منابع مشابه
Constructing k-radius sequences
An n-ary k-radius sequence is a finite sequence of elements taken from an alphabet of size n such that any two distinct elements of the alphabet occur within distance k of each other somewhere in the sequence. These sequences were introduced by Jaromczyk and Lonc to model a caching strategy for computing certain functions on large data sets such as medical images. Let fk(n) be the shortest leng...
متن کاملThe existence of k-radius sequences
Let n and k be positive integers, and let F be an alphabet of size n. A sequence over F of length m is a k-radius sequence if any two distinct elements of F occur within distance k of each other somewhere in the sequence. These sequences were introduced by Jaromczyk and Lonc in 2004, in order to produce an efficient caching strategy when computing certain functions on large data sets such as me...
متن کاملSequences of Radius k for Complete Bipartite Graphs
A k-radius sequence for a graph G is a sequence of vertices of G (typically with repetitions) such that for every edge uv of G vertices u and v appear at least once within distance k in the sequence. The length of a shortest k-radius sequence for G is denoted by fk(G). We give an asymptotically tight estimation on fk(G) for complete bipartite graphs which matches a lower bound, valid for all bi...
متن کاملConstructing Structure in Number Sequences
This paper reports on a design experiment in the domain of number sequences conducted in the course of the WebLabs project1. In this study, we designed and tested a set of activities in which 13-14 year old students use the ToonTalk programming environment to construct models of sequences and series, and then use the WebReports web-based collaboration system to share these models and their obse...
متن کاملConstructing Orthogonal de Bruijn Sequences
A (σ, k)-de Bruijn sequence is a minimum length string on an alphabet set of size σ which contains all σ k-mers exactly once. Motivated by an application in synthetic biology, we say a given collection of de Bruijn sequences are orthogonal if no two of them contain the same (k + 1)-mer; that is, the length of their longest common substring is k. In this paper, we show how to construct large col...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2012
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2011-02510-x