# Three Partition Refinement Algorithms

@article{Paige1987ThreePR, title={Three Partition Refinement Algorithms}, author={Robert Paige and Robert Endre Tarjan}, journal={SIAM J. Comput.}, year={1987}, volume={16}, pages={973-989} }

We present improved partition refinement algorithms for three problems: lexicographic sorting, relational coarsest partition, and double lexical ordering. Our double lexical ordering algorithm uses a new, efficient method for unmerging two sorted sets.

## 1,229 Citations

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### The Parallel Complexity of Coarsest Set Partition Problems

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### A Synthesis on Partition Refinement: A Useful Routine for Strings, Graphs, Boolean Matrices and Automata

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A single routine is proposed to quickly implement all these already known algorithms and to solve a large class of potentially new problems to yield a unique scheme for correctness proofs and complexity analysis.

### A Simple Linear Time Algorithm for the Domatic Partition Problem on Strongly Chordal Graphs

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### The Parallel Complexity of Elimination Ordering Procedures

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- 1993

We prove that lexicographic breadth-first search is P-complete and that a variant of the parallel perfect elimination procedure of P. Klein [11] is powerful enough to compute a semi-perfect…

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Recently in several papers ([10],[22],[42]) independently graphs with maximum neighbourhood orderings were characterized and turned out to be algorithmically useful.

## References

SHOWING 1-10 OF 13 REFERENCES

### Doubly lexical orderings of matrices

- MathematicsSTOC '85
- 1985

A doubly lexical ordering of the rows and columns of any real-valued matrix is defined. This notion extends to graphs. These orderings are used to prove and unify results on several classes of…

### The Design and Analysis of Computer Algorithms

- Computer Science
- 1974

This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.

### Design and Analysis of a Data Structure for Representing Sorted Lists

- Computer ScienceSIAM J. Comput.
- 1980

This analysis leads to a data structure for representing sorted lists when the access pattern exhibits a (perhaps time-varying) locality of reference that is substantially simpler and may be practical for lists of moderate size.

### Variations on the Common Subexpression Problem

- MathematicsJ. ACM
- 1980

Efficient algorithms are described for computing congruence closures in the general case and in the following two special cases to test expression eqmvalence and to test losslessness of joins in relational databases.

### A Linear Time Solution to the Single Function Coarsest Partition Problem

- Computer ScienceTheor. Comput. Sci.
- 1985

### Amortized Computational Complexity

- Computer Science
- 1985

This paper surveys recent work by several researchers on amortized complexity and obtains “self-adjusting” data structures that are simple, flexible and efficient.

### A Calculus of Communicating Systems

- Computer ScienceLecture Notes in Computer Science
- 1980

A case study in synchronization and proof techniques, and some proofs about data structures in value-communication as a model of CCS 2.0.