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In computer science, linear search or sequential search is a method for finding an element within a list. It sequentially checks each element of the list until a match is found or the whole list has been searched. [1] A linear search runs in linear time in the worst case, and makes at most n comparisons, where n is the length 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 ...
This problem is usually called the linear search problem and a search plan is called a trajectory. The linear search problem for a general probability distribution is unsolved. [ 5 ] However, there exists a dynamic programming algorithm that produces a solution for any discrete distribution [ 6 ] and also an approximate solution, for any ...
A 1999 study of the Stony Brook University Algorithm Repository showed that, out of 75 algorithmic problems related to the field of combinatorial algorithms and algorithm engineering, the knapsack problem was the 19th most popular and the third most needed after suffix trees and the bin packing problem.
At the line search step (2.3), the algorithm may minimize h exactly, by solving ′ =, or approximately, by using one of the one-dimensional line-search methods mentioned above. It can also be solved loosely , by asking for a sufficient decrease in h that does not necessarily approximate the optimum.
Each search algorithm performs well on almost all objective functions. [11] So if one is not concerned with the "relatively small" differences between search algorithms, e.g., because computer time is cheap, then you shouldn't worry about no free lunch. An algorithm may outperform another on a problem when neither is specialized to the problem.
The simplest, most general, and least efficient search structure is merely an unordered sequential list of all the items. Locating the desired item in such a list, by the linear search method, inevitably requires a number of operations proportional to the number n of items, in the worst case as well as in the average case. Useful search data ...
Seidel (1991) gave an algorithm for low-dimensional linear programming that may be adapted to the LP-type problem framework. Seidel's algorithm takes as input the set S and a separate set X (initially empty) of elements known to belong to the optimal basis. It then considers the remaining elements one-by-one in a random order, performing ...