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About 10,000 papers for “Randomized algorithm”

RANDOMIZED KACZMARZ ALGORITHM

Deanna Needell, Nathan Srebro, Rachel Ward et al. · 2016

inclusion in CMC Faculty Publications and Research by an authorized administrator of Scholarship @ Claremont. For more information, please

Cited by 0

Seidel’s Randomized Linear Programming Algorithm

Kurt Mehlhorn · 2010

time O(d!m), where m is the number of constraints and d is the number of variables. When discussing Seidel’s algorithm it is customary to use d for the number of variables as d is always used for the dimension in computational geometry and the method has a strong geometric flavor. We consider the problem of maximizing a linear function c T x subject to m linear constraints a T i x ≤ bi, 1 ≤ i ≤ m. We also assume for simplicity that we have explicit bounds on the variables, say −M ≤ x j ≤ M for 1 ≤ j ≤ d. The bound constraints are extra and do not belong to our collection of linear constraints. We formulate the algorithm as a recursive procedure. LINPROG(m linear constraints in d variables, d ≥ 1) if d = 1 then do the obvious and return end if if m = 0 then return the appropriate vertex of the bounding box, i.e., set x ∗ j = M if c j ≥ 0 and x ∗ j = −M if c j < 0. end if

Cited by 0

A Randomized Corner Detection Algorithm

Feng Zu · 2011

There is no parametric formulation of corner feature.Therefore,the conventional Hough transform can not be employed to transform the corner detection into maximum search in parametric space.A randomized Hough transform in Monte Carlo framework is presented,which detects the corner by searching for the local maximum in the intersection point cumulative space instead of parametric space.The intersection point cumulative space is a concept based on the fact that the corner is the intersection point of two lines.The proposed algorithm is demonstrated and the computing procedures are given.The proposed algorithm is isotropic,robust to image rotation,insensitive to noise and not susceptible to diagonal edge.Experimental results show that it outperforms Harris detector,Shen Wang algorithm,and SIFT feature detection algorithm.

Cited by 1

On the Randomized Kaczmarz Algorithm

Liang Dai, Mojtaba Soltanalian, Kristiaan Pelckmans · IEEE Signal Processing Letters · 2014

The Randomized Kaczmarz Algorithm is a randomized method which aims at solving a consistent system of over determined linear equations. This letter discusses how to find an optimized randomization scheme for this algorithm, which is related to the question raised by . Illustrative experiments are conducted to support the findings.

Cited by 37Open access

A Randomized Maximum-Flow Algorithm

Joseph Cheriyan, Torben Hagerup · SIAM Journal on Computing · 1995

A randomized algorithm for computing a maximum flow is presented. For an n-vertex m-edge network, the running time is $O(nm + n^{2}(\log n)^{2})$ with probability at least $1-2^{-\sqrt {nm}}$. The algorithm is always correct, and in the worst case runs in $O(nm \log n)$ time. The only use of randomization is to randomly permute the adjacency lists of the network vertices at the start of the execution. The analysis introduces the notion of premature target relabeling (PTR) events and shows that each PTR event contributes $O(\log n)$ amortized time to the overall running time. The number of PTR events is always $O(nm)$; however, it is shown that when the adjacency lists are randomly permuted, then this quantity is $O(n^{3/2}m^{1/2} + n^{2} \log n)$ with high probability.

Cited by 20

An Accelerated Randomized Kaczmarz Algorithm

Ji Liu, Stephen J. Wright · arXiv (Cornell University) · 2013

The randomized Kaczmarz ($\RK$) algorithm is a simple but powerful approach for solving consistent linear systems $Ax=b$. This paper proposes an accelerated randomized Kaczmarz ($\ARK$) algorithm with better convergence than the standard $\RK$ algorithm on ill conditioned problems. The per-iteration cost of $\RK$ and $\ARK$ are similar if $A$ is dense, but $\RK$ is much more able to exploit sparsity in $A$ than is $\ARK$. To deal with the sparse case, an efficient implementation for $\ARK$, called $\SARK$, is proposed. A comparison of convergence rates and average per-iteration complexities among $\RK$, $\ARK$, and $\SARK$ is given, taking into account different levels of sparseness and conditioning. Comparisons with the leading deterministic algorithm --- conjugate gradient applied to the normal equations --- are also given. Finally, the analysis is validated via computational testing.

Cited by 9Open access

Randomized Pacman maze generation algorithm

Kwan Man Cheng, Hongfan Liu, Xinyu Dou · Applied and Computational Engineering · 2024

Pacman, a cultural icon since its debut in 1980, is celebrated for its captivating static maze design. This research explores innovative algorithms, including an improved version of Sidewinder, in the context of dynamic maze generation for Pacman. Traditional algorithms, constituting the initial focus, serve as counterexamples to highlight their unsuitability in creating Pacman mazes due to their generic design unrelated to the game's unique gameplay. By showcasing these limitations, the study emphasizes the necessity for tailored solutions that align with Pacman's dynamic environment. Subsequently, attention shifts to an innovative algorithm exhibiting promise for Pacman maze generation. An in-depth analysis, using the same rigorous criteria applied to traditional algorithms provides essential insights into its potential for enhancing the Pacman gaming experience.

Cited by 0Open access

Randomized approximate nearest neighbors algorithm

Peter W. Jones, Andrei Osipov, Vladimir Rokhlin · Proceedings of the National Academy of Sciences · 2011

We present a randomized algorithm for the approximate nearest neighbor problem in d -dimensional Euclidean space. Given N points { x j } in , the algorithm attempts to find k nearest neighbors for each of x j , where k is a user-specified integer parameter. The algorithm is iterative, and its running time requirements are proportional to T · N ·( d ·(log d ) + k ·( d + log k )·(log N )) + N · k 2 ·( d + log k ), with T the number of iterations performed. The memory requirements of the procedure are of the order N ·( d + k ). A by-product of the scheme is a data structure, permitting a rapid search for the k nearest neighbors among { x j } for an arbitrary point . The cost of each such query is proportional to T ·( d ·(log d ) + log( N / k )· k ·( d + log k )), and the memory requirements for the requisite data structure are of the order N ·( d + k ) + T ·( d + N ). The algorithm utilizes random rotations and a basic divide-and-conquer scheme, followed by a local graph search. We analyze the scheme’s behavior for certain types of distributions of { x j } and illustrate its performance via several numerical examples.

Cited by 43Open access

Randomized block coordinate DC algorithm

Hoomaan Maskan, Paniz Halvachi, Suvrit Sra et al. · EURO Journal on Computational Optimization · 2025

We introduce an extension of the Difference of Convex Algorithm (DCA) in the form of a randomized block coordinate approach for problems with separable structure. For n coordinate-blocks and k iterations, our main result proves a non-asymptotic convergence rate of O(n/k) in expectation, with respect to a stationarity measure based on a Forward-Backward envelope. Furthermore, leveraging the connection between DCA and Expectation Maximization (EM), we propose a randomized block coordinate EM algorithm.

Cited by 0Open access

Randomized Scheduling Algorithm for Queueing Networks

Devavrat Shah, Jinwoo Shin · arXiv (Cornell University) · 2009

There has recently been considerable interest in design of low-complexity, myopic, distributed and stable scheduling policies for constrained queueing network models that arise in the context of emerging communication networks. Here, we consider two representative models. One, a model for the collection of wireless nodes communicating through a shared medium, that represents randomly varying number of packets in the queues at the nodes of networks. Two, a buffered circuit switched network model for an optical core of future Internet, to capture the randomness in calls or flows present in the network. The maximum weight scheduling policy proposed by Tassiulas and Ephremide in 1992 leads to a myopic and stable policy for the packet-level wireless network model. But computationally it is very expensive (NP-hard) and centralized. It is not applicable to the buffered circuit switched network due to the requirement of non-premption of the calls in the service. As the main contribution of this paper, we present a stable scheduling algorithm for both of these models. The algorithm is myopic, distributed and performs few logical operations at each node per unit time.

Cited by 10Open access

PatchMatch: A Randomized Correspondence Algorithm for . . .

Connelly Barnes, Eli Shechtman, Adam Finkelstein et al. · 2009

This paper presents interactive image editing tools using a new randomized algorithm for quickly finding approximate nearest-neighbor matches between image patches. Previous research in graphics and vision has leveraged such nearest-neighbor searches to provide a variety of high-level digital image editing tools. However, the cost of computing a field of such matches for an entire image has eluded previous efforts to provide interactive performance. Our algorithm offers substantial performance improvements over the previous state of the art (20-100x), enabling its use in interactive editing tools. The key insights driving the algorithm are that some good patch matches can be found via random sampling, and that natural coherence in the imagery allows us to propagate such matches quickly to surrounding areas. We offer theoretical analysis of the convergence properties of the algorithm, as well as empirical and practical evidence for its high quality and performance. This one simple algorithm forms the basis for a variety of tools – image retargeting, completion and reshuffling – that can be used together in the context of a high-level image editing application. Finally, we propose additional intuitive constraints on the synthesis process that offer the user a level of control unavailable in previous methods.

Cited by 0

A reliable randomized algorithm for the . . .

Martin Dietzfelbinger, Torben Hagerup, Jyrki Katajainen et al. · 1997

The following two computational problems are studied: Duplicate grouping: Assume that n items are given, each of which is labeled by an integer key from the set 0,..., U � 1 4. Store the items in an array of size n such that items with the same key occupy a contiguous segment of the array. Closest pair: Assume that a multiset of n points in the d-dimensional Euclidean space is given, where d � 1 is a fixed integer. Each point is represented as a d-tuple of integers in the range 0,..., U � 14 Ž or of arbitrary real numbers.. Find a closest pair, i.e., a pair of points whose distance is minimal over all such pairs.

Cited by 0

Randomized configuration for Algorithm Selector SUNNY

Brugaletta, Luca · AMS Degree Thesis (University of Bologna) · 2019

In questa tesi abbiamo analizzato i comportamenti dell'algoritmo Sunny andando a modificare il metodo di scelta delle feature, principalmente passando da un approccio sequenziale ad uno casuale.
\nAbbiamo implementato e confrontato 3 tecniche oltre a quella di partenza:
\n-randk: sfrutta un approccio puramente casuale per il calcolo delle n feature e della k.
\n-simann: sfrutta la tecnica di ottimizzazione di simulated annealing per calcolare le n feature e il valore di k.
\n-simann-mod: come simann, ma utilizza parametri diversi per il calcolo.
\nAll'interno di questa tesi troviamo i risultati dell'esperimento e i vantaggi che si possono avere nell'utilizzo di una tecnica che non visita tutte le possibili soluzioni, ma solamente un numero ridotto di esse.

Cited by 0

A Randomized Approximate Nearest Neighbors Algorithm

Peter W. Jones, Andrei Osipov, Vladimir Rokhlin · 2010

We present a randomized algorithm for the approximate nearest neighbor problem in d-dimensional Euclidean space. Given N points {x(j)} in R(d), the algorithm attempts to find k nearest neighbors for each of x(j), where k is a user-specified integer parameter. The algorithm is iterative, and its running time requirements are proportional to T·N·(d·(log d) + k·(d + log k)·(log N)) + N·k(2)·(d + log k), with T the number of iterations performed. The memory requirements of the procedure are of the order N·(d + k). A by-product of the scheme is a data structure, permitting a rapid search for the k nearest neighbors among {x(j)} for an arbitrary point x ∈ R(d). The cost of each such query is proportional to T·(d·(log d) + log(N/k)·k·(d + log k)), and the memory requirements for the requisite data structure are of the order N·(d + k) + T·(d + N). The algorithm utilizes random rotations and a basic divide-and-conquer scheme, followed by a local graph search. We analyze the scheme's behavior for certain types of distributions of {x(j)} and illustrate its performance via several numerical examples.

Cited by 45Open access

A randomized, efficient algorithm for MAX2SAT

Cristian Dumitrescu · HAL (Le Centre pour la Communication Scientifique Directe) · 2016

In this paper I present a MAX2SAT algorithm based on the randomized algorithm of Papadimitriou from 1991. We also show that this algorithm finds a solution (if it exists) for a MAX2SAT problem equivalent to a 3SAT problem with high probability in polynomial time.

Cited by 0Open access

A randomized algorithm for exact transduction

G. Esposito, Mario Martín · Frontiers in artificial intelligence and applications · 2014

Random sampling is an efficient method dealing with constrained optimization problems. In computational geometry, it has been applied, through Clarkson's algorithm [10], to solve a general class of problems called violator spaces. In machine learning, TSVM is a learning method used when only a small fraction of labeled data is available, which implies solving a non convex optimization problem. Several approximation methods have been proposed to solve it, but they usually find suboptimal solutions. Global optimal solution may be obtained using exact techniques, costing an exponential time complexity with respect to the number of instances. In this paper, an interpretation of TSVM in terms of violator space is given. Hence, a randomized method is presented extending the use of exact methods now reducing the time complexity to sub-exponential in particular exponential w.r.t. the number of support vectors of the optimal solution instead of exponential w.r.t. the number of instances.

Cited by 0