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# Questions tagged [balls-and-bins]

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### Filling bins with pairs of balls

A bin is called full if it contains at least $k$ balls. Our goal is to make as many bins as possible full. In the simplest scenario, we are given $n$ balls and may arrange them arbitrarily. In that ...
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### Use minimum number of swaps so each bin contains balls of the same color

There are $n$ bins, the $i$th bin contain $a_i$ balls. The balls has $n$ colors, there are $a_i$ balls of color $i$. Let $m=\sum_{i=1}^n a_i$. A swap is take a ball from one bin and swap with a ball ...
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Given numbers $n,k\in \mathbb{N}$, we consider $\mathcal P$ to be the set of all possible partitions of $n$ balls into $k$ bins. Alternatively, $\mathcal P$ is the set of all $k$-ary vectors in $\{0,... • 2,634 2 votes 1 answer 2k views ### Load balancing. Why not use priority queues? I have recently learned about various randomized algorithms for load balancing. The model is always that there are$m$balls and$n$bins and the balls arrive one at a time. The task is to minimize ... • 23 1 vote 1 answer 33 views ### Distribution maximizing ratio of expected maximum over the mean I’m looking for a distribution that is non-negative, or has good tail bounds (so non-negative with high probability) and maximizes the ratio between the expected maximum of$n$iid samples and the ... 1 vote 1 answer 250 views ### Assigning$m$balls to$n$buckets - recursive algorithm I came across the following problem and the answer to that problem: Given$m$balls and$n$bins, find out how many ways to assign the balls to the bins. Notice the bins have no order: for example,$(...
Suppose there're $N$ weighted balls and $M$ equal weight bins, it's guaranteed at least one placement exists that all the balls can be placed into bins. What's the right algorithm to achieve a well-...