Revisiting T. Uno and M. Yagiura’s Algorithm | Zendy

Binh-Minh Bui Xuan | Zendy; Michel Habib | Zendy; Christophe Paul | Zendy

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Revisiting T. Uno and M. Yagiura’s Algorithm

Author(s) -

Binh-Minh Bui Xuan,

Michel Habib,

Christophe Paul

Publication year - 2005

Publication title -

lecture notes in computer science

Language(s) - English

Resource type - Book series

SCImago Journal Rank - 0.249

H-Index - 400

eISSN - 1611-3349

pISSN - 0302-9743

ISBN - 3-540-30935-7

DOI - 10.1007/11602613_16

Subject(s) - algorithm , combinatorics , decomposition , time complexity , running time , mathematics , undirected graph , discrete mathematics , invariant (physics) , graph , computer science , ecology , mathematical physics , biology

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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