Abstract: A database has a plurality of entries and a plurality of attributes common to each entry, where each entry corresponds to an individual. A query is received from a querying entity query and is passed to the database, and an answer is received in response. An amount of noise is generated and added to the answer to result in an obscured answer, and the obscured answer is returned to the querying entity. The noise is normally distributed around zero with a particular variance. The variance R may be determined in accordance with R>8 T log2(T/?)/?2, where T is the permitted number of queries T, ? is the utter failure probability, and ? is the largest admissible increase in confidence. Thus, a level of protection of privacy is provided to each individual represented within the database. Example noise generation techniques, systems, and methods may be used for privacy preservation in such areas as k means, principal component analysis, statistical query learning models, and perceptron algorithms.

Abstract: Methods and systems are provided for efficiently computing page rankings of web pages or other interconnected objects. The rankings are produced by efficiently computing a principal eigenvector of a page ranking transition matrix. The methods and systems provided herein can be used to produce page rankings in a distributed and/or incremental manner, and can be used to allocate computing resources to processing page rankings for those pages that most demand them.

Abstract: Methods and systems are provided for efficiently computing personalized rankings of web pages or other interconnected objects. The personalized rankings are produced by efficiently computing an approximation matrix to an ideal personalized page ranking matrix. The methods and systems provided herein can be used to produce search results with particular relevance to an individual searcher.

Abstract: Methods and systems are described for computing page rankings more efficiently. Using an interconnectivity matrix describing the interconnection of web pages, a new matrix is computed. The new matrix is used to compute the average of values associated with each web page's neighboring web pages. The secondary eigenvector of this new matrix is computed, and indices for web pages are relabeled according to the eigenvector. The data structure storing the interconnectivity information is preferably also physically sorted according to the eigenvector. By reorganizing the matrix used in the web page ranking computations, caching is performed more efficiently, resulting in faster page ranking techniques. Methods for efficiently allocating the distribution of resources are also described.