Search results
Results from the WOW.Com Content Network
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 ...
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are ...
Some problems which do not have a PTAS may admit a randomized algorithm with similar properties, a polynomial-time randomized approximation scheme or PRAS.A PRAS is an algorithm which takes an instance of an optimization or counting problem and a parameter ε > 0 and, in polynomial time, produces a solution that has a high probability of being within a factor ε of optimal.
A notable example of an approximation algorithm that provides both is the classic approximation algorithm of Lenstra, Shmoys and Tardos [2] for scheduling on unrelated parallel machines. The design and analysis of approximation algorithms crucially involves a mathematical proof certifying the quality of the returned solutions in the worst case. [1]
Any randomized algorithm may be interpreted as a randomized choice among deterministic algorithms, and thus as a mixed strategy for Alice. Similarly, a non-random algorithm may be thought of as a pure strategy for Alice. In any two-player zero-sum game, if one player chooses a mixed strategy, then the other player has an optimal pure strategy ...
The optimal algorithm is by Andris Ambainis. [7] Yaoyun Shi first proved a tight lower bound when the size of the range is sufficiently large. [ 8 ] Ambainis [ 9 ] and Kutin [ 10 ] independently (and via different proofs) extended his work to obtain the lower bound for all functions.
The first optimal output-sensitive algorithm. It modifies the divide and conquer algorithm by using the technique of marriage-before-conquest and low-dimensional linear programming. Published by Kirkpatrick and Seidel in 1986. Chan's algorithm — O(n log h) A simpler optimal output-sensitive algorithm created by Chan in 1996.
The basic RO algorithm can then be described as: Initialize x with a random position in the search-space. Until a termination criterion is met (e.g. number of iterations performed, or adequate fitness reached), repeat the following: Sample a new position y by adding a normally distributed random vector to the current position x