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 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.
REF reached a linear time algorithm in the definition framework of PQ trees.
Revisiting T. Uno and M. Yagiura’s algorithm
Proc. 16th International Symposium on Algorithms and Computation, in Lecture Notes in Comput. Sci
Mathematics Computer Science