Algorithm 23: MATH SORT

Feurzeig, Wallace

doi:10.1145/367436.367450

Cited by 9 publications

(10 citation statements)

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“…From complexity point of view, associative sort shows similar characteristics with distribution counting sort [15,16] and bucket sort [23,24]. the worst case is when n = 2 w−1 and the complexity is the recursion…”

Section: Complexitymentioning

confidence: 99%

“…The adjective "associative" derived from two facts where the first one will be realized with the description of the technique. The second one is that, although it replaces all derivatives of the content based sorting algorithms such as distribution counting sort [15,16], address calculation sort [17][18][19][20][21][22] and bucket sort [23,24] on a RAM, it seems to be more efficient on a"content addressable memory" (CAM) known as "associative memory" which in one word time find a matching segment in tag portion of the word and reaches the remainder of the word [29]. In the current version of associative sort developed on a RAM, the nodes of the imaginary subspace (tagged words) and the integers of the array space (untagged words) are processed sequentially which will be a matter of one word time for a CAM to retrieve previous or next tagged or untagged word.…”

Section: Introductionmentioning

confidence: 99%

“…Each key is associated with a position depending on its content. Some important examples are distribution counting sort [15,16], address calculation sort [17][18][19][20][21][22], bucket sort [23,24] and radix sort [23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The technique of in-place associative sorting

Cetin¹

2013

Preprint

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In the first place, a novel, yet straightforward in-place integer value-sorting algorithm is presented. It sorts in linear time using constant amount of additional memory for storing counters and indices beside the input array. The technique is inspired from the principal idea behind one of the ordinal theories of "serial order in behavior" and explained by the analogy with the three main stages in the formation and retrieval of memory in cognitive neuroscience: (i) practicing, (ii) storage and (iii) retrieval. It is further improved in terms of time complexity as well as specialized for distinct integers, though still improper for rank-sorting.Afterwards, another novel, yet straightforward technique is introduced which makes this efficient value-sorting technique proper for rank-sorting. Hence, given an array of n elements each have an integer key, the technique sorts the elements according to their integer keys in linear time using only constant amount of additional memory. The devised technique is very practical and efficient outperforming bucket sort, distribution counting sort and address calculation sort family of algorithms making it attractive in almost every case even when space is not a critical resource.

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Section: Complexitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The technique of in-place associative sorting

Cetin¹

2013

Preprint

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“…defining the characteristic function implicitly, the idempotent permutation π can be determined in-place of ι in O(n) time using log n bits, (iii). the linearly ordered arrangement of ι (and hence f ) can be obtained in-place of π in O(n) time using 4 log n bits with associative permuting, resulting in an algorithm setting the theoretical lower bound of time and space complexity of sorting n integer keys each in [1, n], whereas distribution counting sort, address calculation sort and bucket sort family of algorithms require at least additional n log n bits [3][4][5][6][7][8][9][10][11][12] .…”

Section: Introductionmentioning

confidence: 99%

Idempotent permutations

Cetin

2013

Preprint

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Together with a characteristic function, idempotent permutations uniquely determine idempotent maps, as well as their linearly ordered arrangement simultaneously. Furthermore, in-place linear time transformations are possible between them. Hence, they may be important for succinct data structures, information storing, sorting and searching.In this study, their combinatorial interpretation is given and their application on sorting is examined. Given an array of n integer keys each in [1, n], if it is allowed to modify the keys in the range [−n, n], idempotent permutations make it possible to obtain linearly ordered arrangement of the keys in O(n) time using only 4 log n bits, setting the theoretical lower bound of time and space complexity of sorting. If it is not allowed to modify the keys out of the range [1, n], then n + 4 log n bits are required where n of them is used to tag some of the keys.

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“…From complexity point of view, associative sort shows similar characteristics with bucket sort [2,3] and distribution counting sort [4,5]…”

Section: Introductionmentioning

confidence: 99%

Sorting distinct integer keys using in-place associative sort

Cetin

2012

Preprint

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In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms. The technique was explained by the analogy with the three main stages in the formation and retrieval of memory in cognitive neuroscience which are (i) practicing, (ii) storing and (iii) retrieval.In this study, the technique is specialized with two variants one for read-only integer keys and the other for modifiable integers. Hence, a novel algorithm is obtained that does not require additional memory other than a constant amount and sorts faster than all no matter how large is the list provided that m = O(n log n) where m is the range and n is the number of keys (or integers).

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Algorithm 23: MATH SORT

Cited by 9 publications

References 0 publications

The technique of in-place associative sorting

The technique of in-place associative sorting

Idempotent permutations

Sorting distinct integer keys using in-place associative sort

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