Daniel D Sleator; Robert E Tarjan; William P Thurston
|物理形態：||26 pages : illustrations ; 28 cm.|
|シリーズタイトル：||Research paper (Carnegie Mellon University. School of Computer Science), CMU-CS-91-206.|
|責任者：||Daniel D.K. Sleator, Robert E. Tarjan, William P. Thurston.|
We show for example that [omega](n log n) applications of the associative and commutative laws are required in the worst case to transform an n-variable expression over a binary associative, commutative operation into some other equivalent expression. Similarly, we show that [omega](n log n) 'diagonal flips' are required in the worst case to transform one n-vertex numbered triangulated planar graph into some other one. Both of these lower bounds have matching upper bounds. An O(n log n) upper bound for associative, commutative operations was known previously, whereas we obtain here an O(n log n) upper bound for diagonal flips."