Related papers: Choice-memory tradeoff in allocations
We consider the unbalanced allocation of $m$ balls into $n$ bins by a randomized algorithm using the "power of two choices". For each ball, we select a set of bins at random, then place the ball in the fullest bin within the set.…
We consider a variation of balls-into-bins which randomly allocates $m$ balls into $n$ bins. Following Godfrey's model (SODA, 2008), we assume that each ball $t$, $1\le t\le m$, comes with a hypergraph…
In balanced allocations, the goal is to place $m$ balls into $n$ bins, so as to minimize the gap (difference of max to average load). The One-Choice process places each ball to a bin sampled independently and uniformly at random. The…
We study the repeated balls-into-bins process introduced by Becchetti, Clementi, Natale, Pasquale and Posta (2019). This process starts with $m$ balls arbitrarily distributed across $n$ bins. At each round $t=1,2,\ldots$, one ball is…
The study of hashing is closely related to the analysis of balls and bins. It is well-known that instead of using a single hash function if we randomly hash a ball into two bins and place it in the smaller of the two, then this dramatically…
Allocation of balls into bins is a well studied abstraction for load balancing problems.The literature hosts numerous results for sequential(single dimensional) allocation case when m balls are thrown into n bins. In this paper we study the…
In the standard ball-in-bins experiment, a well-known scheme is to sample $d$ bins independently and uniformly at random and put the ball into the least loaded bin. It can be shown that this scheme yields a maximum load of $\log\log n/\log…
Suppose that we are to place $m$ balls into $n$ bins sequentially using the $d$-choice paradigm: For each ball we are given a choice of $d$ bins, according to $d$ hash functions $h_1,\dots,h_d$ and we place the ball in the least loaded of…
Balls-and-bins games have been a wildly successful tool for modeling load balancing problems. In this paper, we study a new scenario, which we call the ball recycling game, defined as follows: Throw m balls into n bins i.i.d. according to a…
In dynamic load balancing, we wish to distribute balls into bins in an environment where both balls and bins can be added and removed. We want to minimize the maximum load of any bin but we also want to minimize the number of balls and bins…
Designing algorithms for balanced allocation of clients to servers in dynamic settings is a challenging problem for a variety of reasons. Both servers and clients may be added and/or removed from the system periodically, and the main…
The graphical balls-into-bins process is a generalization of the classical 2-choice balls-into-bins process, where the bins correspond to vertices of an arbitrary underlying graph $G$. At each time step an edge of $G$ is chosen uniformly at…
A single-player game of Memory is played with $n$ distinct pairs of cards, with the cards in each pair bearing identical pictures. The cards are laid face-down. A move consists of revealing two cards, chosen adaptively. If these cards…
We consider the sequential allocation of $m$ balls (jobs) into $n$ bins (servers) by allowing each ball to choose from some bins sampled uniformly at random. The goal is to maintain a small gap between the maximum load and the average load.…
We consider leader election in clique networks, where $n$ nodes are connected by point-to-point communication links. For the synchronous clique under simultaneous wake-up, i.e., where all nodes start executing the algorithm in round $1$, we…
The power of two choices is a classic paradigm for load balancing when assigning $m$ balls to $n$ bins. When placing a ball, we pick two bins according to two hash functions $h_0$ and $h_1$, and place the ball in the least loaded bin.…
We explore the fundamental limits of distributed balls-into-bins algorithms. We present an adaptive symmetric algorithm that achieves a bin load of two in log* n+O(1) communication rounds using O(n) messages in total. Larger bin loads can…
For nearly six decades, the central open question in the study of hash tables has been to determine the optimal achievable tradeoff curve between time and space. State-of-the-art hash tables offer the following guarantee: If keys/values are…
Concentration bounds are given for throwing balls into bins independently according to a distribution $p$. The probability of a $k$-loaded bin after $m$ balls is shown to be controlled on both sides by $\rho_{m,k} := m \|p\|_k / k$. This…
Online load balancing for heterogeneous machines aims to minimize the makespan (maximum machine workload) by scheduling arriving jobs with varying sizes on different machines. In the adversarial setting, where an adversary chooses not only…