What is the fastest way in PHP to take a keyword list and match it to a search result (like an array of titles) for all words?

For instance, if my keyword phrase is "great leather shoes", then the following titles would be a match...

• Get Some Really Great Leather Shoes
• Leather Shoes Are Great
• Great Day! Those Are Some Cool Leather Shoes!
• Shoes, Made of Leather, Can Be Great

...while these would not be a match:

• Leather Shoes on Sale Today!
• You'll Love These Leather Shoes Greatly
• Great Shoes Don't Come Cheap

I imagine there's some trick with array functions or a RegEx (Regular Expression) to achieve this rapidly.