Abstract: The present invention provides a unique system and method that facilitates reducing network traffic between a plurality of servers located on a social-based network. The system and method involve identifying a plurality of vertices or service users on the network with respect to their server or network locations. The vertices' contacts or connections can be located or determined as well. In order to minimize communication traffic, the vertices and their connections with respect to their respective server locations can be analyzed to determine whether at least a subset of nodes should be moved or relocated to another server to facilitate mitigating network traffic while balancing user load among the various servers or parts of the network. Thus, an underlying social network can be effectively partitioned. In addition, the network can be parsed into a collection of nested layers, whereby each successively less dense layer can be partitioned with respect to the previous (partitioned) more dense layer.

Abstract: Hash tables comprising load factors of up to and above 97% are disclosed. The hash tables may be associated with three or more hash functions, each hash function being applied to a key to identify a location in a hash table. The load factor of a hash table may be increased, obviating any need to increase the size of the hash table to accommodate more insertions. Such increase in load factor may be accomplished by a combination of increasing the number of cells per bucket in a hash table and increasing the number of hash functions associated with the hash table.

Abstract: An input or query is determined for which a search engine's static ranking computation is the answer. By understanding how this input or query differs from the posed input or query, the precise termination point of an iterative convergence problem can be determined. An iterative process provides the following inputs to the system: a graph of hyperlinks, and a vector of how the probability mass is redistributed. Given the set of ranks (the output results), it is determined how the input (e.g., the query) would have to be changed to get the rank(s) as the answer or result. Backward answer analysis is provided in the web page context. The difference between what was asked and what should have been asked is determined. After the difference is computed, it is determined if the iterative process should be stopped or not.

Abstract: An amount of noise to add to a query output may be selected to preserve privacy of inputs while maximizing utility of the released output. Noise values can be distributed according to a substantially symmetric exponential density function (“exponential distribution”). That is, the most likely noise value can be zero, and noise values of increasing absolute value can decrease in probability according to the exponential function.

Abstract: Documents that are near-duplicates may be determined using techniques such as min-hashing. Randomness that is used in these techniques may be based on sequences of bits. The sequences of bits may be generated from a string of bits, with the sequences determined by parsing the string at each occurrence of a particular value, such as the value “1”.

Abstract: Methods and systems for finding a low rank approximation for an m×n matrix A are described. The described embodiments can independently sample and/or quantize the entries of an input matrix A, and can thus speed up computation by reducing the number of non-zero entries and/or their representation length. The embodiments can be used in connection with Singular Value Decomposition techniques to greatly benefit the processing of high-dimensional data sets in terms of storage, transmission and computation.

Abstract: Methods and systems for finding a low rank approximation for an m×n matrix A are described. The described embodiments can independently sample and/or quantize the entries of an input matrix A, and can thus speed up computation by reducing the number of non-zero entries and/or their representation length. The embodiments can be used in connection with Singular Value Decomposition techniques to greatly benefit the processing of high-dimensional data sets in terms of storage, transmission and computation.

Abstract: Techniques are provided that identify near-duplicate items in large collections of items. A list of (value, frequency) pairs is received, and a sample (value, instance) is returned. The value is chosen from the values of the first list, and the instance is a value less than frequency, in such a way that the probability of selecting the same sample from two lists is equal to the similarity of the two lists.

Abstract: A histogram can be generated and displayed with noisy category values, where the noise values are selected from a noise distribution that is calculated using a histogram diameter. The noise values are combined with histogram category values, thereby producing noisy histogram category values that do not reveal information about the contributors.

Abstract: Methods and systems for finding a low rank approximation for an m×n matrix A are described. The described embodiments can independently sample and/or quantize the entries of an input matrix A, and can thus speed up computation by reducing the number of non-zero entries and/or their representation length. The embodiments can be used in connection with Singular Value Decomposition techniques to greatly benefit the processing of high-dimensional data sets in terms of storage, transmission and computation.

Abstract: Methods and systems for finding a low rank approximation for an m×n matrix A are described. The described embodiments can independently sample and/or quantize the entries of an input matrix A, and can thus speed up computation by reducing the number of non-zero entries and/or their representation length. The embodiments can be used in connection with Singular Value Decomposition techniques to greatly benefit the processing of high-dimensional data sets in terms of storage, transmission and computation.