A synthesis on partition refinement: A useful routine for strings, graphs, boolean matrices and automata
Partition refinement techniques are used in many algorithms. This tool allows efficient computation of equivalence relations and is somehow dual to union-find algorithms. The goal of this paper is to propose a single routine to quickly implement all these already known algorithms and to solve a large class of potentially new problems. Our framework yields to a unique scheme for correctness proofs and complexity analysis. Various examples are presented to show the different ways of using this routine.
KeywordsMaximal Clique Interval Graph Correctness Proof Boolean Matrix Permutation Graph
Unable to display preview. Download preview PDF.
- A.V. Aho, J.E. Hopcroft, and J.D. Ullman. Design and analysis of computer algorithms. Addison-Wesley, 1974.Google Scholar
- J. Amilhastre. Représentation par automates de l'ensemble des solutions d'un problème de satisfaction de contraintes. Technical Report 94056, LIRMM, 1994.Google Scholar
- D.G Corneil, S. Olariu, and L. Stewart. The ultimate interval graph recognition algorithm. Extended abstract, 1997.Google Scholar
- E. Dahlhaus, J. Gustedt, and R.M. McConnell. Efficient and practical modular decomposition. In Proc. of SODA, 1997.Google Scholar
- M. Habib, R. McConnell, C. Paul, and L. Viennot. Lex-bfs and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing. Theoritical Computer Science, 1997. to appear.Google Scholar
- J.E. Hopcropft. A nlogn algorithm for minizing states in a finite automaton. Theory of Machine and Computations, pages 189–196, 1971.Google Scholar
- W.L. Hsu. A simple test for the consecutive ones property. In LNCS 650, pages 459–468, 1992.Google Scholar
- R.M. McConnell and J.P. Spinrad. Linear-time modular decomposition and efficient transitive orientation of comparability graphs. In Proc. of SODA, pages 536–545, 1994.Google Scholar
- R.M. McConnell and J.P. Spinrad. Linear-time modular decomposition and efficient transitive orientation of undirected graphs. In Proc. of SODA, 1997.Google Scholar
- J.P. Spinrad. Graph partitioning. preprint, 1986.Google Scholar