AppEngine Approximate Partial String Matching Algorithm

So, I realize that this covers a wide array of topics and pieces of them have been covered before on StackOverflow, such as this question. Similarly, Partial String Matching and Approximate String Matching are popular algorithmic discussions, it seems. However, using these ideas in conjunction to suit a problems where both need to be discussed seems highly inefficient. I'm looking for a way to combine the two problems in to one solution, efficiently.

Right now, I'm using AppEngine with Java and the Persistent DataStore. This is somewhat annoying, since it doesn't seem to have any arithmetic usage in the queries to make things easier, so I'm currently considering doing some precalculation and storing it as an extra field in the database. Essentially, this is the idea that a friend and I were having on how to possibly implement a system for matching and I was more or less hoping for suggestions on how to make it more efficient. If it needs to be scrapped in favor of something better that already exists, I can handle that, as well.

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Let's start off with a basic example of what I'd look to do a search for. Consider the following nonsense sentence:

The isolating layer rackets the principal beneath your hypocritical rubbish.

If a user does a search for

isalatig pri

I would think that this would be a fairly good starting match for the string, and the value should be returned. The current method that we are considering using basically assigns a value to test divisibility. Essentially, there is a table with the following data

A: 2        B: 3        C: 5
D: 7        E: 11       F: 13
...

with each character being mapped to a prime number (multiple characters don't make a difference, only one character is needed). And if the query string divides the string in the database, then the value is returned as a possible match.

After this, keywords that aren't listed as stopwords are compared from the search string to see if they are starting substrings of words in the possible match under a given threshold of an edit distance (currently using the Levenshtein distance).

distance("isalatig", "isolating") == 2
distance("pri", "principal开发者_StackOverflow中文版") == 0 // since principal has a starting 
                                  // substring of pri it passes

The total distance for each query is then ranked in ascending order and the top n values are then returned back to the person doing the querying.

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This is the basic idea behind the algorithm, though since this is my first time dealing with such a scenario, I realize that I'm probably missing something very important (or my entire idea may be wrong). What is the best way to handle the current situation that I'm trying to implement. Similarly, if there are any utilities that AppEngine currently offers to combat what I'm trying to do, please let me know.

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First off, a clarification: App Engine doesn't allow arithmetic in queries because there's no efficient way to query on the result of an arbitrary arithmetic expression. When you do this in an SQL database, the planner is forced to select an inefficient query plan, which usually involves scanning all the candidate records one by one.

Your scheme will not work for the same reason: There's no way to index an integer such that you can efficiently query for all numbers that are divisible by your target number. Other potential issues include words that translate into numbers that are too large to store in a fixed length integer, and being unable to distinguish between 'rental', 'learnt' and 'antler'.

If we discard for the moment your requirement for matching arbitrary prefixes of strings, what you are searching for is full-text indexing, which is typically implemented using an inverted index and stemming. Support for fulltext search is on the App Engine roadmap but hasn't been released yet; in the meantime your best option appears to be SearchableModel, or using an external search engine such as Google Site Search.