Unranking of small combinations from large sets

Unranking Combinations in Parallel

In this report a parallel algorithm is presented for unranking k out of n set subsets. The computations run in a specialized architecture that combines some systolic and some associative features. The algorithm has O(k) time complexity and can be applied in specialized systems for parallel adaptive generation of the set of all combinations, its ordered subsets and any random sequences. This pro...

Algorithms for Unranking Combinations and Other Related Choice Functions

In this report new unranking algorithms are developed for a large class of choice functions representing various classes of combinatorial objects: combinations, complementary combinations, conjugative nondecreasing choice functions, ordered partitions. Presented algorithms differ with the type of lexicographical order they deal with and the method of binomial coefficient evaluation. The proofs ...

Some small large sets of t-designs

On Extracting Feature Models from Sets of Valid Feature Combinations

Rather than developing individual systems, Software Product Line Engineering develops families of systems. The members of the software family are distinguished by the features they implement and Feature Models (FMs) are the de facto standard for defining which feature combinations are considered valid members. This paper presents an algorithm to automatically extract a feature model from a set ...

Convex Sets and Convex Combinations

Convexity is one of the most important concepts in a study of analysis. Especially, it has been applied around the optimization problem widely. Our purpose is to define the concept of convexity of a set on Mizar, and to develop the generalities of convex analysis. The construction of this article is as follows: Convexity of the set is defined in the section 1. The section 2 gives the definition...