Revisiting T. Uno and M. Yagiura's Algorithm

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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