De Bruijn Covering Codes for Rooted Hypergraphs
نویسندگان
چکیده
What is the length of the shortest sequence S of reals so that the set of consecutive n-words in S form a covering code for permutations on {1, 2, . . . , n} of radius R ? (The distance between two n-words is the number of transpositions needed to have the same order type.) The above problem can be viewed as a special case of finding a De Bruijn covering code for a rooted hypergraph. Each edge of a rooted hypergraph contains a special vertex, called the root of the edge, and each vertex is the root of a unique edge, called its ball. A De Bruijn covering code is a subset of the roots such that every vertex is in some edge containing a chosen root. Under some mild conditions, we obtain an upper bound for the shortest length of a De Bruijn covering code of a rooted hypergraph, a bound which is within a factor of log n of the lower bound.
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