Using the techniques of “specification and transformation by parts”, algorithms are derived for the longest upsequence problem. First Dijkstra's algorithm and then two new modified merge algorithms are derived and presented in detail. The merge algorithms take advantage of natural runs in the input sequence and have a worst caseO(n logn) time complexity when appropriate merging techniques are used, but can be linear if long runs are present in the sequence. The first merge algorithm is logically equivalent to Dijkstra's algorithm; the second algorithm is based on the first one but uses a different merging technique. Expository remarks describe related results which evolved out of our work in programming by transformation; in particular, parallels are drawn between algorithms for the longest upsequence problem and algorithms for sorting.
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Work on this paper has been supported in part by: ONR Grant N00014-75-C-0571; NSF Grant MCS-80-04349; USDOE Contract EY-76-C-02-3077
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Dewar, R.B.K., Merritt, S.M. & Sharir, M. Some modified algorithms for Dijkstra's longest upsequence problem. Acta Informatica 18, 1–15 (1982). https://doi.org/10.1007/BF00625277
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