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Topic: Radix sort

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	Radix sort - Wikipedia, the free encyclopedia
		A radix sort is an algorithm, a procedure, which can rearrange integer representations based on the processing of individual digits in such a way that the integer representations are eventually in either ascending or descending order.
		One disadvantage of an LSD radix sort is that it does not run in place, which means that the keys or pointers to the keys must be temporarily stored outside of their original memory space during processing.
		A trie essentially represents a set of strings or numbers, and a radix sort which uses a trie structure is not necessarily stable, which means that the original order of duplicate keys is not necessarily preserved, because a set does not contain duplicate elements.
	en.wikipedia.org /wiki/Radix_sort (4052 words)

	Radix sort
		Radix sort has resurfaced as an alternative to other high performance sorting algorithms (like quicksort, heapsort and merge sort) which require O(n lg n) comparisons, where n is the number of items to be sorted.
		The greatest disadvantages of radix sort are that it usually cannot be made to run in place, so O(n) additional memory space is needed, and that it requires one pass for each symbol of the key, so it is very slow for potentially-long keys.
		sort the list of elements based on that digit, but keep the order of elements with the same digit (this is the definition of a stable sort).
	www.ebroadcast.com.au /lookup/encyclopedia/ra/Radix_sort.html (533 words)

	Radix sort
		Radix sort is a fast, stable, sort algorithm which can be used to sort items that are identified by unique keys.
		Radix sort has resurfaced as an alternative to other high performance sorting algorithms (like heapsort and mergesort) which require O(n · lg n) comparisons, where n is the number of items to be sorted.
		The greatest disadvantages of radix sort are that it usually cannot be made to run in place, so O(n) additional memory space is needed, and that it requires one pass over the input list for each symbol in the key, so it is very slow for potentially-long keys.
	www.xasa.com /wiki/en/wikipedia/r/ra/radix_sort.html (641 words)

	Radix Sort
		Radix sorting is based on the bucket sorting algorithm discussed in the preceding section.
		Radix sorting can be used when each element of the universal set can be viewed as a sequences of digits (or letters or any other symbols).
		The key characteristic of the radix sort is that the second pass is done in such a way that it does not destroy the effect of the first pass.
	www.brpreiss.com /books/opus7/html/page514.html (744 words)

	Counting sort - Wikipedia, the free encyclopedia
		Counting sort has a running time of Θ(n+k), where n and k are the lengths of the arrays A (the input array) and C (the counting array), respectively.
		Counting sort may for example be the best algorithm for sorting numbers whose range is between 0 and 100, but it is probably unsuitable for sorting a list of names alphabetically (again, see bucket sort and pigeonhole sort).
		However counting sort can be used in radix sort to sort a list of numbers whose range is too large for counting sort to be suitable alone.
	en.wikipedia.org /wiki/Counting_sort (494 words)

	Sorting and Merging (Site not responding. Last check: 2007-10-08)
		Our implementation of radix sort, although not as fast on large data sets, is deterministic, much simpler to code, stable, faster with small keys, and faster on small data sets (few elements per processor).
		Our implementation of bitonic sort, which is pipelined to use all the hypercube wires simultaneously, is the least efficient of the three on large data sets, but is the most efficient on small data sets, and is considerably more space efficient.
		Radix Sort for Vector Multiprocessors: We have implemented an efficient fully vectorized and parallelized radix sort algorithm for the Cray Y-MP.
	www.cs.cmu.edu /~scandal/alg/sort.html (652 words)

	Radix Sort (Site not responding. Last check: 2007-10-08)
		Radix sort is one of the linear sorting algorithms for integers.
		However, the process adopted by this sort method is somewhat counterintuitive, in the sense that the numbers are sorted on the least-significant digit first, followed by the second-least significant digit and so on till the most significant digit.
		To appreciate Radix Sort, consider the following analogy: Suppose that we wish to sort a deck of 52 playing cards (the different suits can be given suitable values, for example 1 for Diamonds, 2 for Clubs, 3 for Hearts and 4 for Spades).
	www.cse.iitk.ac.in /users/dsrkg/cs210/applets/sortingII/radixSort/radix.html (404 words)

	Radix Sort Algorithm Report
		However, the emergence of the radix sort is closely associated with the mechanical sorting of data containing punch cards that were distributed into buckets during a single pass through the machine card sorter.
		The MSD sort is most commonly illustrated by the example of sorting the letters into piles in the post office according to the first digit of a five-digit zip code.
		The three-way radix Quicksort is a combination of an ordinary Quicksort and the MSD radix sort.
	www2.hawaii.edu /~lejla/RadixAlgorithmReport.html (1612 words)

	Chapter 10
		Radix sort is stable, very fast and generally is an excellent algorithm on modern computers that usually have large memory.
		MSD radix sorts partition the file according to the leading digits of the keys, then recursively apply the same method to the subfiles.
		The sort time of the C version of the radix algorithm is linear in n, the number of records, in contrast to most currently used sorts, which are proportional to n log n.
	www.softpanorama.org /Algorithms/Sorting/radixsort.shtml (1020 words)

	Dr. Dobb's \| Sorting Strings with Three-Way Radix Quicksort \| July 22, 2001 (Site not responding. Last check: 2007-10-08)
		A standard way to sort an array of pointers to strings in C is to call the qsort library function (historically implemented by quicksort); one of the parameters to the qsort function is the strcmp function to compare strings.
		The primary challenge in implementing a radix sort is the case when the number of distinct keys is much less than the number of bins, either because the keys are all equal or because there are not many of them.
		Three-way radix quicksort may be thought of as a radix sort that gracefully adapts to handle this case, at the cost of slightly more work when the bins are all full.
	www.ddj.com /184410724 (2810 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Radix Sort Files: sort.c, short.h Radix sort works by extracting the values of digits within numbers, and sorting according to the value of each digit.
		Any practical radix (or base) can be used for extracting the values of digits, although the optimal setting depends on the properties of the values being sorted.
		Using the same process, the list is sorted again, this time using the value of the second least significant digit, to give a list of data items sorted according to the value of the two least significant digits.
	www.cosc.canterbury.ac.nz /tad.takaoka/alg/sorting/radixsort.txt (493 words)

	Radix Sort
		Radix sort is one of the best general sorting techniques known.
		So it can be seen from this example that radix sort is somewhat similar in principle to merge or quick sort, except that instead of having two sublists at each level, there are usually many.
		If you were sorting complex objects, for instance, where their key could be perhaps tens of fields long, and each field could be one of maybe hundreds of values...m*(p^m) very quickly becomes gigantic, and simply not practical in any sense.
	homepage.mac.com /wadetregaskis/Sorting/RadixSort.html (2064 words)

	[No title]
		The first is a radix sort, and the second a sample sort, based on the algorithm used by the Berkeley NOW (Network of Workstations) group.
		Processor 0 sorts the kn samples using radix* sort, then chooses every kth number to be a splitter (n-1 total splitters).
		The classes used are as follows: class Sort This is the interface to the program, and where the distributed sort code resides.
	www.cs.berkeley.edu /~kamil/titanium/sort/readme.txt (671 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Unsorted -> 1st radix sorted -> 2nd radix sorted 435Fh 5A1Bh 4320h 5A36h 4320h 435Fh 4320h 5A36h 5A1Bh 5A1Bh 435Fh 5A36h To sort a list with the entrysize of one byte (one radix to sort by): We have a sourcelist with the unsorted values.
		To sort a list with the entrysize n (n radices to sort by): Sort the least significant radix, just as you sort a list with only one-radix-sized values.
		As soon as you sort more then one or two times you gain on allocating and deallocating it outside only once instead of every time you enter and leave the sorting procedure.
	thorkildsen.no /faqsys/docs/radix.txt (1300 words)

	Radix Sort Revisited
		Radix is O(kN), with k = 4 most of the time, and although this is not an in-place sort* (i.e.
		But a Radix Sort, due to the initial overhead, is not something to use blindly on little data sets.
		For example when sorting words instead of dwords, the two last passes are useless since all involved bytes are null – in other words, none of those two passes will change the order in which the list already is. The idea then, is to detect those pathological cases and take advantage of them.
	codercorner.com /RadixSortRevisited.htm (3330 words)

	radixsort() -- perform radix sort
		The table argument is useful for applications which wish to sort different characters equally, for example, providing a table with the same weights for A-Z as for a-z results in a case-insensitive sort.
		The implementation is a variant of most-significant-byte radix sorting.
		Is the table of byte strings to be sorted.
	www.mkssoftware.com /docs/man3/radixsort.3.asp (270 words)

	AI Horizon: Radix Sort Part 2
		This can be one of the slowest parts of Radix Sort, and it is one of the hardest to make efficient.
		In short, Radix Sort takes more time to write, and it is very difficult to write a general purpose Radix Sort that can handle all kinds of data.
		Still, there are faster sorts, which is one reason why Radix Sort is not used as much as some other sorts.
	www.aihorizon.com /essays/basiccs/lists/sorting/radix2.htm (361 words)

	7.3 Example Program: Radix Sort
		The radix sort algorithm is a good illustration of how lists and deques can be combined with other containers.
		In the radix sort, a vector of deques is manipulated much like a hash table.
		Radix sorting is a technique for ordering a list of positive integer values.
	www.nd.edu /~hpcc/solaris_opt/SUNWspro.forte6u2/SUNWspro/WS6U2/lib/locale/C/html/manuals/stdlib/user_guide/general/7_3.htm (473 words)

	AI Horizon: Radix Sort Source Code
		This sort also uses queues, so the queue.h file that AI Horizon supplies should be used with this sort.
		Array is the actual array to be sorted, and Num is the number of elements that are to be sorted.
		Since this sort uses queues, a limit is imposed upon the maximum size of the array to be sorted.
	www.aihorizon.com /resources/sourcecode/sorts/radix_h.htm (152 words)

	Radix Sort (Site not responding. Last check: 2007-10-08)
		A category of sorting algorithms (not just a single algorithm, although it is usually casually referred to as if it were) based on characteristics of values rather than just on comparisons.
		RadixSort is useful when the key you are sorting on is a very small integer (0..k), but you have such a large data set keys tend to be repeated many times.
		For example, if you are sorting strings, you can use RadixSort to (partially) sort by the first 2 letters of the string (interpreted as a number between 0 and 65 535).
	c2.com /cgi/wiki?RadixSort (450 words)

	Radix Sort (Site not responding. Last check: 2007-10-08)
		Radix sort is the algorithm used by the card-sorting machines you find only in computer museums.
		Radix sort solves the problem of card sorting counterintuitively by sorting on the least significant digit first.
		When each digit is in the range 1 to k, and k is not too large, counting sort is the obvious choice.
	www.cs.uml.edu /~skaminen/ALGO/sec93.html (204 words)

	Bucket and radix sorting
		We say that a sorting algorithm is stable if, when two records have the same key, they stay in their original order.
		Any comparison sorting algorithm can be made stable by modifying the comparisons to break ties according to the original positions of the objects, but only some algorithms are automatically stable.
		The previous bucket sorting passes are used only to take care of the case in which two items have the same key (mod 10) on the last pass.
	www.ics.uci.edu /~eppstein/161/960123.html (1899 words)

	radix sort (Site not responding. Last check: 2007-10-08)
		Definition: A multiple pass distribution sort algorithm that distributes each item to a bucket according to part of the item's key beginning with the least significant part of the key.
		Radix sort can be particularly effective on a linked list.
		Paul E. Black, "radix sort", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
	www.nist.gov /dads/HTML/radixsort.html (338 words)

	sort man document
		sort sorts lines of all the files together and writes the result on the standard output.
		Check that the single input file is sorted according to the ordering rules; give no output unless the file is out of sort.
		Sorting is done by a method determined by the -x option.
	www.research.att.com /~gsf/man/man1/sort.html (1008 words)

	Radix Sort
		The card sorting machine was the size of three or four large filing cabinets.
		It is possible do the sorting on each digit-position in-situ and then only O(log(n)) space is needed to keep track of the array sections yet to be processed, either recursively or on an explicit stack.
		The radix sort is easily made stable if a temporary array is used.
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Sort/Radix (667 words)

	Radix Sort For Vector Multiprocessors - Zagha, Blelloch (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		Radix Sort For Vector Multiprocessors - Zagha, Blelloch (ResearchIndex)
		summing operations [20] This parallel radix sort algorithm has been efficiently implemented on the CM 2 [8] CM 5 [37] and Cray Y MP This algorithm has the advantages that it is stable, and that the time to compute the rank of the keys does not depend on the...
		In, a radix sort for integer keys implemented on an eight processor Cray Y MP was discussed.
	citeseer.ist.psu.edu /zagha91radix.html (566 words)

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