How do search engines conduct 'AND' operation? - search

Consider the following search results:
Google for 'David' - 591 millions hits in 0.28 sec
Google for 'John' - 785 millions hits in 0.18 sec
OK. Pages are indexed, it only needs to look up the count and the first few items in the index table, so speed is understandable.
Now consider the following search with AND operation:
Google for 'David John' ('David' AND 'John') - 173 millions hits in 0.25 sec
This makes me ticked ;) How on earth can search engines get the result of AND operations on gigantic datasets so fast? I see the following two ways to conduct the task and both are terrible:
You conduct the search of 'David'. Take the gigantic temp table and conduct a search of 'John' on it. HOWEVER, the temp table is not indexed by 'John', so brute force search is needed. That just won't compute within 0.25 sec no matter what HW you have.
Indexing by all possible word
combinations like 'David John'. Then
we face a combinatorial explosion on the number of keys and
not even Google has the storage
capacity to handle that.
And you can AND together as many search phrases as you want and you still get answers under a 0.5 sec! How?

What Markus wrote about Google processing the query on many machines in parallel is correct.
In addition, there are information retrieval algorithms that make this job a little bit easier. The classic way to do it is to build an inverted index which consists of postings lists - a list for each term of all the documents that contain that term, in order.
When a query with two terms is searched, conceptually, you would take the postings lists for each of the two terms ('david' and 'john'), and walk along them, looking for documents that are in both lists. If both lists are ordered the same way, this can be done in O(N). Granted, N is still huge, which is why this will be done on hundreds of machines in parallel.
Also, there may be additional tricks. For example, if the highest-ranked documents were placed higher on the lists, then maybe the algorithm could decide that it found the 10 best results without walking the entire lists. It would then guess at the remaining number of results (based on the size of the two lists).

I think you're approaching the problem from the wrong angle.
Google doesn't have a tables/indices on a single machine. Instead they partition their dataset heavily across their servers. Reports indicate that as many as 1000 physical machines are involved in every single query!
With that amount of computing power it's "simply" (used highly ironically) a matter of ensuring that every machine completes their work in fractions of a second.
Reading about Google technology and infrastructure is very inspiring and highly educational. I'd recommend reading up on BigTable, MapReduce and the Google File System.
Google have an archive of their publications available with lots of juicy information about their techologies. This thread on metafilter also provides some insight to the enourmous amount of hardware needed to run a search engine.

I don't know how google does it, but I can tell you how I did it when a client needed something similar:
It starts with an inverted index, as described by Avi. That's just a table listing, for every word in every document, the document id, the word, and a score for the word's relevance in that document. (Another approach is to index each appearance of the word individually along with its position, but that wasn't required in this case.)
From there, it's even simpler than Avi's description - there's no need to do a separate search for each term. Standard database summary operations can easily do that in a single pass:
SELECT document_id, sum(score) total_score, count(score) matches FROM rev_index
WHERE word IN ('david', 'john') GROUP BY document_id HAVING matches = 2
ORDER BY total_score DESC
This will return the IDs of all documents which have scores for both 'David' and 'John' (i.e., both words appear), ordered by some approximation of relevance and will take about the same time to execute regardless of how many or how few terms you're looking for, since IN performance is not affected much by the size of the target set and it's using a simple count to determine whether all terms were matched or not.
Note that this simplistic method just adds the 'David' score and the 'John' score together to determine overall relevance; it doesn't take the order/proximity/etc. of the names into account. Once again, I'm sure that google does factor that into their scores, but my client didn't need it.

I did something similar to this years ago on a 16 bit machine. The dataset had an upper limit of around 110,000 records (it was a cemetery, so finite limit on burials) so I setup a series of bitmaps each containing 128K bits.
The search for "david" resulting in me setting the relevant bit in one of the bitmaps to signify that the record had the word "david" in it. Did the same for 'john' in a second bitmap.
Then all you need to do is a binary 'and' of the two bitmaps, and the resulting bitmap tells you which record numbers had both 'david' and 'john' in them. Quick scan of the resulting bitmap gives you back the list of records that match both terms.
This technique wouldn't work for google though, so consider this my $0.02 worth.

Related

Find the most similar text in a list of strings

First of all, I want to acknowledge that this is perhaps a very sophisticated problem; however, I have not been able to find a definitive answer for it online so I'm looking for suggestions.
Suppose I want to collect a list containing over hundred thousand strings, values of these strings are sentences that a user has typed. The values are added to the list as soon as a user types a new message. For example:
["Hello world!", "Good morning, my name is John", "Good morning, everyone"]
But I also want to have a timeout for each string so if they are not repeated within 5 min, they should be removed, so I change it to following format:
[{message:"Hello world!", timeout: NodeJS.Timeout, count: 1}, {message:"Good morning, my name is John", timeout: NodeJS.Timeout, count: 1}, {message:"Good morning, everyone", timeout: NodeJS.Timeout, count: 1}]
Now suppose a user types the following message:
Good morning, everyBODY
I want to compare this string to all the messages in list and if one is 70% or more similar, update the count of that message, otherwise insert it as a new message. For this message for example, the application should update the count for Good morning, everyone to be equal to 2.
Since users can type a lot of messages in a short amount of time, the algorithm must also support fast insertion, searching, and deleting after the timeout.
What is the best way to implement this? or are there any libraries to help me with this?
NOTE: The strings do not need to be in an array, any data structure would work.
The main purpose of this algorithm is to detect similar messages when the count reaches a predefined value. For example warning: Over 5 users typed messages similar to "Hello everybody" within 5 minutes
I have looked at B-Trees, Nearest Neighbor, etc but I can't figure out what would be the best solution.
Update:
I plan on using Levenshtein distance for string similarity, however the main problem is how to apply that to a list of strings in most time efficient way, without having to check every single string every time a new message is added.
Levenshtein distance
Unlike the other answer I think Levenshtein distance is perfectly capable of dealing with spelling mistakes. Indeed, Levenshtein and LevXenshtein only have Levenshtein distance 1, and thus can be concluded to likely be the same message.
However, if you want to use this distance, you will have to compute the distance between the new message and every message stored, every time a new message comes in. There is likely no way around this.
Unfortunately there is no real useful pre-processing you can do for this.
Other possibilities
If you can find a way to map every message to a fixed-size vector, you can use essentially any nearest neighbor search technique. I suggest doing so.
This leaves us with two problems to solve. Generating the fixed-length vector, and doing the search.
Fixed-size vector representation
There are multiple ways of doing this, all with their own set of drawbacks. I'll specifically mention two, but it will depend on your architecture and data which method is best for you.
First, you could go the machine-learning way. You could map every word to a pre-trained vector with fastText, average the words in the message, and use that as your vector. The drawbacks of this method are that it will ignore word order, and it will work less well if the words used tend to be very informal. If your messages have their own culture to them (such as for example Twitch chat) you would have to retrain these vectors instead of using pre-trained ones.
Alternatively, you could use the structure of the text directly, and make an occurrence vector of bigrams. That is, jot down how often every 2-character combination occurs in a message. This is fairly robust, but has the drawback that the vectors will become relatively large.
Regardless, these are just two options, and it's impossible to tell what method is ideal for you. Unless of course someone has a brilliant idea.
Nearest neighbor search
Given that we have fixed length vectors, we can now do nearest neighbor search. As you've probably found, there are once again many different methods for this, all with their own drawbacks. Exhausting, I know.
I'll choose to discuss three categories.
Approximate search: This method may seem a little silly, but it could be what you want. Specifically, Locality-sensitive hashing is essentially just making some hashing function where "similar" vectors are likely to end up in the same bucket. You could then do anything you want, such as Levenshtein, with all of the other members of the bucket, because there should not be too many of them. The advantage of such an approximate algorithm is that it can be fast, and with some smart hashing you don't even need fixed-length vectors. A downside, of course, is that it is not guaranteed to work.
Exact search: We can also choose to instead solve the problem of Fixed-radius near neighbors. That is, find the points within some distance of the target point. You could do this by mapping vectors to integers (if they aren't already) and simply checking every lattice point within the distance you want to search. The primary drawback here is that the search time grows very fast not with the number of points, but with the number of dimensions of the vector. This method would necessitate small vectors.
Fancy datastructures: This seems to me most likely to be the right solution. Unfortunately you have a lot of letter-trees. You mention B-trees, but there's also R-trees, R+-Trees, R*-Trees, X-Trees, and that's just the direct descendants of the R-tree. With the risk of missing the trees for the forest, I'd suggest taking a look at the k-d tree. It can do nearest neighbor search in logarithmic time, as well as insertion and deletion.
You want to covert all of the words to their Soundex value.
Then you need a database for the soundex values that ranks the importance of the word in the sentence, e.g. the should probably get 0. The more information the word carries the higher its value.
Then sort the words in the sentence into a list of integers.
Use the list of integers as the key to find similar sentences.
Since the key is a list of integers a Rose tree should work as data structure.
While some may suggest measuring using something like Levenshtein distance that presupposes that the sentences have no spelling mistakes or such. You need something that is flexible enough to deal with human error.
I would suggest you to use Algolia. Which has their own ranking algorithm rates each matching record on several criteria (such as the number of typos or the geo-distance), to which they individually assign a integer value score.
I would totally take a loook on it, since they have Search-as-you-type and different Ranking algorithm criterias.
https://blog.algolia.com/search-ranking-algorithm-unveiled/
I think Search Engine like SOLR or Elastic Search are best fit for your problem.
You have to create single collection in which you can store data as you have mention in the question after that you just have to add data to solr and search it in the solr search with your time limit.

Which algorithm to match most similar string from a set?

Let's say I have a database of books that includes their titles. For a given listing from eBay or Craigslist or some other such site, I want to compare its title string to all of the book titles in my database to try to find a match.
It's unlikely there will ever be exact string equality as users on those sites like to include things like "perfect condition" and "fast shipping" to their listing titles to attract buyers.
What algorithm(s) should I use to do this type of correlation? I'm aware of n-grams and Levenshtein distance, but I don't know which would do the most accurate job.
For the various applicable algorithms, how does their computational performance compare? Would it make sense to use multiple algorithms and average their results to balance their strengths and weaknesses? Would it be possible to set a minimum level of confidence? I'd rather have no match than a very poor quality match.
For the task at hand, I think you'd get best results with some pre-processing: remove common "null" phrases (those you don't want to see), such that you have a smaller title that is likely to have the actual title as a major part.
The next step depends on your DB size and request overhead. If those are inexpensive, then pull a list of titles from your DB, and see which exists in the eBay text (a single command in many languages). If that works for you, then even that pre-processing is likely unnecessary overhead.
If the full DB listing is expensive, but the DB is indexed well, then try grabbing likely n-grams (say, 2-3 words) from the eBay text, and searching for them in the DB. You should get relatively few return values, which you can then try in toto against the full eBay text for a match.

Solr: how to manage irrelevant results when not sorting by relevance?

Case in point: say we have a search query that returns 2000 results ranging from very relevant to hardly relevant at all. When this is sorted by relevance this is fine, as the most relevant results are listed on the first page.
However, when sorting by another field (e.g. user rating) the results on the first page are full of hardly-relevant results, which is a problem for our client. Somehow we need to only show the 'relevant' results with highest ratings.
I can only think of a few solutions, all of which have problems:
1 - Filter out listings on Solr side if relevancy score is under a threshold. I'm not sure how to do this, and from what I've read this isn't a good idea anyway. e.g. If a result returns only 10 listings I would want to display them all instead of filter any out. It seems impossible to determine a threshold that would work across the board. If anyone can show me otherwise please show me how!
2 - Filter out listings on the application side based on score. This I can do without a problem, except that now I can't implement pagination, because I have no way to determine the total number of filtered results without returning the whole set, which would affect performance/bandwidth etc... Also has same problems of the first point.
3 - Create a sort of 'combined' sort that aggregates a score between relevancy and user rating, which the results will then be sorted on. Firstly I'm not sure if this is even possible, and secondly it would be weird for the user if the results aren't actually listed in order of rating.
How has this been solved before? I'm open to any ideas!
Thanks
If they're not relevant, they should be excluded from the result set. Since you want to order by a dedicated field (i.e. user rating), you'll have to tweak how you decide which documents to include in the result at all.
In any case you'll have to define "what is relevant enough", since scores aren't really comparable between queries and doesn't say anything about "this was xyz relevant!".
You'll have to decide why those documents that are included aren't relevant and exclude them based on that criteria, and then either use the review score as a way to boost them further up (if you want the search to appear organic / by relevance). Otherwise you can just exclude them and sort by user score. But remember that user score, as an experience for the user, is usually a harder problem to make relevant than just order by the average of the votes.
Usually the client can choose different ordering options, by relevance or ratings for example. But you are right that ordering by rating is probably not useful enough. What you could do is take into account the rating in the relevance scoring. For example, by multiplying an "organic" score with a rating transformed as a small boost. In Solr you could do this with Function Queries. It is not hard science, and some magic is involved. Much is common sense. And it requires some very good evaluation and testing to see what works best.
Alternatively, if you do not want to treat it as a retrieval problem, you can apply faceting and let users do filtering of the results by rating. Let users help themselves. But I can imagine this does not work in all domains.
Engineers can define what relevancy is. Content similarity scoring is not only what constitutes relevancy. Many Information Retrieval researchers and engineers agree that contextual information should be used besides only the content similarity. This opens a plethora of possibilities to define a retrieval model. For example, what has become popular are Learning to Rank (LTR) approaches where different features are learnt from search logs to deliver more relevant documents to users given their user profiles and prior search behavior. Solr offers this as module.

Advice on how to search and return strings

Forgive me, this will be my first every post to SO, so do let me know how I can improve.
I am currently looking for advice on a problem I am facing. I have a list of one billion unique strings of text. These text strings also have a list of tags associated with them to indicate the content of the string.
Example:
StringText: The cat ate on Sunday
AnimalCode: c001
ActionCode: a001
TimeCode: d001
where
c001 = The cat
a001= ate
d001 = on Sunday
I have loaded all of the strings and their codes as individual documents in an instance of MongoDB
At present, I am trying to devise a method by which I can enter a string and search against the database to return the match. My problem is that the search is taking far to long to return results.
I have created an index on the StringText field, but am guessing that it is too large to hold in memory.
Each string has an equal probability of being searched for so I can't reliably predict which strings have a higher probability of being searched for and pull them out into another collection.
Currently, I am running the DB off a single box with 16GB of RAM and a 4TB HDD.
Does anybody have any advice on how I might accomplish my task more efficiently? Is Mongo the right technology or are there others more adept at doing this kind of search and return?
My goal (forgive me if foolish) would be to try and return a result within 2 seconds or less.
I am very new to this whole arena so any and all advice would be welcome.
Thanks much to all in advance for the help and time.
Sincerely,
Zinga
As discussed in the comments, you could preprocess the input string to find the associated Animal and Action codes and search for StringText based on the indexed codes, which is much faster than text search.
You can't totally avoid text search, so reduce it to the Animal and/or Action collection by tokenizing the input string. See how you can use map/reduce techniques just for queries of this sort.
In your case, if you know that the first word or two will always contain the name of the animal, just use those one or two words to search for the relevant animal. Searching through the Animal/Actions collection shouldn't take long. In case it does, you can keep a periodically updating list of most common animals/actions (based on their frequency) and search against that to make it faster. This is also discussed in the articles on the linked page.
If even after that your search against StringText is slow, you could shard the StringText collection by Animal/Action codes. The official doc should suffice for this and there's not much that's involved in the setup so you might try this anyway. The basic ideology everywhere is to restrict your target space as much as possible. Searching through a billion records for every query is plain overkill. Cache where you can, preprocess where you can, show guesses while you run a slow query.
Good luck!

Ways to do "related searches" functionality

I've seen a few sites that list related searches when you perform a search, namely they suggest other search queries you may be interested in.
I'm wondering the best way to model this in a medium-sized site (not enough traffic to rely on visitor stats to infer relationships). My initial thought is to store the top 10 results for each unique query, then when a new search is performed to find all the historical searches that match some amount of the top 10 results but ideally not matching all of them (matching all of them might suggest an equivalent search and hence not that useful as a suggestion).
I imagine that some people have done this functionality before and may be able to provide some ideas of different ways to do this. I'm not necessarily looking for one winning idea since the solution will no doubt vary substantially depending on the size and nature of the site.
have you considered a matrix of with keywords on 1 axis vs. documents on another axis. once you find the set of vetors representing the keywords, find sets of keyword(s) found in your initial result set and then find a way to rank the other keywords by how many documents they reference or how many times they interset the intial result set.
I've tried a number of different approaches to this, with various degrees of success. In the end, I think the best approach is highly dependent on the domain/topics being searched, and how the users form queries.
Your thought about storing previous searches seems reasonable to me. I'd be curious to see how it works in practice (I mean that in the most sincere way -- there are many nuances that can cause these techniques to fail in the "real world", particularly when data is sparse).
Here are some techniques I've used in the past, and seen in the literature:
Thesaurus based approaches: Index into a thesaurus for each term that the user has used, and then use some heuristic to filter the synonyms to show the user as possible search terms.
Stem and search on that: Stem the search terms (eg: with the Porter Stemming Algorithm and then use the stemmed terms instead of the initially provided queries, and given the user the option of searching for exactly the terms they specified (or do the opposite, search the exact terms first, and use stemming to find the terms that stem to the same root. This second approach obviously takes some pre-processing of a known dictionary, or you can collect terms as your indexing term finds them.)
Chaining: Parse the results found by the user's query and extract key terms from the top N results (KEA is one library/algorithm that you can look at for keyword extraction techniques.)

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