# Questions tagged [balls-and-bins]

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### 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 ...
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### Algorithms of placing N weighted balls into M uniform bins while striving for balanced weight?

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-...
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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, $(... 13 votes 1 answer 703 views ### Filling bins with pairs of balls A bin is called full if it contains at least$k$balls. Our goal is to make as many bins as possible full. In the simplest scenario, we are given$n$balls and may arrange them arbitrarily. In that ... 2 votes 1 answer 143 views ### Finding a specific "balls-into-bins" partition given its index in the lexicographical ordering Given numbers$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,...
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 ...
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 ...