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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 ...
Randomized algorithms that solve the problem in linear time are known, in Euclidean spaces whose dimension is treated as a constant for the purposes of asymptotic analysis. [ 2 ] [ 3 ] [ 4 ] This is significantly faster than the O ( n 2 ) {\displaystyle O(n^{2})} time (expressed here in big O notation ) that would be obtained by a naive ...
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 ...
If we start with an initial solution made with a greedy algorithm, then the average number of moves greatly decreases again and is ; however, for random starts, the average number of moves is ( ()) . While this is a small increase in size, the initial number of moves for small problems is 10 times as big for a random start ...
The k-server conjecture has also a version for randomized algorithms, which asks if exists a randomized algorithm with competitive ratio O(log k) in any arbitrary metric space (with at least k + 1 points). [2] In 2011, a randomized algorithm with competitive bound Õ(log 2 k log 3 n) was found.
A metric on a set X is a function (called the distance function or simply distance) d : X × X → R + (where R + is the set of non-negative real numbers). For all x, y, z in X, this function is required to satisfy the following conditions: d(x, y) ≥ 0 (non-negativity) d(x, y) = 0 if and only if x = y (identity of indiscernibles.
Dijkstra's algorithm (/ ˈ d aɪ k s t r ə z / DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later.
Emo Welzl [8] proposed a simple randomized algorithm for the minimum covering circle problem that runs in expected time (), based on a linear programming algorithm of Raimund Seidel. Subsequently, the smallest-circle problem was included in a general class of LP-type problems that can be solved by algorithms like Welzl's based on linear ...