Related papers: Load balancing under $d$-thinning

We study the following synchronous process that we call "repeated balls-into-bins". The process is started by assigning $n$ balls to $n$ bins in an arbitrary way. In every subsequent round, from each non-empty bin one ball is chosen…

Effective load balancing lies at the heart of many applications in operations. Frequently tackled via the balls-into-bins paradigm, seminal results established the power of two choices in load balancing: a limited amount of costly…

Consider the following process whereby $n$ balls are distributed into $k$ bins. Repeatedly, a ball is removed from a non-empty bin chosen uniformly at random. The process ends when a single non-empty bin remains. Will Ma…

Assume that $2n$ balls are thrown independently and uniformly at random into $n$ bins. We consider the unlikely event $E$ that every bin receives at least one ball, showing that $\Pr[E] = \Theta(b^n)$ where $b \approx 0.836$. Note that, due…

In multi-server distributed queueing systems, the access of stochastically arriving jobs to resources is often regulated by a dispatcher, also known as load balancer. A fundamental problem consists in designing a load balancing algorithm…

In a balancing network each processor has an initial collection of unit-size jobs (tokens) and in each round, pairs of processors connected by balancers split their load as evenly as possible. An excess token (if any) is placed according to…

We consider the online bin packing problem under the advice complexity model where the 'online constraint' is relaxed and an algorithm receives partial information about the future requests. We provide tight upper and lower bounds for the…

For fixed weights w_1,...,w_n, and for d>0, we let B denote a collection of d*n balls, with d balls of weight w_i for each i=1,...,n. We consider the problem of assigning the balls to n bins with capacities C_1,...,C_n, in such a way that…

In this work, we examine a generic class of simple distributed balls-into-bins algorithms. Exploiting the strong concentration bounds that apply to balls-into-bins games, we provide an iterative method to compute accurate estimates of the…

Load balancing is a well-studied problem, with balls-in-bins being the primary framework. The greedy algorithm $\mathsf{Greedy}[d]$ of Azar et al. places each ball by probing $d > 1$ random bins and placing the ball in the least loaded of…

We propose a sorting-based greedy algorithm called SortedGreedy[m] for approximately solving the offline version of the d-choice weighted balls-into-bins problem where the number of choices for each ball is equal to the number of bins. We…

Balls and bins models are classical probabilistic models where balls are added to bins at random according to a certain rule. The balls and bins model with feedback is a non-linear generalisation of the P\'olya urn, where the probability of…

We revisit the random allocation model in which $n$ balls are independently placed into $N$ boxes with probabilities $q_1,\ldots,q_N$. A classical asymptotic result due to Kolchin, Sevastyanov, and Chistyakov for the expectations,…

We consider the problem of deterministic load balancing of tokens in the discrete model. A set of $n$ processors is connected into a $d$-regular undirected network. In every time step, each processor exchanges some of its tokens with each…

Bin packing is a classic optimization problem with a wide range of applications, from load balancing to supply chain management. In this work, we study the online variant of the problem, in which a sequence of items of various sizes must be…

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…

To facilitate load balancing, distributed systems store data redundantly. We evaluate the load balancing performance of storage schemes in which each object is stored at $d$ different nodes, and each node stores the same number of objects.…

We study the placement of n balls into n bins where balls and bins are represented as two vector spaces over Z 2 . The placement is done according to a linear transformation between the two vector spaces. We analyze the expected size of a…

We consider constrained sampling problems in paid research studies or clinical trials. When qualified volunteers are more than the budget allowed, we recommend a D-optimal sampling strategy based on the optimal design theory and develop a…

Distributed systems store data objects redundantly to balance the data access load over multiple nodes. Load balancing performance depends mainly on 1) the level of storage redundancy and 2) the assignment of data objects to storage nodes.…