Meanders and Stamp Foldings: Fast Generation Algorithms
نویسندگان
چکیده
By considering a permutation representation for meanders, semi-meanders, and stamp foldings we construct a new data structure that will allow us to extend the order of a given meander, semi-meander, or stamp folding in constant time. Then using this data structure, we develop a constant amortized time algorithm to generate all semi-meanders of order n. By maintaining the wind-factor for semi-meanders and applying an additional optimization, the algorithm can be modified to produce the fastest known algorithm to generate meanders. Finally, by handling an additional special case, the semi-meander algorithm can be modified to generate all stamp foldings of order n in constant amortized time.
منابع مشابه
Stamp Foldings, Semi-Meanders, and Open Meanders: Fast Generation Algorithms
By considering a permutation representation for stamp-foldings and semi-meanders we construct tree-like data structures that will allow us to generate these objects in constant amortized time. Additionally, by maintaining the wind-factor and applying an additional optimization, the algorithm for semi-meanders can be modified to produce the fastest known algorithm to generate open meanders.
متن کاملFoldings and meanders
We review the stamp folding problem, the number of ways to fold a strip of n stamps, and the related problem of enumerating meander configurations. The study of equivalence classes of foldings and meanders under symmetries allows to characterize and enumerate folding and meander shapes. We describe symmetric foldings and meanders, and we give formulas relating folding and meander sequences. We ...
متن کاملMeander , Folding and Arch Statistics
The statistics of meander and related problems are studied as particular realizations of compact polymer chain foldings. This paper presents a general discussion of these topics, with a particular emphasis on three points: (i) the use of a direct recursive relation for building (semi) meanders (ii) the equivalence with a random matrix model (iii) the exact solution of simpler related problems, ...
متن کاملCritical exponents of plane meanders
Meanders form a set of combinatorial problems concerned with the enumeration of self-avoiding loops crossing a line through a given number of points, n. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We use a recently developed algorithm, based on transfer matrix methods, to enumerate plane meanders. This allows us to calculate the number of closed meander...
متن کاملRiver and Coastal Action in Automatic Terrain Generation
The erosive action of rivers and seas has immense influence on the appearance of the physical landscape. However, the creation of several important river and coastal features are not available in terrain creation software and systems. We have designed algorithms to easily create these features, namely (1) river meanders, (2) river deltas, (3) coastal cliffs, and (4) beaches. A terrain that does...
متن کامل