## What is/are Randomized Algorithm?

Randomized Algorithm - This estimation not only allows for size estimation of a solution, but also for an early detection of failure in randomized algorithms, so that a correcting procedure can be executed.^{[1]}The extensive experimental results demonstrate that the proposed #GNN algorithm achieves accuracy comparable to the learning-based algorithms and outperforms the randomized algorithm, while running significantly faster than the learning-based algorithms.

^{[2]}We also show how to modify their randomized algorithm to count the pairs w.

^{[3]}Then, we examine the edge augmentation while preserving the distance-based bound and present a randomized algorithm that guarantees an $\alpha $ –approximate solution with high probability.

^{[4]}We show that, even in regular trees of degree at most Δ, in the standard ŁOCAL model, there exists a constant ε>0 such that for k ≤Δ^ε, for the problem of computing a k-outdegree dominating set, any randomized algorithm requires at least Ω(min logΔ,√log log n ) rounds and any deterministic algorithm requires at least Ω(min logΔ,√log n ) rounds.

^{[5]}15% compared to the basic models such as Naive Bayes, multi-attribute decision tree and randomized algorithm.

^{[6]}Previously, the cost O ∼ ( n ω − 1 t d ) has only been reached with randomized algorithms finding a single solution for the case t n.

^{[7]}Some of the well known algorithms are i) exact algorithms ii) approximation algorithms and iii) randomized algorithms.

^{[8]}together with a randomized algorithm which requires $\tilde O(n^{3/2})$ probes.

^{[9]}Though a global optimization procedure using a randomized algorithm and a commercial process simulator is relatively easy to implement for complex design problems (i.

^{[10]}1 Both bounds are near optimal (up to a logarithmic factor), since Ω(D) and Ω(m) are the respective lower bounds for time and messages for leader election even for synchronous networks and even for (Monte-Carlo) randomized algorithms.

^{[11]}In addition to inapproximability results, we present algorithmic results along two different flavors: (1) We design a randomized algorithm to verify if a given directed graph on $n$ vertices contains a binary tree of size $k$ in $2^k \text{poly}(n)$ time.

^{[12]}The strongest possible guarantee for a randomized algorithm is that it is always correct (Las Vegas) and has high-probability worst-case update time, which gives a bound on the time for each individual operation that holds with high probability.

^{[13]}We also propose a true-biased, randomized algorithm for this problem.

^{[14]}The strong revitalization of randomized algorithms can be framed in this prospect steering.

^{[15]}Our contributions are as follows: First, we present a randomized algorithm that samples the sensor locations with replacement as per a specified distribution.

^{[16]}Inspired by recent advances in online algorithms with Machine Learned (ML) advice, we develop parameterized deterministic and randomized algorithms for this problem such that the level of reliance on the advice can be adjusted by a trust parameter.

^{[17]}In this work, we break the quadratic barrier with a randomized algorithm guaranteeing Õ(n9/5) independence queries with high probability, and a deterministic algorithm guaranteeing Õ(n11/6) independence queries.

^{[18]}This paper proposes a technique that uses a randomized algorithm to assign robust eigen-structures for a multivariable system, such as Unmanned Aerial Vehicles (UAVs).

^{[19]}Such a near-optimal bound for this problem has been so far only achieved using a randomized algorithm [Orlin et al.

^{[20]}More precisely, we present a randomized algorithm that performs each operation in time Õ(n4/5) and, after each update, reports the answer to the LIS problem correctly with high probability.

^{[21]}In a graph with n vertices and m edges, our randomized algorithm computes the minimum cut with high probability in O(m log4 n) work and O(log3 n) depth.

^{[22]}Our results imply that randomized algorithms are strictly more powerful than deterministic ones in that the former can achieve sensitivity independent of $n$ whereas the latter cannot.

^{[23]}Methodology: We use techniques such as randomized algorithms and graph-based algorithms to provide a tractable solution heuristic that we analyze through asymptotic analysis.

^{[24]}Solving the NP-hard optimization program is then transformed to solving a linear program and finding a randomized algorithm to find an integral solution.

^{[25]}The goal of this work is to survey various implementations and applications of randomized algorithms for SVD.

^{[26]}org/1998/Math/MathML">

^{[27]}We investigate how the $c$-chain property influences the stretch factor in the plane: (i) we show that for every $\varepsilon>0$, there is a noncrossing $c$-chain that has stretch factor $\Omega(n^{1/2-\varepsilon})$, for sufficiently large constant $c=c(\varepsilon)$; (ii) on the other hand, the stretch factor of a $c$-chain $P$ is $O\left(n^{1/2}\right)$, for every constant $c\geq 1$, regardless of whether $P$ is crossing or noncrossing; and (iii) we give a randomized algorithm that can determine, for a polygonal chain $P$ in $\mathbb{R}^2$ with $n$ vertices, the minimum $c\geq 1$ for which $P$ is a $c$-chain in $O\left(n^{2.

^{[28]}By means of Randomized Algorithms, two fault detection threshold setting algorithms are provided subsequently to achieve residual performance assessment by taking into account the fault detection rate and false alarm rate in the probabilistic framework.

^{[29]}In particular, randomized algorithms are currently having a resurgence, given their generalized elementary approach.

^{[30]}We prove that the resultant of two “sufficiently generic” bivariate polynomials over a finite field can be computed in quasi-linear expected time, using a randomized algorithm of Las Vegas type.

^{[31]}Specifically, we give a randomized algorithm which takes $\widetilde{O}\left( f^{1-1/k} n^{2+1/k} + mf^2\right)$ time.

^{[32]}The first one is a randomized algorithm running in time $O(m\log^2 m)$, that is based solely on rolling hash and an elementary data-structure for prefix sums; to illustrate its simplicity we provide a short and efficient implementation of the algorithm in Python.

^{[33]}Specifically, we propose a deterministic algorithm with approximation ratio 6 and a randomized algorithm with approximation ratio 4, and show that both of them can be accelerated to achieve nearly linear running time at the cost of weakening the approximation ratio by an additive factor of ε.

^{[34]}However, unlike related online assortment problems, no randomized algorithm can achieve a better competitive ratio, even in asymptotic regimes.

^{[35]}To solve the problem of poor security and performance caused by traditional encryption algorithm in the cloud data storage, we propose a cascade ciphering with randomized algorithm.

^{[36]}This paper aims at the development of a randomized algorithm based probabilistic analysis approach for parametric uncertainties in unmanned helicopter systems.

^{[37]}While this topic has been quite extensively examined for randomized algorithms, this is, to the best of our knowledge, the first paper to discuss to which extent deterministic contention resolution algorithms can be efficient in terms of both channel utilization and energy consumption.

^{[38]}We present MaNIACS, a sampling-based randomized algorithm for computing high-quality approximations of the collection of the subgraph patterns that are frequent in a single, large, vertex-labeled graph, according to the Minimum Node Image-based (MNI) frequency measure.

^{[39]}We then provide an admission framework of user requests by placing primary VNF instances of network functions in the SFC to different cloudlets, and then develop a randomized algorithm with a good approximation ratio and high probability for the service reliability augmentation problem, at the expense of moderate resource constraint violations.

^{[40]}We establish an information complexity lower bound of randomized algorithms for simulating underdamped Langevin dynamics.

^{[41]}SCN uses a supervisory random mechanism to assign its input weights and hidden biases, which makes it more stable than other randomized algorithms but also leads to time-consuming model training.

^{[42]}In addition, \cite{DBLP:journals/corr/abs-2002-07152} showed a randomized algorithm yielding a $+8W_{max}$ spanner of size $O(n^{4/3})$, here $W_{max}$ is the maximum edge weight in the entire graph.

^{[43]}In contrast, it follows from results in communication complexity that any randomized algorithm even just to decide whether the graph is connected or not must make at least $\Omega(n/\log(n))$ many cut queries.

^{[44]}We present an randomized algorithm based on weighted group coverage maximization for GPM and apply sandwich framework to get theoretical results.

^{[45]}Recent work has focused on the regime in which machines have sublinear (in n, the number of nodes in the input graph) space, with randomized algorithms presented for the fundamental problems of Maximal Matching and Maximal Independent Set.

^{[46]}We leverage the vast prior work on broadcast and Byzantine consensus algorithms to design, implement and evaluate a set of randomized algorithms, with only a single synchronization barrier and varying message complexities, that can be used to achieve interactive consistency in real-world distributed systems.

^{[47]}modelling huge social networks), randomized algorithms are the answer as the exact computation is prohibitively complex, both for runtime and space.

^{[48]}We demonstrate the capability of our algorithms to greatly improve a rough initial estimate, such as those obtained using least squares or a randomized algorithm.

^{[49]}This is in contrast to randomized algorithms that can find a matching whose size is $99\%$ of the maximum in O(\log n) rounds, each making n demand queries.

^{[50]}

## singular value decomposition

Based on the formula and the randomized singular value decomposition, we first propose a randomized algorithm for solving high-dimension and large-sample dense trace-ratio problems.^{[1]}The improved methods first use the randomized algorithm to compute an approximate generalized singular value decomposition (GSVD) with less computational time.

^{[2]}In this paper, we focus on developing randomized algorithms for the computation of low multilinear rank approximations of tensors based on the random projection and the singular value decomposition.

^{[3]}

## Efficient Randomized Algorithm

While deterministic streaming algorithms are inherently robust, many central problems in the streaming literature do not admit sublinear-space deterministic algorithms; on the other hand, classical space-efficient randomized algorithms for these problems are generally not adversarially robust.^{[1]}Two efficient randomized algorithms EPSL and EPAL are proposed in which the opinion ranges of experts are examined in order to decide whether to acquire a label from users for a given instance.

^{[2]}By combining the thin QR decomposition and the subsampled randomized Fourier transform (SRFT), we obtain an efficient randomized algorithm for computing the approximate Tucker decomposition with a given target multilinear rank.

^{[3]}As a result that may be of independent interest in graph theory, we give an efficient randomized algorithm to construct a weakly fundamental cycle basis for a graph, such that each edge appears only polylogarithmically times in the basis.

^{[4]}Specifically, our results include the following: • For the pairwise spanner problem, in which the pairs of vertices to be spanned arrive online, we present an efficient randomized algorithm with competitive ratio Õ(n) for graphs with general lengths, where n is the number of vertices of the given graph.

^{[5]}We attempt to better understand randomization in local distributed graph algorithms by exploring how randomness is used and what we can gain from it: We first ask the question of how much randomness is needed to obtain efficient randomized algorithms.

^{[6]}In addition, we also propose an efficient randomized algorithm for finding TPP triples, which adopts a greedy randomized strategy to randomly generate possible TPP candidates.

^{[7]}

## Time Randomized Algorithm

For Problem 1 we 10 design an O∗(2k)-time randomized algorithm and for Problem 2 we obtain a kernel with at most 11 3k vertices.^{[1]}We obtain a (1 + )-approximation for rooted vertex connectivity in Õ(nW/ ) time where W is the total vertex weight (assuming integral vertex weights); in particular this yields an Õ ( n/ ) time randomized algorithm for unweighted graphs.

^{[2]}We show, for the first time, that a polynomial time randomized algorithm can outperform the best deterministic algorithms when there are at least two blockages, and surpass the lower bound of $$2k+1$$ 2 k + 1 by an o (1) factor.

^{[3]}Our main contribution is a polynomial-time randomized algorithm, that is asymptotically optimal: we derive an upper bound of $O(\log \ell + \log k)$ on its competitive ratio and show that no randomized online algorithm can achieve a competitive ratio of less than $\Omega(\log \ell + \log k)$.

^{[4]}Karger's longstanding $O(m \log^3 n)$ time randomized algorithm for this problem was very recently improved in two independent works to $O(m \log^2 n)$ [ICALP'20] and to $O(m \log^2 n + n\log^5 n)$ [STOC'20].

^{[5]}

## Distributed Randomized Algorithm

We present a distributed randomized algorithm that produces, with high probability, a maximal matching.^{[1]}Second, we develop a distributed randomized algorithm SINR-Spanner to construct a required t-spanner with high probability.

^{[2]}In this paper, we propose a distributed randomized algorithm for computing the weighted girth in weighted graphs with integral edge weights in the range [1, nc], where n is the number of vertices and c is a constant.

^{[3]}A replication-based distributed randomized algorithm is proposed, in which a balanced network status can be achieved after average operations among the nodes.

^{[4]}

## New Randomized Algorithm

In this paper we provide new randomized algorithms with improved runtimes for solving linear programs with two-sided constraints.^{[1]}First, we propose a new randomized algorithm that computes the quotient of two sparse polynomials when the division is exact.

^{[2]}Motivated by applications in hyper-differential sensitivity analysis (HDSA), we propose new randomized algorithms for computing the GSVD which use randomized subspace iteration and weighted QR factorization.

^{[3]}We introduce a new randomized algorithm, Hutch++, which computes a $(1 \pm \epsilon)$ approximation to $tr(A)$ for any positive semidefinite (PSD) $A$ using just $O(1/\epsilon)$ matrix-vector products.

^{[4]}

## Competitive Randomized Algorithm

We give an O(łog^2 k) competitive randomized algorithm, answering an open question of Beckmann ηl~BGHM20 and Even et al.^{[1]}99)-competitive randomized algorithm for GAP.

^{[2]}We consider metrical task systems on tree metrics, and present an $O(\mathrm{depth} \times \log n)$-competitive randomized algorithm based on the mirror descent framework introduced in our prior work on the $k$-server problem.

^{[3]}

## Known Randomized Algorithm

These running times essentially match the best known randomized algorithms of Williams [46] and Abboud, Williams, and Yu [8], respectively, and the ability to count was open even for randomized algorithms.^{[1]}The achieved round complexity of O(logloglog n) rounds matches the bound of log(T_local ), which currently serves an upper bound barrier for all known randomized algorithms for locally-checkable problems in this model.

^{[2]}For d-regular graphs, we observe that a known randomized algorithm which achieves an approximation ratio of O(log d) can be derandomized and implemented to run in polynomial time and use O(log n) bits of space.

^{[3]}

## Error Randomized Algorithm

Surprisingly, we can phrase our algorithm as a reduction from the sparse case to the dense case of nonnegative convolution, showing that, under some mild assumptions, sparse nonnegative convolution is equivalent to dense nonnegative convolution for constant-error randomized algorithms.^{[1]}Suppose a language $L$ can be decided by a bounded-error randomized algorithm that runs in space $S$ and time $n \cdot \text{poly}(S)$.

^{[2]}

## Novel Randomized Algorithm

Our major contribution is to propose a novel randomized algorithm (named eM-KOFL), which can enjoy the advantage of multiple kernels while having a similar communication overhead with S-KOFL.^{[1]}We present a novel randomized algorithm to factor polynomials over a finite field $\F_q$ of odd characteristic using rank $2$ Drinfeld modules with complex multiplication.

^{[2]}

## Improved Randomized Algorithm

Near-term, quantum technologies provide a radically new toolset to realize stronger encryption systems as well as improved randomized algorithms.^{[1]}In this paper, we present improved randomized algorithms for nonmonotone functions.

^{[2]}

## Space Randomized Algorithm

We also give an $\tilde O(n^{1+\varepsilon}t)$-time, $O(\log(nt))$-space randomized algorithm, improving upon previous $(nt)^{O(1)}$-time $O(\log(nt))$-space algorithms by Elberfeld, Jakoby, and Tantau (FOCS 2010), and Kane (2010).^{[1]}249999n) space randomized algorithm for solving worst-case Subset Sum instances with n integers.

^{[2]}

## Correlative Randomized Algorithm

A new correlative randomized algorithm is constructed by applying simple randomization of the majorant cross section (alignment, delta tracking) algorithm and using a one-dimensional distribution and the correlation length of the stochastic medium.^{[1]}Correlative randomized algorithms are constructed by simple randomization of the algorithm of maximum cross-section (equalization, delta tracking) with the use of a one-dimensional distribution and the correlation function or only correlation length of a random medium.

^{[2]}

## randomized algorithm running

The first one is a randomized algorithm running in time $O(m\log^2 m)$, that is based solely on rolling hash and an elementary data-structure for prefix sums; to illustrate its simplicity we provide a short and efficient implementation of the algorithm in Python.^{[1]}With read-only access to the exponentially many random bits, we show a randomized algorithm running in $O^{*}(2.

^{[2]}