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Fast Stable Merging And Sorting In Constant Extra Space
, 1990
"... In an earlier research paper [HL1], we presented a novel, yet straightforward lineartime algorithm for merging two sorted lists in a fixed amount of additional space. Constant of proportionality estimates and empirical testing reveal that this procedure is reasonably competitive with merge routines ..."
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In an earlier research paper [HL1], we presented a novel, yet straightforward lineartime algorithm for merging two sorted lists in a fixed amount of additional space. Constant of proportionality estimates and empirical testing reveal that this procedure is reasonably competitive with merge routines free to squander unbounded additional memory, making it particularly attractive whenever space is a critical resource. In this paper, we devise a relatively simple strategy by which this efficient merge can be made stable, and extend our results in a nontrivial way to the problem of stable sorting by merging. We also derive upper bounds on our algorithms' constants of proportionality, suggesting that in some environments (most notably external file processing) their modest runtime premiums may be more than offset by the dramatic space savings achieved.
Linesegment intersection made inplace
, 2007
"... We present a spaceefficient algorithm for reporting all k intersections induced by a set of n line segments in the plane. Our algorithm is an inplace variant of Balaban’s algorithm and, in the worst case, runs in O(n log2 n+k) time using O(1) extra words of memory in addition to the space used f ..."
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We present a spaceefficient algorithm for reporting all k intersections induced by a set of n line segments in the plane. Our algorithm is an inplace variant of Balaban’s algorithm and, in the worst case, runs in O(n log2 n+k) time using O(1) extra words of memory in addition to the space used for the input to the algorithm.
A.: Stable minimum storage merging by symmetric comparisons
 Algorithms  ESA 2004. Volume 3221 of Lecture Notes in Computer Science
, 2004
"... Abstract. We introduce a new stable minimum storage algorithm for merging that needs O(m log ( n + 1)) element comparisons, where m and m n are the sizes of the input sequences with m ≤ n. According to the lower bound for merging, our algorithm is asymptotically optimal regarding the number of compa ..."
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Abstract. We introduce a new stable minimum storage algorithm for merging that needs O(m log ( n + 1)) element comparisons, where m and m n are the sizes of the input sequences with m ≤ n. According to the lower bound for merging, our algorithm is asymptotically optimal regarding the number of comparisons. The presented algorithm rearranges the elements to be merged by rotations, where the areas to be rotated are determined by a simple principle of symmetric comparisons. This style of minimum storage merging is novel and looks promising. Our algorithm has a short and transparent definition. Experimental work has shown that it is very efficient and so might be of high practical interest. 1
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 ...
Ratio based stable inplace merging
"... Abstract. We investigate the problem of stable inplace merging from a ratio k = n based point of view where m, n are the sizes of the input m sequences with m ≤ n. We introduce a novel algorithm for this problem that is asymptotically optimal regarding the number of assignments as well as compariso ..."
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Abstract. We investigate the problem of stable inplace merging from a ratio k = n based point of view where m, n are the sizes of the input m sequences with m ≤ n. We introduce a novel algorithm for this problem that is asymptotically optimal regarding the number of assignments as well as comparisons. Our algorithm uses knowledge about the ratio of the input sizes to gain optimality and does not stay in the tradition of Mannila and Ukkonen’s work [8] in contrast to all other stable inplace merging algorithms proposed so far. It has a simple modular structure and does not demand the additional extraction of a movement imitation buffer as needed by its competitors. For its core components we give concrete implementations in form of Pseudo Code. Using benchmarking we prove that our algorithm performs almost always better than its direct competitor proposed in [6]. As additional subresult we show that stable inplace merging is a quite simple problem for every ratio k ≥ √ m by proving that there exists a primitive algorithm that is asymptotically optimal for such ratios. 1