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- W2952893155 abstract "The problem of merging sorted lists in the least number of pairwise comparisons has been solved completely only for a few special cases. Graham and Karp cite{taocp} independently discovered that the tape merge algorithm is optimal in the worst case when the two lists have the same size. In the seminal papers, Stockmeyer and Yaocite{yao}, Murphy and Paullcite{3k3}, and Christencite{christen1978optimality} independently showed when the lists to be merged are of size $m$ and $n$ satisfying $mleq nleqlfloorfrac{3}{2}mrfloor+1$, the tape merge algorithm is optimal in the worst case. This paper extends this result by showing that the tape merge algorithm is optimal in the worst case whenever the size of one list is no larger than 1.52 times the size of the other. The main tool we used to prove lower bounds is Knuth's adversary methods cite{taocp}. In addition, we show that the lower bound cannot be improved to 1.8 via Knuth's adversary methods. We also develop a new inequality about Knuth's adversary methods, which might be interesting in its own right. Moreover, we design a simple procedure to achieve constant improvement of the upper bounds for $2m-2leq nleq 3m $." @default.
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- W2952893155 date "2016-10-11" @default.
- W2952893155 modified "2023-09-22" @default.
- W2952893155 title "On the Optimality of Tape Merge of Two Lists with Similar Size" @default.
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- W2952893155 doi "https://doi.org/10.48550/arxiv.1610.03266" @default.
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