Pattern matching with wildcards is a string matching problem with the goal of finding all factors of a text t of length n that match a pattern x of length m, where wildcards (characters that match everything) may be present. In this paper we ...
We consider problems such as selecting the k-th smallest of n numbers in as few comparisons as possible on average. n + k - 0(1) comparisons are proved to be necessary for this particular problem when k ≤ n/2. This shows a technique of Floyd and Rivest ...
MergeInsertion, also known as the Ford-Johnson algorithm, is a sorting algorithm which, up to today, for many input sizes achieves the best known upper bound on the number of comparisons. Indeed, it gets extremely close to the information-...
Don Goelman
The authors examine the problem of selecting the kth smallest element from a list of n elements. Special cases of this problem include determining the median, the maximum, and the minimum; also of interest are various combinations of these cases and the general kth value. The authors present and discuss upper and lower bounds, including some lower-order terms, for worst and average cases. In general, the selection algorithms take a random sample of specified size and then compare elements (at large) to strategic values obtained from the sample. In deriving their bounds, the authors use various interesting methods that include studying the effect of an algorithm on input permutations which differ only on a specific comparison, developing (in the case of lower bounds) estimates of path lengths in the tree program that models the algorithm's execution, and solving the linear program that represents a bound under examination. The authors omit the details when the derivations are tedious or repetitive. The methods of proof presented in the paper, and the results themselves, will interest those engaged in the research or study of sorting and selection algorithms, and the bibliography is appropriate.
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