Abstract
In 2000, T. Uno and M. Yagiura published an algorithm that computes all the K common intervals of two given permutations of length n in \(\mathcal{O}(n+ K)\) time. Our paper first presents a decomposition approach to obtain a compact encoding for common intervals of d permutations. Then, we revisit T. Uno and M. Yagiura’s algorithm to yield a linear time algorithm for finding this encoding. Besides, we adapt the algorithm to obtain a linear time modular decomposition of an undirected graph, and thereby propose a formal invariant-based proof for all these algorithms.
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Xuan, BM.B., Habib, M., Paul, C. (2005). Revisiting T. Uno and M. Yagiura’s Algorithm. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_16
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DOI: https://doi.org/10.1007/11602613_16
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