Balanced Allocations with Incomplete Information: The Power of Two Queries

@inproceedings{Los2022BalancedAW,
  title={Balanced Allocations with Incomplete Information: The Power of Two Queries},
  author={Dimitrios Los and Thomas Sauerwald},
  booktitle={ITCS},
  year={2022}
}
We consider the allocation of m balls into n bins with incomplete information. In the classical Two-Choice process a ball first queries the load of two randomly chosen bins and is then placed in the least loaded bin. In our setting, each ball also samples two random bins but can only estimate a bin’s load by sending binary queries of the form “Is the load at least the median?” or “Is the load at least 100?”. For the lightly loaded case m = O(n), Feldheim and Gurel-Gurevich (2021) showed that… 

Figures and Tables from this paper

Balanced Allocations: The Heavily Loaded Case with Deletions
TLDR
A new strategy is presented, called M ODULATED G REEDY, that guarantees a maximum load of m / n + O ( log m ) , at any given moment, with high probability in m .
Balanced Allocations in Batches: Simplified and Generalized
TLDR
A new analysis of the allocation of m balls (jobs) into n bins (servers) based on exponential potential functions is presented, which includes not only Two-Choice, but also processes with fewer bin samples like (1+β), processes which can only receive one bit of information from each bin sample and graphical allocation, where bins correspond to vertices in a graph.
Long-term balanced allocation via thinning
TLDR
It is shown that when m and n are sufficiently large, a typical maximum load of (log n) can be achieved with high probability, asymptotically the same as the optimal maximum load that could be achieved at time m.
The Power of Filling in Balanced Allocations
It is well known that if m balls (jobs) are placed sequentially into n bins (servers) according to the One-Choice protocol – choose a single bin in each round and allocate one ball to it – then, for
Tight Bounds for Repeated Balls-into-Bins
We study the repeated balls-into-bins process introduced by Becchetti, Clementi, Natale, Pasquale and Posta [3]. This process starts with m balls arbitrarily distributed across n bins. At each step t

References

SHOWING 1-10 OF 56 REFERENCES
Parallel Balanced Allocations: The Heavily Loaded Case
TLDR
A simple parallel threshold algorithm is presented that obtains a maximal load of $m/n+O(1)$ w.h.p. within $O(łogłog ( m/n)+łog^* n)$ rounds, and this work gives a simple asymmetric algorithm that goes to show that, similar to the case of £m=n, asymmetry allows for highly efficient solutions.
Parallel randomized load balancing
TLDR
This work explores extensions of this result to parallel and distributed settings and focuses on the tradeoff between the amount of space in the fullest bin and the least full bin.
Choice-Memory Tradeoff in Allocations
TLDR
This work finds a tradeoff between the number of choices, k, and theNumber of memory bits available, m, which has a sharp threshold governing the performance: If km≫≫n then one can achieve a constant maximal load.
Approximated Two Choices in Randomized Load Balancing
TLDR
The maximum load in the approximatedd-choice balls-and-bins game where the current load of each bin is available only approximately is studied, and the bound matches the (tight) bound in the original d-choice model given by Azar et al.
Graphical balanced allocations and the (1 + β)‐choice process
TLDR
The technique involves a tight analysis of what the authors call the "1+β-choice" process for some parameter β∈0,1: each ball goes to a random bin with probability 1-β and the lesser loaded of two random bins with probability β, irrespective of m.
The power of two random choices: a survey of tech-niques and results
TLDR
The important implication of this result is that even a small amount of choice can lead to drastically di erent results in load balancing.
Balanced Allocations: Caching and Packing, Twinning and Thinning
TLDR
A general framework is presented that allows us to analyze various allocation processes that slightly prefer allocating into underloaded, as opposed to overloaded bins, and implies a gap of $\mathcal{O}(\log n)$ between the maximum load and average load, even when an arbitrary number of balls $m \geq n$ are allocated (heavily loaded case).
Balanced allocations: the weighted case
TLDR
If the fourth moment of the weight distribution is finite, the expected value of the gap is shown to be independent of the number of balls, which is especially striking whenconsidering heavy tailed distributions such as Power-Law andLog-Normal distributions.
Balls and Bins: Smaller Hash Families and Faster Evaluation
TLDR
The size of families (or, equivalently, the description length of their functions) that guarantee a maximal load of O(log n / log n)) with high probability are studied, as well as the evaluation time of their function.
Balanced allocations with heterogenous bins
TLDR
This work investigates the power of the multiple choice paradigm in the setting where bins are not sampled from the uniform distribution, and proves tight upper and lower bounds for the number of choices needed in the 1-out-of-d scheme in order to maintain a balanced allocations when thenumber of items is arbitrarily high.
...
1
2
3
4
5
...