# Questions tagged [randomized-algorithms]

Questions about algorithms whose behaviour is determined not only by its input but also by a source of random numbers.

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### Why is 0-BPP equal to P

Sorry if it is an obvious question, since all my searches lead to "clearly 0-BPP=P" (like Papadimitriou text book or Complexity Zoo). I understand that any P machine can be seen as a 0-BPP machine ...
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### Is it possible to use a random seed in the form of an integer to uniformly sample items from an array in sublinear time?

For example, given an array of reservation IDs: ...
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### Is there some kind of expected error margin for my Monte Carlo algorithm?

My Monte Carlo algorithm starts by placing some circles in the plane with potential overlaps. I then place a large circle somewhere and compute the overlapping area of this larger circle with the ...
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### Karger's min cut and tips on bounding nonlinear recurrences

I was recently working on an old qualifying exam problem asking us to generalize Karger's randomized global min cut algorithm to that of a global min $k$-cut. I recalled the strategy of running a ...
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### Las Vegas algorithm for finding 00000 in bit string

Problem 1: Consider the following problem: given a binary string $w=a_1a_2\cdots a_n \in\{0,1\}^*$, decide whether $w$ contains 00000 as a substring (i.e., where $w$ contains five consecutive 0's). ...
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### Is there any proof that says "For each problem in NP there is a randomized algorithm that solves that problem in expected polynomial time."

Is it known that "For each problem in NP there is a randomized algorithm that solves it in polynomial time"? If not true then is there any proof of that. Or does it belongs to the unknown ...