19. The method of claim 18 , further comprising: accessing query log data that includes queries submitted by users and the frequency with which each query was submitted; determining most likely sequences of initial query characters from the query log data; for each most likely sequence, determining most likely queries from the most likely sequence and the query log data, each most likely query having an initial sequence of query characters matching the most likely sequence of initial query characters; and designating the most likely queries determined for each of the most likely sequences of initial query characters as the initial query characters.
20. The method of claim 19 , further comprising: receiving query characters input into the first query input field from the client device; determining most likely sequences of subsequent query characters from the query log data, the subsequent query characters being query characters that are subsequent in sequence to the query characters received from the client device; for each most likely sequence of subsequent query characters, determining most likely additional queries from the most likely sequence of subsequent query characters and the query log data, each most likely query having an initial sequence of query characters matching the query characters received from the client device and the most likely sequence of subsequent query characters; and designating the most likely additional queries determined for each of the most likely sequences of subsequent query characters as additional query suggestions; and providing the additional query suggestions to the client device.