Quick Search for a Person's name

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I was curious to know about the best quick search query that is used to retrieve a person's info. Currently, we have a database which has columns for first name, last name and salutation. The user should be allowed to search for any permutation and combination of these columns. The simple search query is taking a lot of time and thus making this quick search slow (As the query needs to scan all the rows for first name, last name and salutation). Could you please share the various fast or advanced techniques that could be used for this purpose.

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