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- W3032185101 abstract "We investigate the following sorting problem: We are given n bins with two balls in each bin. Balls in the ith bin are numbered n + 1 − i. We can swap two balls from adjacent bins. How many number of swaps are needed in order to sort balls, i.e., move every ball to the bin with the same number. For this problem the best known solution requires almost 4 n 2 swaps. In this paper, we show an algorithm which solves this problem using less than 2n 2 3 swaps. Since it is known that the lower bound of the number of swaps is 2n 2 /3 = 2n 2 3 − n 3 , our result is almost tight. Furthermore, we show that for n = 2 m + 1( m ≥ 0) the algorithm is optimal." @default.
- W3032185101 created "2020-06-05" @default.
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- W3032185101 date "2012-03-01" @default.
- W3032185101 modified "2023-10-01" @default.
- W3032185101 title "An almost optimal algorithm for Winkler's sorting pairs in bins" @default.
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- W3032185101 doi "https://doi.org/10.2201/niipi.2012.9.2" @default.
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