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.
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. 21. The method of claim 20 , wherein: the initial query suggestions and additional query suggestions are in the form of key value pairs, the key value pairs being pairs of query input sequences and query suggestions having initial query characters that match the query input sequences; and the query characters input in the first query input field or second input field are provided as a query suggestion request only in response to determining that the query characters input in the first query input field or the second input field do not match any of the query input sequences of the key value pairs.