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Sorting small arrays optimally (in the fewest comparisons and swaps) or fast (i.e. taking into account machine-specific details) is still an open research problem, with solutions only known for very small arrays (<20 elements). Similarly optimal (by various definitions) sorting on a parallel machine is an open research topic.
The List Update or the List Access problem is a simple model used in the study of competitive analysis of online algorithms.Given a set of items in a list where the cost of accessing an item is proportional to its distance from the head of the list, e.g. a linked List, and a request sequence of accesses, the problem is to come up with a strategy of reordering the list so that the total cost of ...
Specific applications of search algorithms include: Problems in combinatorial optimization, such as: . The vehicle routing problem, a form of shortest path problem; The knapsack problem: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as ...
Note that the final result of an insertion sort is optimum, i.e., a correctly sorted list. For many problems, online algorithms cannot match the performance of offline algorithms. If the ratio between the performance of an online algorithm and an optimal offline algorithm is bounded, the online algorithm is called competitive. [1]
Interpolation search is an algorithm for searching for a key in an array that has been ordered by numerical values assigned to the keys (key values).It was first described by W. W. Peterson in 1957. [1]
Pigeonhole sorting is a sorting algorithm that is suitable for sorting lists of elements where the number n of elements and the length N of the range of possible key values are approximately the same. [1]
Bubble sort. The list was plotted in a Cartesian coordinate system, with each point (x, y) indicating that the value y is stored at index x. Then the list would be sorted by bubble sort according to every pixel's value. Note that the largest end gets sorted first, with smaller elements taking longer to move to their correct positions.
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