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Short encodings of evolving structures

著者: Daniel D Sleator; Robert E Tarjan; William P Thurston
出版: Pittsburgh, Pa. : School of Computer Science, Carnegie Mellon University, [1991]
シリーズ: Research paper (Carnegie Mellon University. School of Computer Science), CMU-CS-91-206.
エディション/フォーマット:   書籍 : Englishすべてのエディションとフォーマットを見る
データベース:WorldCat
概要:
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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ドキュメントの種類: 図書
すべての著者/寄与者: Daniel D Sleator; Robert E Tarjan; William P Thurston
OCLC No.: 25683200
注記: "December 1991."
物理形態: 26 p. : ill. ; 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.

概要:

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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