What algorithm does google use to make Chrome browser's address bar to act as a default search bar for many websites?

This feature is powered by what is known as OpenSearch. It allows you to specify how queries are supposed to be formed when searching a website. You can read the documentation here: http://www.opensearch.org/Home

For example, StackOverflow has the following in their HTML source code:

<link rel="search" type="application/opensearchdescription+xml" title="Stack Overflow" href="/opensearch.xml">

If you then open the file /opensearch.xml you can see the following:

<?xml version="1.0" encoding="UTF-8" ?><OpenSearchDescription xmlns="http://a9.com/-/spec/opensearch/1.1/" xmlns:moz="http://www.mozilla.org/2006/browser/search/">  <ShortName>Stack Overflow</ShortName>  <Description>Search Stack Overflow: Q&A for professional and enthusiast programmers</Description>  <InputEncoding>UTF-8</InputEncoding>  <Image width="16" height="16" type="image/x-icon">http://sstatic.net/stackoverflow/img/favicon.ico</Image>  <Url type="text/html" method="get" template="http://stackoverflow.com/search?q={searchTerms}"></Url></OpenSearchDescription>

The most important part is the line that specifies the search term string in line 7.

Chrome uses search engines mechanism. It is described here how to use ithttp://support.google.com/chrome/bin/answer.py?hl=en&answer=95653&topic=14676&ctx=topic

Chrome automatically identifies search boxes and adds corresponding rules to search engines list. Maybe it's engine relies on document parsing. Hense a particular site may be added or not because of it's search box markup.https://superuser.com/questions/276069/google-chrome-automatically-adding-websites-to-my-list-of-search-engines

If you want to know about parsing algorithm, the only way i see is to dig through chrome sources

Also, you can edit search engine list manually.

PS: And it's not only chrome's feature, other browsers have similar things. Opera as an example http://tech.gaeatimes.com/index.php/archive/how-to-easily-use-manage-your-search-engines-in-opera-browser/