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The number of moves of the largest disc in shortest paths on Hanoi graphs [Elektronski vir]Aumann, Simon ...Kljub širšemu zanimanju za Frame-Stewartovo domnevo o optimalnem številu potez v klasičnem problemu hanojskega stolpa z več kot tremi položaji, je to prva študija o najkrajših poteh v hanojskih ... grafih ▫$H_p^n$▫, kjer ▫$p$▫ predstavlja število položajev in ▫$n$▫ število ploščic, če graf interpretiramo kot graf stanj hanojskega stolpa. Študija se še posebej loti analize premikov največje ploščice. Vzorec teh premikov je zakodiran kot binarni niz dolžine ▫$p-1$▫ in prirejen vsakemu paru začetnega in končnega stanja posebej. K analizi problema se pristopa tako analitično kot tudi numerično. Glavni teoretični dosežek je obstoj optimalnih poti za vse ▫$n \geqslant p(p-2)$▫, na katerih so nujni ▫$p-1$▫ premiki največje ploščice. Numerični rezultati so pridobljeni z modificiranim algoritmom, zasnovanim na algoritmu iskanja v širino. V namene optimizacije iskanja se uporabijo simetrije grafov. Numerična evidenca vodi k nekaj domnevam o (ne)obstoju, ki jih teoretični rezultati ne pokrivajo in mogoče nam pomaga razkriti tudi kakšno skrivnost še nerazrešene Frame-Stewartove domneve.Source: The Electronic journal of combinatorics [Elektronski vir]. - ISSN 1077-8926 (Vol. 21, iss. 4, 2014, P4.38 (22 str.))Type of material - e-articlePublish date - 2014Language - englishCOBISS.SI-ID - 17173081
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Aumann, Simon | ![]() |
Götz, Katharina A. M. | ![]() |
Hinz, Andreas M., 1954- | 36905 |
Petr, Ciril | 16013 |
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