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We consider the problem of combining ranking results from various sources. In the context of the Web, the main applications include building meta-search engines, combining ranking functions, selecting documents based on multiple criteria, and improving search precision through word associations. We d e v elop a set of techniques for the rank aggregation problem and compare their performance to that of well-known methods. A primary goal of our work is to design rank aggregation techniques that can e ectively combat \spam," a serious problem in Web searches. Experiments show that our methods are simple, e cient, and e ective.

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We live in a ''small world,'' where two arbitrary people are likely connected by a short chain of intermediate friends. With scant information about a target individual, people can successively forward a message along such a chain. Experimental studies have verified this property in real social networks, and theoretical models have been advanced to explain it. However, existing theoretical models have not been shown to capture behavior in real-world social networks. Here, we introduce a richer model relating geography and social-network friendship, in which the probability of befriending a particular person is inversely proportional to the number of closer people. In a large social network, we show that one-third of the friendships are independent of geography and the remainder exhibit the proposed relationship. Further, we prove analytically that short chains can be discovered in every network exhibiting the relationship.routing algorithms ͉ small worlds ͉ population networks ͉ rank-based friendships ͉ six degrees of separation

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We present a new method for proving strong lower bounds in communication complexity. This method is based on the notion of the conditional information complexity of a function which is the minimum amount of information about the inputs that has to be revealed by a communication protocol for the function. While conditional information complexity is a lower bound on the communication complexity,we show that it also admits a direct sum theorem. Direct sum decomposition reduces our task to that of proving (conditional) information complexity lower bounds for simple problems (such as the AND of two bits). For the latter, we develop novel techniques based on Hellinger distance and its generalizations.Our paradigm leads to two main results:(1) An improved lower bound for the multi-party setdisjointness problem in the general communication complexity model, and a nearly optimal lower bound in the oneway communication model. As a consequence, we show that for any real ¾, approximating the -th frequency moment in the data stream model requires ª´Ò ½ ¾ µ space; this resolves a conjecture of Alon, Matias, and Szegedy [3].(2) A lower bound for the Ä Ô approximation problem in the general communication model; this solves an open problem of Saks and Sun [23]. As a consequence, we show that for Ô ¾, approximating the Ä Ô norm to within a factor of Ò¯in the data stream model with constant number of passes requires ª´Ò ½ ¯ ¾ Ô µ space.

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