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Questions tagged [randomized-algorithms]

An algorithm whose behaviour is determined by its input and a generator producing uniformly random numbers.

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Bound the number of rounds in the sampling

Suppose we have a sequence $a_1,a_2,\ldots, a_n$, each $a_i$ is sampled uniformly and independently from $[0,1]$. Define $$ J_1=1,\\ \text{for}~i>1, ~J_i = 1 \iff a_i < \min \{a_1,a_2,...
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Naive shuffle algorithm [closed]

Let us have a "shuffle algorithm": for i in range(len(vec)): swap(vec[i], vec[rand()%len(vec)]) Why the reshuffles we get using this algoritm for a number ...
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1answer
209 views

Proving properties of Random Graphs

I am asking the question on a slightly abstract level and it may depend on the specifics but it would be great to have related references or ideas. Consider the random graph model $G_{n,p}$ where its ...
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1answer
86 views

Efficiently picking free position from array with uniform probability.

For each array position it is known if position filled or not. How efficiently pick one free position with uniform probability? That task happen during implementation of AI by Monter-Carlo method ...
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1answer
356 views

PAC algorithms for APX-Hard problems

Do there exist polynomial time algorithms that admit Probably Approximately Correct (PAC) bounds for APX-Hard problems? That is, does there exist a problem $P$ that is APX-Hard, such that for every $\...
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1answer
291 views

Maximum Independent Set using Maximal MIS

I want to use multiple runs of maximal independent set (Luby's algorithm) to find a lower bound on the size of maximum independent set. Are there any bounds on the number of times the maximal ...
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1answer
285 views

Randomized Algorithm with random input

As per the Yao's principle, in order to lower bound the cost of Randomized algorithm it suffices to find an appropriate distribution of difficult inputs, and to prove that no deterministic algorithm ...
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1answer
386 views

karger's algorithm contracting nodes not edges [closed]

Karger's algorithm works by contracting edges, not merging nodes (this is different because nodes need not share an edge). Is there a reason why this is so?
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21 views

Is there a stochastic/online version of the GLM-Tron algorithm?

The GLM-Tron algorithm appeared in Theorem $1$ in this paper, https://arxiv.org/pdf/1104.2018.pdf Is there a stochastic version of this? (...essentially something that will randomly sample a few ...
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29 views

Expected size of the min-cut, under edge perturbations

Suppose we have a graph $G(V, E)$. Assume that the min-cut of this graph is given $C=(A/B)$ and denote the size of the cut with $|C|$. Create a random modification of the graph: Drop each ...
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0answers
221 views

Steiner Tree and minimum spanning tree

If I must connect: $$2^k$$ terminals in a Steiner Tree choosen randomly and connect them with the cheapest component; "loss - contracting algorithm" is a good way? Or is an "Iterative Randomized ...
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94 views

To find OR of $\sqrt{n}$ numbers each of $n$ bits?

Given $\sqrt{n}$ numbers of $n$ bits each. I need to find its OR and store it at another number RESULT of $n$ bits. Trivially it can be done in $\mathcal{O}(n \sqrt{n})$ time, or $\mathcal{O}(n \sqrt{...
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1answer
100 views

Reducing disjoint or indexing or inner-product problem to s-t connectivity problem in directed graph

I am asked to prove that an O(1)-pass randomized streaming algorithm that solves s-t connectivity problem in a simple directed graph $G=(V,E)$ with $|V|=n$ vertices, with sucess possibility $>\frac{...
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1answer
229 views

Is there a randomized complexity class analogous to $\mathsf{P/Poly}$?

$\mathsf{P/Poly}$ captures those problems that could be solved in polynomial time given some precomputed polynomial number of constants. Is there an analogous complexity class in randomized world ...
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1answer
722 views

Finding cliques in weighted graph

We have given a weighted graph $G=\{V,E\}$, where $V=\{v_1, v_2,...,v_n\}$, and for all $i,j$, the weight of edges $w(v_i, v_j)\in (0,W)$. And we have also given a weight threshold s $w$ (where $0<...
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1answer
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Using Yao's minimax principle [closed]

Consider the basic problem in which the input is an array A of n bits, and we need to output some index i with A[i]=1 (we can read a single bit each time). Can you give me an example using Yao's ...
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1answer
121 views

Proving that a random permutation generator is not fair [closed]

If I'm generating random permutations using the following algorithm: ...
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1answer
52 views

what does NP ⊆ DTIME(…) mean?

Recently I've seen inside theory of a paper. This time complexity, DTIME, is completely new for me. Can somebody explain it? Also, the paper shows that the misinformation containment problem cannot ...
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1answer
64 views

Probabilistic protocols [closed]

I want to model a probabilistic protocol using a model checker, but a lot of protocols are already implemented (e.g. Randomised Dining Philosophers, Dining cryptographers, Synchronous leader election ...
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0answers
46 views

Randomized algorithm for clique that proves P = NP [closed]

Suppose there is a polynomial-time randomized algorithm which for graph $G$ and natural number $k$ with probability not less than $2/3$ correctly answers the question whether or not there is a clique ...