On strings containing all subsets as substrings

AbstractLet Sπ be the length of a shortest sequence of positive integers which contains every Y ⊆{1,…,n} as a subsequence of |Y| consecutive terms. We give the following asymptotic estimation: (2πn)122n≲Sn≲(2π)2n. The upper bound is derived constructively

Universal Cycles for Minimum Coverings of Pairs by Triples, with Application to 2-Radius Sequences

A new ordering, extending the notion of universal cycles of Chung {\em et al.} (1992), is proposed for the blocks of $k$-uniform set systems. Existence of minimum coverings of pairs by triples that possess such an ordering is established for all orders. Application to the construction of short 2-radius sequences is given, with some new 2-radius sequences found through computer search.Comment: 18 pages, to appear in Mathematics of Computatio

MKS: a multisensor kernel system

Journal ArticleThe multisensor kernel system (MKS) is presented as a means for multisensor integration and data acquisition. This system has been developed in the context of a robot work station equipped with various types of sensors utilizing three-dimensional laser range finder data and two-dimensional camera data. Specific goals that have been achieved include 1) Developing a suitable low-level representation of raw data and/or features extracted from the raw data of the various sensors; 2) Providing a method for efficient reconfiguration of the sensor system in terms of "logical" sensors which map onto physical sensors and computation; and 3) Providing a basis for high-level object modeling techniques