I am trying to add search support in my website(hosted on a shared web hosting ... hostgator.com) for that I am looking for an open source solution for full text and faceted search which doesn't requires any server side support(apart from php and mysql).
I have already looked a number of solutions like Lucene, Solr, Sphinx, Zend Lucene including Mysql Full text search support. And also know that Solr is the best solution for such things. But as I said my website is hosted on a shared web hosting with no admin rights so I can't go with Solr. Also I can't go with inbuild full text support in mysql as currently my website's database is using InnoDB engine.
Consider manually constructing an inverted index in a MyISAM table. The tricky part would be to keep the index up-to-date though, which will either require a lot of code upon updating/inserting rows, or require that you do a complete re-index every x days (or hours).
If you don't know what an inverted index is: it's an index where you map a word to a document ID. For example, if you wanted to index the table (id,name,description) with (1,"Test product","This product is awesome"), you can separate the words into "Test","product","This","is","awesome". You could then put all these words into a database table (id,word,docID) => (1,"test",1),(2,"product",1),(3,"this",1), etc.
If you then want to search something, ask this index. A search query "test" would pull all entries with word="test", which would be (1,"test",1). It then knows it needs docID 1, and you're done.
It's definitely harder than using a standard solution, but it should work for your situation :)
Of course, it only works with space-separated languages. If you want Chinese, you'll have a problem.
[edit] Ah, yes, the wikipedia entry may help: http://en.wikipedia.org/wiki/Inverted_index