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An upper bound for a decision-tree model was given by Meyer auf der Heide [17] who showed that for every n there exists an O(n 4)-deep linear decision tree that solves the subset-sum problem with n items. Note that this does not imply any upper bound for an algorithm that should solve the problem for any given n.
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 probability distribution, with any desired accuracy. [7] The linear search problem was solved by Anatole Beck ...
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
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.
[1] [3] [4] Other more technical rate definitions are needed if the sequence converges but | + | | | = [5] or the limit does not exist. [1] This definition is technically called Q-convergence, short for quotient-convergence, and the rates and orders are called rates and orders of Q-convergence when that technical specificity is needed.
In Smale's words, the third version of the problem "is the main unsolved problem of linear programming theory." While algorithms exist to solve linear programming in weakly polynomial time, such as the ellipsoid methods and interior-point techniques, no algorithms have yet been found that allow strongly polynomial-time performance in the number ...
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 ...
For most graphs, this transformation is not useful because it creates cycles of negative length in −G. But if G is a directed acyclic graph (DAG), then no negative cycles can be created, and a longest path in G can be found in linear time by applying a linear time algorithm for shortest paths in −G, which is also a directed acyclic graph. [4]