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Short encodings of evolving structures

作者: Daniel D Sleator; Robert E Tarjan; William P Thurston
出版商: Pittsburgh, Pa. : School of Computer Science, Carnegie Mellon University, [1991]
叢書: Research paper (Carnegie Mellon University. School of Computer Science), CMU-CS-91-206.
版本/格式:   圖書 : 英語所有版本和格式的總覽
資料庫:WorldCat
提要:
Abstract: "A derivation in a transformational system such as a graph grammar may be redundant in the sense that the exact order of the transformations may not affect the final outcome; all that matters is that each transformation, when applied, is applied to the correct substructure. By taking advantage of this redundancy, we are able to develop an efficient encoding scheme for such derivations. This encoding scheme
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文件類型: 圖書
所有的作者/貢獻者: Daniel D Sleator; Robert E Tarjan; William P Thurston
OCLC系統控制編碼: 25683200
注意: "December 1991."
描述: 26 p. : ill. ; 28 cm.
叢書名: Research paper (Carnegie Mellon University. School of Computer Science), CMU-CS-91-206.
責任: Daniel D.K. Sleator, Robert E. Tarjan, William P. Thurston.

摘要:

Abstract: "A derivation in a transformational system such as a graph grammar may be redundant in the sense that the exact order of the transformations may not affect the final outcome; all that matters is that each transformation, when applied, is applied to the correct substructure. By taking advantage of this redundancy, we are able to develop an efficient encoding scheme for such derivations. This encoding scheme has a number of diverse applications. It can be used in efficient enumeration of combinatorial objects or for compact representation of program and data structure transformations. It can also be used to derive lower bounds on lengths of derivations.

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."

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