Getting the most frequent items without counting every item

Question

Hi. I was wondering if there was an algorithm for counting "most frequent items" without having to keep a count of each item? For example, let's say I was a search engine and wanted to keep track of the 10 most popular searches. What I don't want to do is keep a counter of every query since there could be too many queries for me to count (and most them will be singletons). Is there a simple algorithm for this? Maybe something that is probabilistic? Thanks!

Answer 1

Well, if you have a very large number of queries (like a search engine presumably would), then you could just do "sampling" of queries. So you might be getting 1,000 queries per second, but if you just keep a count one per second, then over a longish period of time, you'd get an answer that would be relatively close to the "real" answer.

This is how, for example, a "sampling" profiler works. Every n mililiseconds it looks at what function is currently being executed. Over a long period of time (several seconds) you get a good idea of the "expensive" functions, because they're the ones that appear in your samples more often.

You still have to do "counting" but by doing periodic samples, instead of counting every single query you can get an upper bound on the amount of data that you actually have to store (e.g. max of one query per second, etc)

Answer 2

Storing each and every query would be expensive, yet necessary to ensure the top 10 are actually the top 10. You'll have to cheat.

One idea is to store a table of URLs, hit counters, and timestamp indexed by count, then timestamp. When the table reaches some arbitrary near-maximum size, start removing low-end entries that are older than a given number of days. Although old, infrequent queries won't be counted, the queries likely to make the top 10 should make it on the table because of the faster query rate.

Another idea would be to write a 16-bit (or more) hash function for search queries. Have a 65536-entry table holding counters and URLs. When a search is performed, increment the respective table entry and set the URL if necessary. However, this approach has a major drawback. A spam bot could make repeated queries like "cheap viagra", possibly making legitimate queries increment the spam query counters instead, placing their messages on your main page.

Answer 3

You want a cache, of which there are many kinds; see Wikipedia Cache algorithms and Page replacement algorithm Aging.

Answer 4

If you want the most frequent searches at any given time, you don't need to have endless counters keeping track of each query submitted. Instead, you need an algorithm to measure the amount of submissions for any given query divided by a set period of time. This is a pretty simple algorithm. Any search submitted to your search engine, for example the word “cache,” is stored for a fixed period of time called a refresh rate, (the length of your refresh rate depends on the kind of traffic your search engine is getting and the amount of “top-results” you want to keep track of). If the refresh rate time period expires and searches for the word “cache” have not persisted, the query is deleted memory. If searches for the word “cache” do persist, your algorithm only needs to keep track of the rate at which the word “cache” is being searched. To do this, simply store all searches on a “leaky-counter.” Every entry is pushed onto the counter with an expiration date after which the query is deleted. Your active counters are the indicators of your top queries.