind was the Levenshtein Distance, but it is more focused on words similarities.
You could use tf-idf, but it will probably work better if your corpus contains more than only two documents.
An alternative could be representing the documents (posts) using a vector space model, like:
(w_0, w_1, ..., w_k)
where
k is the total of terms (words) in your document
w_i is the i-th term.
and then compute the Hamming Distance, which basically compares two vectors (arrays) and count the positions where they are different. You can discard stop-words first (i.e. words like prepositions, etc.)
Take in count that the user might change some words, use synonyms, etc. There are lots of models for representing documents, computing similarity between them. Some of them take in count words dependency, which gives more semantic to the process, and others don't.

google-diff-match-patch will be a good choice for you. you can look the demo for testing.

Creating a "spell check" that checks against a database with a reasonable runtime

I'm not asking about implementing the spell check algorithm itself. I have a database that contains hundreds of thousands of records. What I am looking to do is checking a user input against a certain column in a table for all these records and return any matches with a certain hamming distance (again, this question's not about determining hamming distance, etc.). The purpose, of course, is to create a "did you mean" feature, where a user searches a name, and if no direct matches are found in the database, a list of possible matches are returned.
I'm trying to come up with a way to do all of these checks in the most reasonable runtime possible. How can I check a user's input against all of these records in the most efficient way possible?
The feature is currently implemented, but the runtime is exceedingly slow. The way it works now is it loads all records from a user-specified table (or tables) into memory and then performs the check.
For what it's worth, I'm using NHibernate for data access.
I would appreciate any feedback on how I can do this or what my options are.

Calculating Levenshtein distance doesn't have to be as costly as you might think. The code in the Norvig article can be thought of as psuedocode to help the reader understand the algorithm. A much more efficient implementation (in my case, approx 300 times faster on a 20,000 term data set) is to walk a trie. The performance difference is mostly attributed to removing the need to allocate millions of strings in order to do dictionary lookups, spending much less time in the GC, and you also get better locality of reference so have fewer CPU cache misses. With this approach I am able to do lookups in around 2ms on my web server. An added bonus is the ability to return all results that start with the provided string easily.
The downside is that creating the trie is slow (can take a second or so), so if the source data changes regularly then you need to decide whether to rebuild the whole thing or apply deltas. At any rate, you want to reuse the structure as much as possible once it's built.

As Darcara said, a BK-Tree is a good first take. They are very easy to implement. There are several free implementations easily found via Google, but a better introduction to the algorithm can be found here: http://blog.notdot.net/2007/4/Damn-Cool-Algorithms-Part-1-BK-Trees.
Unfortunately, calculating the Levenshtein distance is pretty costly, and you'll be doing it a lot if you're using a BK-Tree with a large dictionary. For better performance, you might consider Levenshtein Automata. A bit harder to implement, but also more efficient, and they can be used to solve your problem. The same awesome blogger has the details: http://blog.notdot.net/2010/07/Damn-Cool-Algorithms-Levenshtein-Automata. This paper might also be interesting: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.16.652.

I guess the Levenshtein distance is more useful here than the Hamming distance.
Let's take an example: We take the word example and restrict ourselves to a Levenshtein distance of 1. Then we can enumerate all possible misspellings that exist:
1 insertion (208)
aexample
bexample
cexample
...
examplex
exampley
examplez
1 deletion (7)
xample
eample
exmple
...
exampl
1 substitution (182)
axample
bxample
cxample
...
examplz
You could store each misspelling in the database, and link that to the correct spelling, example. That works and would be quite fast, but creates a huge database.
Notice how most misspellings occur by doing the same operation with a different character:
1 insertion (8)
?example
e?xample
ex?ample
exa?mple
exam?ple
examp?le
exampl?e
example?
1 deletion (7)
xample
eample
exmple
exaple
examle
exampe
exampl
1 substitution (7)
?xample
e?ample
ex?mple
exa?ple
exam?le
examp?e
exampl?
That looks quite manageable. You could generate all these "hints" for each word and store them in the database. When the user enters a word, generate all "hints" from that and query the database.
Example: User enters exaple (notice missing m).
SELECT DISTINCT word
FROM dictionary
WHERE hint = '?exaple'
OR hint = 'e?xaple'
OR hint = 'ex?aple'
OR hint = 'exa?ple'
OR hint = 'exap?le'
OR hint = 'exapl?e'
OR hint = 'exaple?'
OR hint = 'xaple'
OR hint = 'eaple'
OR hint = 'exple'
OR hint = 'exale'
OR hint = 'exape'
OR hint = 'exapl'
OR hint = '?xaple'
OR hint = 'e?aple'
OR hint = 'ex?ple'
OR hint = 'exa?le'
OR hint = 'exap?e'
OR hint = 'exapl?'
exaple with 1 insertion == exa?ple == example with 1 substitution
See also: How does the Google “Did you mean?” Algorithm work?

it loads all records from a user-specified table (or tables) into memory and then performs the check
don't do that
Either
Do the match match on the back end
and only return the results you need.
or
Cache the records into memory early
on a take the working set hit and do
the check when you need it.

You will need to structure your data differently than a database can. Build a custom search tree, with all dictionary data needed, on the client. Although memory might become a problem if the dictionary is extremely big, the search itself will be very fast. O(nlogn) if I recall correctly.
Have a look at BK-Trees
Also, instead of using the Hamming distance, consider the Levenshtein distance

The answer you marked as correct..
Note: when i say dictionary.. in this post, i mean hash map .. map..
basically i mean a python dictionary
Another way you can improve its performance by creating an inverted index of words.
So rather than calculating the edit distance against whole db, you create 26 dictionary.. each has a key an alphabet. so english language has 26 alphabets.. so keys are "a","b".. "z"
So assume you have word in your db "apple"
So in the "a" dictionary : you add the word "apple"
in the "p" dictionary: you add the word "apple"
in the "l" dictionary: you add the word "apple"
in the "e" dictionary : you add the word "apple"
So, do this for all the words in the dictionary..
Now when the misspelled word is entered..
lets say aplse
you start with "a" and retreive all the words in "a"
then you start with "p" and find the intersection of words between "a" and "p"
then you start with "l" and find the intersection of words between "a", "p" and "l"
and you do this for all the alphabetss.
in the end you will have just the bunch of words which are made of alphabets "a","p","l","s","e"
In the next step, you calculate the edit distance between the input word and the bunch of words returned by the above steps.. thus drastically reducing your run time..
now there might be a case when nothing might be returned..
so something like "aklse".. there is a good chance that there is no word which is made of just these alphabets..
In this case, you will have to start reversing the above step to a stage where you have finite numbers of word left.
So somethng like start with *klse (intersection between words k, l,s,e) num(wordsreturned) =k1
then a*lse( intersection between words a,l,s,e)... numwords = k2
and so on..
choose the one which have higher number of words returned.. in this case, there is really no one answer.. as a lot of words might have same edit distance.. you can just say that if editdistance is greater than "k" then there is no good match...
There are many sophisticated algorithms built on top of this..
like after these many steps, use statistical inferences (probability the word is "apple" when the input is "aplse".. and so on) Then you go machine learning way :)

Can a "pre-computed" map-reduce index (à la RavenDB/CouchDB) be used for this kind of algorithm?

I'm trying to see if a specific algorithm can be translated to the kind of map-reduce index RavenDB/CouchDB uses, ie, "pre-computed" map-reduce (which means the indexes are refreshed on insertion and updates, not when performing the actual query).
Let's say we have a typical online store with 50,000 products, grouped in categories. Every product has a collection of "Attribute Values", ie, something like "[Red, Round, Metal]".
Since we have so much products on our website, and there's probably a lot of items in each of the categories, we want to give the user another way to "filter" the products he's currently seeing.
For example, if a category is "Less than $20", there's a whole bunch of products in this category. But our user only need to see products which are less than $20 and Red. Unfortunately, there's no sub-category "Red" in the "Less than $20" category.
Our algorithm would take the current list of products, and generate a list of "interesting" Attributes and Attribute Values, ie, given a list of products, it would output something like:
Color
Red (40)
Blue (32)
Yellow (17)
Material
Metal (37)
Plastic (36)
Wood (23)
Shape
Square (56)
Round (17)
Cylinder (12)
Could this sort of algorithm be somehow pre-computed à la RavenDB/CouchDB map-reduce index? If not, why exactly (so I can identify that kind of algorithm in the future) and if yes, how?
A C# 4.0 Visual Studio Test Solution is available that demonstrates the potential data structures and sample data, as well as a try at a map-reduce implementation (which doesn't seem to be pre-computable).

General case: It's always possible to use a CouchDB-style map-reduce view, but it's not necessarily practical.
In the end, it's mostly a counting-based argument: if you need to ask the question for any subset of your 500,000 products, then your database must be able to provide a distinct answer to each of 2500,000 different possible questions, which uses a prohibitive amount of memory if you have to emit a B-tree leaf for every one of them (and you need to emit data unless the answer to most of these queries is zero, false, an empty set or a similar null value).
CouchDB provides a first small optimization through the existence of range queries (meaning that in an ideal case, it can use as little as N B-tree leaves to answer N2 questions). However, in your example, this would only reduce the number of leaves down to 2250,000 (and that's a theoretical lower bound).
CouchDB provides a second small optimization through key prefix queries, meaning that you can compress [A], [A,B] and [A,B,C] queries into a single [A,B,C] key. So, instead of your 2250,000 possibilities, you're down to a "mere" 2249,999 ...
So, while you could think up an emitting strategy for answering the question for any subset, it would take more storage space than is actually available on our planet. In the general case, to answer N different questions you need to emit at least sqrt(N/2) B-tree leaves, so count your questions and determine if that lower bound on the number of leaves is acceptable.
Only for categories and subcategories: if you give up on arbitrary lists of products and only ask questions of the form "give me the significant attributes in category A filtered by attributes B and C", then your number of emits drops to:
AvgCategories * AvgAttr * 2 ^ (AvgAttr - 1) * 500,000
You're basically emitting for each product the keys [Category,Attr,Attr,...] for all categories of the product and all combinations of attributes of the product, which lets you query by category + attributes. If you have on average 1 category and 3 attributes per product, this works out to about 6 million entries, which is fairly acceptable.

This should be quite straightforward to implement in something like CouchDB. Have the map phase of your index output one key, value pair for each attribute the object has, with the value simply being '1'. Then, have the reduce phase sum up all input values and output the sum. The end result will be an index of the form you describe.

How do I determine if two similar band names represent the same band?

I'm currently working on a project that requires me to match our database of Bands and venues with a number of external services.
Basically I'm looking for some direction on the best method for determining if two names are the same. For Example:
Our database venue name - "The Pig and Whistle"
service 1 - "Pig and Whistle"
service 2 - "The Pig & Whistle"
etc etc
I think the main differences are going to be things like missing "the" or using "&" instead of "and" but there could also be things like slightly different spelling and words in different orders.
What algorithms/techniques are commonly used in this situation, do I need to filter noise words or do some sort of spell check type match?
Have you seen any examples of something simlar in c#?
UPDATE: In case anyone is interested in a c# example there is a heap you can access by doing a google code search for Levenshtein distance

The canonical (and probably the easiest) way to do this is to measure the Levenshtein distance between the two strings. If the distance is small relative to the size of the string, it's probably the same string. Note that if you have to compare a lot of very small strings it'll be harder to tell whether they're the same or not. It works better with longer strings.
A smarter approach might be to compare the Levenshtein distance between the two strings but to assign a distance of zero to the more obvious transformations, like "and"/"&", "Snoop Doggy Dogg"/"Snoop", etc.

I did something like this a while ago, I used the the Discogs database (which is public domain), which also tracks artist aliases;
You can either:
Use an API call (namevariations field).
Download the monthly data dumps (*_artists.xml.gz) & import it in your database. This contains the same data, but is obviously a lot faster.
One advantage of this over the Levenshtein distance) solution is that you'll get a lot less false matches.
For example, Ryan Adams and Bryan Adams have a score of 2, which is quite good (lower is better matches, Pig and Whistle and Pig & Whistle has a score of 3), yet they're obviously different people.
While you could make a smarter algorithm (which also looks at string length, for example), using the alias DB is a lot simpler & less error-phone; after implementing this, I could completely remove the solution that was suggested in the other answer & had better matches.

soundex may also be useful

In bioinformatics we use this to compare DNA- or protein sequences all the time.
There are plenty of algorithms, you probably want to look at global alignments.
In this respect the Needleman-Wunsch algorithm is probably what you seek.
If you have particularly long recurring strings to compare you might also want to consider heuristic searches like BLAST.