Improved Recommendation Systems ∗ Extended

We consider a model of competitive recommendation systems proposed by Drineas et al. [4]. In recommendation systems (e.g., for books or movies), the system tracks which product each user chose in the past, and tries to deduce which other products an asking user is likely to be satisfied with. Obviously, recommendation systems can be effective only for users who share preferences with many other users. Such users are said to belong to a “dominant type.” Current approaches to on-line recommendation systems involve using Singular Value Decomposition (SVD), which is computationally intensive and, more important, often applicable only under additional strong conditions. Specifically, correctness is guaranteed in [4] only if users of different dominant types essentially do not share a product they like (“type separability”), and only if the number of users in non-dominant types is significantly smaller than the number of users in dominant types (“gap assumption”). The complexity of that algorithm is O(mn), where m and n denote the number of users and products, respectively. In this paper, we show that in fact, very simple combinatorial algorithms can make good recommendations without using SVD. Our algorithms require neither the type separability nor the gap assumption, they are naturally amenable to distibuted computation, and their complexity is lower. In particular, the paper presents an O(m + n) time centralized algorithm and a distributed algorithm that can be implemented in a peer-to-peer model even in the presence of adaptively colluding malicious players, with only logarithmic overhead. ∗Research conducted at Hewlett-Packard Cambridge Research Laboratory, One Cambridge Center, Cambridge, MA 02142. †Computer Science Department, Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218. Email: [email protected]. ‡Dept. of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel. Email: [email protected]. §Dept. of Computer Science and Applied Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel. Email: [email protected]. ¶Cambridge Research Laboratory, HP Labs, One Cambridge Center, Cambridge, MA 02142. Email: [email protected].