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On optimal and efficient in place merging
 SOFSEM 2006. Volume 3831 of Lecture Notes in Computer Science
, 2006
"... Abstract. We introduce a new stable in place merging algorithm that needs O(m log ( n +1)) comparisons and O(m+n) assignments. According m to the lower bounds for merging our algorithm is asymptotically optimal regarding the number of comparisons as well as assignments. The stable algorithm is devel ..."
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Abstract. We introduce a new stable in place merging algorithm that needs O(m log ( n +1)) comparisons and O(m+n) assignments. According m to the lower bounds for merging our algorithm is asymptotically optimal regarding the number of comparisons as well as assignments. The stable algorithm is developed in a modular style out of an unstable kernel for which we give a definition in pseudocode. The literature so far describes several similar algorithms but merely as sophisticated theoretical models without any reasoning about their practical value. We report specific benchmarks and show that our algorithm is for almost all input sequences faster than the efficient minimum storage algorithm by Dudzinski and Dydek. The proposed algorithm can be effectively used in practice. 1
InSitu, Stable Merging by way of the Perfect Shuffle.
, 1999
"... We introduce a novel approach to the classical problem of insitu, stable merging, where "insitu" means the use of no more than O(log 2 n) bits of extra memory for lists of size n. Shufflemerge reduces the merging problem to the problem of realising the "perfect shuffle" permutation, that is, the ..."
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We introduce a novel approach to the classical problem of insitu, stable merging, where "insitu" means the use of no more than O(log 2 n) bits of extra memory for lists of size n. Shufflemerge reduces the merging problem to the problem of realising the "perfect shuffle" permutation, that is, the exact interleaving of two, equal length lists. The algorithm is recursive, using a logarithmic number of variables, and so does not use absolutely minimum storage, i.e., a fixed number of variables. A simple method of realising the perfect shuffle uses one extra bit per element, and so is not insitu. We show that the perfect shuffle can be attained using absolutely minimum storage and in linear time, at the expense of doubling the number of moves, relative to the simple method. We note that there is a worst case for Shufflemerge requiring time\Omega\Gamma n log n), where n is the sum of the lengths of the input lists. We also present an analysis of a variant of Shufflemerge which uses a ...
Parallel methods for Solving Fundamental File Rearrangement Problems
, 1990
"... We present parallel algorithms for the elementary binary set operations that, given an EREW PRAM with k processors, operate on two sorted lists of total length n in O(n=k + log n) time and O(k) extra space, and are thus timespace optimal for any value of k n=(log n). Our methods are stable, requir ..."
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We present parallel algorithms for the elementary binary set operations that, given an EREW PRAM with k processors, operate on two sorted lists of total length n in O(n=k + log n) time and O(k) extra space, and are thus timespace optimal for any value of k n=(log n). Our methods are stable, require no information other than a record's key, and do not modify records as they execute. ii Symbols Used O capital Greek omicron of "big oh" notation 6 capital Greek sigma for summations [ set union " set intersection 8 set exclusive or iii 1. Introduction The design and analysis of optimal parallel file rearrangement algorithms has long been a topic of widespread attention. The vast majority of the published literature has concentrated on the search for algorithms that are time optimal , that is, those that achieve optimal speedup (see, for example, [AS]). Unfortunately, space management issues have often taken a back seat in these efforts, leaving those who seek to implement optima...