International Business Machines Corporation

Atri Rudra

Vijayshankar Raman

Vijay A Kumar

Pankaj Rohatgi

Charanjit Singh Jutla

Josyula R Rao

Pradeep Kumar Dubey

Robert Krauthgamer

Aranyak Mehta

The embodiments of the invention provide a method of ordering an intersecting of a group of lists into a left-deep AND-tree. The method begins by performing a first selecting process including selecting a top list, corresponding to a top leaf of the left-deep AND-tree, from the group of lists to leave remaining lists of the group of lists. The top list can be the smallest list of the group of lists. The method can also select a pair of lists from the group of lists, such that the pair of lists has the smallest intersection size relative to other pairs of lists of the group of lists. Next, the method estimates intersections of the remaining lists with the top list by estimating an amount of intersection between the remaining lists and the top list. This involves sampling a portion of the remaining lists. The method also includes identifying larger list pairs having smaller intersections sizes when compared to smaller list pairs having larger intersections sizes.

Adaptive greedy method for ordering intersecting of a group of lists into a left-deep AND-tree

Efficient parallel processing of algorithms involving Galois Field arithmetic use data slicing techniques to execute arithmetic operations on a computing hardware having SIMD (single-instruction, multiple-data) architectures. A W-bit wide word computer capable of operating on one or more sets of k-bit operands executes Galois Field arithmetic by mapping arithmetic operations of Galois Field GF(2 ) to corresponding operations in subfields lower order (m<n), which one selected on the basis of an appropriate cost function. These corresponding operations are able to be simultaneously executed on the W-bit wide computer such that the results of the arithmetic operations in Galois Field GF(2 ) are obtained in k/W as many cycles of the W-bit computer compared with execution of the corresponding operations on a k-bit computer.

Processing Galois Field arithmetic

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Atri Rudra