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A Case Study: Vision Control
Published in Ivan Cibrario Bertolotti, Gabriele Manduchi, Real-Time Embedded Systems, 2017
Ivan Cibrario Bertolotti, Gabriele Manduchi
The big-O notation provides a very important measurement of the efficiency for computer algorithms, which normally become unmanageable when the dimension of the problem increases. Take as an example the algorithms for sorting a given array of values. Elementary sorting algorithms such as Bubble Sort or Insertion Sort require a number of operation that is proportional to N2, where N is the dimension of the array to be sorted and therefore are O(N2). Other sorting algorithms, such as Shell Sort and Quick Sort are instead O(Nlog(N)). This implies that for very large arrays, only the latter algorithms can be used in practice because the number of operations becomes orders of magnitude lower in this case.
Trees and Cycles
Published in Kenneth H. Rosen, Graphs, Algorithms, and Optimization, 2005
However, this can easily create LB-trees that are really linear linked lists, as shown below. This algorithm then becomes an insertion sort, taking O(n2) steps, where n is the number of nodes inserted.
Binarily Gapped Binary Insertion Sorting Technique
Published in IETE Journal of Research, 2018
Swapan Kumar Ray, Surajeet Ghosh
Sorting of an array of data elements (DE) is a fundamental operation in computer science and is a basic requirement in many engineering and commercial systems that perform searching or displaying of data. It is also a key subroutine used in running many formal algorithms. A host of different sorting techniques exists [1,2] which often meet the various general performance criteria like sorting time, memory requirement, implementational simplicity, etc. of different applications. An important feature in a sorting technique is its in-place operation which implies that, during the process of sorting, a constant number of DEs of the input unsorted array is ever stored outside the array. Among the most well-known in-place sorting algorithms are the Heap Sort, the Quick Sort, and the Insertion Sort, which, respectively, sorts n numbers in O(nlog n), O(nlog n), and O(n2) time [1,2]. In spite of its relatively poor performance as an in-place sorting technique, the Insertion Sort counts among the popular sorting techniques because it is simple, incremental (i.e., on line), stable, more efficient than most of the other simple O(n2) algorithms like Selection Sort or Bubble Sort, and, finally, its output array remains sorted all the time – both before and after every insertion.