Questions tagged [balls-and-bins]
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6
questions
13
votes
1answer
949 views
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 ...
12
votes
1answer
447 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
1answer
129 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,...
2
votes
1answer
1k 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 ...
1
vote
1answer
90 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, ...
1
vote
0answers
38 views
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-...
