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Lecture Notes on Bucket Algorithms
In this paper a comparison is made for different sorting algorithms used in computation. Keywords— best sorting algorithm, bubble sort algorithms, quick sort algorithms, sorting algorithms, efficient sorting I. In sorting process data is organized in an order. Different algorithms are used for this purpose. Sorting is of two types one is internal sorting and second is external sorting.
Internal sorting is performed when small amount of data that can be hold in the memory is sorted. For sorting the large amount of data, a part of whose exists in some external storage device during sorting process another type of sorting called external sorting is used. The most used sorting orders are numerical and lexicographical orders. In this paper an overview of both internal and external sorting algorithms is discussed. It is not possible to store all data into the main memory of computer and a part of data must reside on some external storage device.
The strategy used for such sorting is hybrid sort-merge. In this strategy small portions of data are read from external storage device according to the main memory size, sorted and saved in temporary file and at last these all sorted files are merged together for making a single file containing sorted data. Following sorting algorithms are mostly used for external sorting. External Merge Sort External merge sort is used to sort huge amount of data. It uses chunks of data according to the size of main memory.
When every chunk is sorted successfully it merges these chunks into a large file that is now fully sorted. It usually includes two pass sort, firstly a sort pass and afterwards a merge pass. In regular merge sort there are total log n merge passes but in external merge sort it is avoided for the reason that in every merge pass every data value has to be read from and write on the disk and in case of external merge sort data resides on an external storage device that are very slow rather than main memory.
Performing efficient external sort needs O n log n time. Every exponential increase in data amount causes linear increase in time used for sorting. If memory is increased then a single merge pass can be efficient. In other words increase in memory decreases the number of passes in sorting process. The second method to perform external sort efficiently is the use of parallelism. In this method multiple disk drives are used and multiple sorting threads run at the same time increasing the speed of sorting process.
Several machines are linked in a speedy network to perform sorting on huge data sets in parallel. Another technique for enhancing the speed of sorting process is increasing the hardware speed. Use of a large RAM reduces the number of disk seeks and reduces the number of passes. Faster external storage devices such as solid state drives also reduce the number of passes during sorting process. In this regard cost efficiency and absolute speed can be critical specifically in cluster environment.
Use of efficient and faster software for sorting also enhances the efficiency of the sorting process. Distribution Sort The other major category of external sort is distribution sort. It has further types that fit for different types of data and situations. These include bucket sort, linear probing sort, shuffle sort, merge sort, radix sort, strand sort, distributive partitioning sort etc.
Figure 2 : Distribution Sorting Method The main technique which is used in distribution sort is the division of data into small chunks using some intermediary structure and then combines app portions in one large output file.
Any algorithm that requires sorting of data using comparison of keys at least requisites O n log n time for sorting. These are efficient and quicker option because memory or RAM is faster than any secondary storage device. These are the more efficient in sense that their working is swift and less time consuming. Efficient algorithms are mostly based on average complexity O n log n.
The common types of efficient sorts are merge sort, heap sort and quick sort. Here under is a review of efficient internal algorithms. Merge Sort The merge sort algorithms use the sorted lists and merge them. In this process it uses swapping of data elements if it is necessary. It continues the process till the production of final sorted list. It can be easily applied to lists and arrays because it needs sequential access rather than random access.
It can handle very large lists due to its worst case running time O n log n.
The O n additional space complexity and involvement of huge amount of copies in simple implementation made it a little inefficient. Merge sort is very popular in practical implementations because of its use and popularity in sophisticated algorithm Timsort. It is divide and conquer type of algorithm. Initially it divides the supplied data set into sub-lists consisting of only one element as these lists are sorted ones. Then it starts comparing and merging the elements of these sorted list until a single list is left behind. This list will be ordered list of provided data.
Heap Sort The most efficient version of selection sort is heap sort.
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It firstly determine the largest or the smallest element of the list and places it at the beginning in case of largest and at the end in case of the smallest element. It continues the process for the remaining list and complete the task very efficiently and quickly. For performing the process of sorting it uses a special data structure called heap. Heap is particular type of binary tree. This algorithm makes the heap from given data that is going to be sorted. Once the heap is constructed it ensures that root node is the largest or smallest in case of opposite sorting order element of given data.
algorithm - Suggestions on speeding up edge selection - Stack Overflow
To create the ordered list the root node is removed and placed at the beginning of list or end of list according to sorting order. When root node is removed the next largest or smallest node moves to the root node and heap is rearranged. By continuing this process a sorted data list is gained. Figure 4 : Heap sorting method Using the heap structure requires O log n time for searching the next largest or smallest data element rather than O n for a linear scan in simple selection sort. This lets the heap sort execution in O n log n time which is the worst case time complexity.
Quick Sort Quick sort also belongs to the divide and conquer category of algorithms. This course continues the study of data structures, their applications, and the algorithms associated with them. Topics include abstract data types, dictionaries, graphs, searching, and sorting.
The design and analysis of algorithms is also covered, with topics such as efficiency and complexity, NP-completeness, dynamic programming, and amortized analysis. Stina Bridgeman bridgeman hws. M pm, W pm, Th am, F pm or by appointment schedule. This course explores a topic at the very core of computer science: designing efficient solutions to problems, and implementing those solutions in efficient and organized ways. The course has three main goals:. Algorithm Analysis: You've thought of several algorithms for solving a particular problem - which is the best?
Time- and space-efficiency will be discussed, and big-Oh notation will be introduced - concepts which will be the fundamental tools used in the rest of the course. There will also be a quick review of several basic data structures including stacks, queues, vectors, and lists with an emphasis on applying the new algorithm analysis tools to compare possible implementations of these data structures. Searching, Sorting, and Selection: Searching, sorting, and selection picking the kth smallest or largest item problems are extremely common, so it is worth considering how to solve these problems efficiently.
This section will expand the toolbox of known data structures and algorithms with a number of new data structures including balanced search trees and hashtables and algorithms including sorting and selection algorithms. These three problems will also serve as a case study of how different data structures and algorithms can greatly affect a program's efficiency, and will provide a motivation for introducing some additional tools for algorithm analysis. Algorithm Design: The next unit will examine three fundamental techniques of algorithm design greedy algorithms, divide-and-conquer, and dynamic programming , along with examples of applications of each technique.
This continues to build the toolbox of known solutions, but more importantly begins to build a repertoire of strategies for solving new problems. Graphs: The graph is a data structure with a wide variety of applications.
We'll define a graph ADT, consider how that ADT might be implemented, and introduce a number of common graph algorithms including traversal, shortest path, and minimum spanning tree and their applications. Complexity and NP-Completeness: After a semester-long focus on the efficiency of algorithms, some questions might come to mind: Are some problems fundamentally harder to solve than others?
Are there problems that can't be solved? We'll delve briefly back into more theoretical topics to examine these questions and what "hard" actually means , and to look at some of the hardest problems in computer science. If time permits, some additional data structures such as sets and heaps and algorithms for different domains such as text processing, computational geometry, and network security will be considered.
This course is a problem-solving course.
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