Frequent Item Mining When Obtaining Support Is Costly

Suppose there are n users and m items, and the preference of each user for the items is revealed only upon probing, which takes time and is therefore costly. How can we quickly discover all the frequent items that are favored individually by at least a given number of users? This new problem not only has strong connections with several well-known problems, such as the frequent item mining problem, it also finds applications in fields such as sponsored search and marketing surveys. Unlike traditional frequent item mining, however, our problem assumes no prior knowledge of users' preferences, and thus obtaining the support of an item becomes costly. Although our problem can be settled naively by probing the preferences of all n users, the number of users is typically enormous, and each probing itself can also incur a prohibitive cost. We present a sampling algorithm that drastically reduces the number of users needed to probe to O(logm)-regardless of the number of users-as long as slight inaccuracy in the output is permitted. For reasonably sized input, our algorithm needs to probe only 0.5% of the users, whereas the naive approach needs to probe all of them.