The authors introduce a new characteristic of net frequency that simplifies the original definition. They then study the net frequency of strings in Fibonacci words and use this to develop efficient algorithms for two key problems related to net frequency computation:
For single-nf, the authors present an O(m + σ) time algorithm, where m is the length of the query string and σ is the size of the alphabet. This is achieved by leveraging suffix arrays, the Burrows-Wheeler transform, LCP arrays, and a solution to the coloured range listing problem.
For all-nf, the authors establish a connection between strings with positive net frequency and branching strings. They then solve all-nf-report in O(n) time and all-nf-extract in O(n log δ) time, where n is the length of the text and δ is a repetitiveness measure. Their algorithms make use of LCP intervals and irreducible LCP values.
The authors also conduct extensive experiments that demonstrate the efficiency of their algorithms compared to reasonable baselines.
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