Recovery of cyclic words by their subwords

Abstract

The problem of reconstructing words from their subwords involves determining the minimum amount of information needed, such as multisets of scattered subwords of a specific length or the frequency of scattered subwords from a given set, in order to uniquely identify a word. In this paper we show that a cyclic word on a binary alphabet can be reconstructed by its scattered subwords of length $\frac{3}{4}n+4$, and for each $n$ one can find two cyclic words of length $n$ which have the same set of scattered subwords of length $\frac{3}{4}n-\frac{3}{2}$.