Asynchronous Active Recommendation Systems
ABSTRACT We consider the following abstraction of recommendation systems. There are players and objects, and each player has an arbitrary
binary preference grade (“likes” or “dislikes”) for each object. The preferences are unknown at start. A player can find his
grade for an object by “probing” it, but each probe incurs cost. The goal of a recommendation algorithm is to find the preferences
of the players while minimizing cost. To save on cost, players post the results of their probes on a public “billboard” (writing
and reading from the billboard is free). In asynchronous systems, an adversary controls the order in which players probe.
Active algorithms get to tell players which objects to probe when they are scheduled. In this paper we present the first lowoverhead
algorithms that can provably reconstruct the preferences of players under asynchronous scheduling. “Low overhead” means that
the probing cost is only a polylogarithmic factor over the best possible cost; and by “provably” we mean that the algorithm
works with high probability (over internal coin tosses) for all inputs, assuming that each player gets some minimal number
of probing opportunities. We present algorithms in this model for exact and approximate preference reconstruction.

 "In that algorithm, if for every user there is a set of αn other users whose preferences are at most Hammingdistance log(n) away, then the number of queries by each user is O m n log 3.5 n/α . Awerbuch et al. [3] study recommendations algorithms in an asynchronous model, where an adversarial (oblivious) schedule determines which user will make the next probe, and the algorithm may only say which object should that user probe. "
Conference Paper: Recommender systems with nonbinary grades.
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ABSTRACT: We consider the interactive model of recommender systems, in which users are asked about just a few of their preferences, and in return the system outputs an approximation of all their preferences. The measure of performance is the probe complexity of the algorithm, defined to be the maximal number of answers any user should provide (probe complexity typically depends inversely on the number of users with similar preferences and on the quality of the desired approximation). Previous interactive recommendation algorithms assume that user preferences are binary, meaning that each object is either "liked" or "disliked" by each user. In this paper we consider the general case in which users may have a more refined scale of preference, namely more than two possible grades. We show how to reduce the nonbinary case to the binary one, proving the following results. For discrete grades with s possible values, we give a simple deterministic reduction that preserves the approximation properties of the binary algorithm at the cost of increasing probe complexity by factor s. Our main result is for the general case, where we assume that user grades are arbitrary real numbers. For this case we present an algorithm that preserves the approximation properties of the binary algorithm while incurring only polylogarithmic overhead.SPAA 2011: Proceedings of the 23rd Annual ACM Symposium on Parallelism in Algorithms and Architectures, San Jose, CA, USA, June 46, 2011 (Colocated with FCRC 2011); 01/2011 
 "Other theoretical work on recommendation systems. There have been many other theoretical efforts on recommendation systems [2] [4] [7] [8] [9] [10] [27] [39]. They largely deal with finding good objects out of a fixed set of objects, while our model involves multiple rounds where each round has its own set of objects. "
Conference Paper: DSybil: Optimal SybilResistance for Recommendation Systems
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ABSTRACT: Recommendation systems can be attacked in various ways, and the ultimate attack form is reached with a sybil attack, where the attacker creates a potentially unlimited number of sybil identities to vote. Defending against sybil attacks is often quite challenging, and the nature of recommendation systems makes it even harder. This paper presents DSybil, a novel defense for diminishing the influence of sybil identities in recommendation systems. DSybil provides strong provable guarantees that hold even under the worstcase attack and are optimal. DSybil can defend against an unlimited number of sybil identities over time. DSybil achieves its strong guarantees by i) exploiting the heavytail distribution of the typical voting behavior of the honest identities, and ii) carefully identifying whether the system is already getting "enough help" from the (weighted) voters already taken into account or whether more "help" is needed. Our evaluation shows that DSybil would continue to provide highquality recommendations even when a million node botnet uses an optimal strategy to launch a sybil attack.Security and Privacy, 2009 30th IEEE Symposium on; 06/2009 
Conference Paper: Reputation, Trust and Recommendation Systems in PeertoPeer Systems.
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ABSTRACT: The Internet has brought about the notion of peertopeer computing, whose reliance on a central authority (let alone a central server) is minimal. It seems fair to say that one of the Great Promises of the Internet is that such unmoderated direct interaction between users will reduce much of the traditional overhead due to the “man in middle” taking his share: either financially (in the context of ecommerce) or conceptually (in the context of opinion shaping, say). The flip side of this prospect, of course, is the danger that the system will deteriorate into a lawless jungle: some users in a peertopeer system, possibly coordinated, might exploit honest users to their advantage, since it appears that there is no effective way to enforce rules in this game.Structural Information and Communication Complexity, 15th International Colloquium, SIROCCO 2008, VillarssurOllon, Switzerland, June 1720, 2008, Proceedings; 01/2008