Related papers: Balls and Bins and the Infinite Process with Rando…

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…

We introduce a new class of balanced allocation processes which bias towards underloaded bins (those with load below the mean load) either by skewing the probability by which a bin is chosen for an allocation (probability bias), or…

We propose a natural process for allocating n balls into n bins that are organized as the vertices of an undirected graph G. Each ball first chooses a vertex u in G uniformly at random. Then the ball performs a local search in G starting…

In a balls-in-bins process with feedback, balls are sequentially thrown into bins so that the probability that a bin with n balls obtains the next ball is proportional to f(n) for some function f. A commonly studied case where there are two…

We consider the allocation of $m$ balls (jobs) into $n$ bins (servers). In the standard Two-Choice process, at each step $t=1,2,\ldots,m$ we first sample two bins uniformly at random and place a ball in the least loaded bin. It is…

In the classical balls-and-bins paradigm, where $n$ balls are placed independently and uniformly in $n$ bins, typically the number of bins with at least two balls in them is $\Theta(n)$ and the maximum number of balls in a bin is…

We use the holonomic ansatz to estimate the asymptotic behavior, in $T$, of the average maximal number of balls in a bin that is obtained when one throws uniformly at random (without replacement) $r$ balls into $n$ bins, $T$ times. Our…

Suppose that there are n bins, and balls arrive in a Poisson process at rate \lambda n, where \lambda >0 is a constant. Upon arrival, each ball chooses a fixed number d of random bins, and is placed into one with least load. Balls have…

Balanced allocation of online balls-into-bins has long been an active area of research for efficient load balancing and hashing applications.There exists a large number of results in this domain for different settings, such as parallel…

This paper investigates a general version of the multiple choice model called the $(k,d)$-choice process in which $n$ balls are assigned to $n$ bins. In the process, $k<d$ balls are placed into $k$ least loaded out of $d$ bins chosen…

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…

We estimate the size of a most loaded bin in the setting when the balls are placed into the bins using a random linear function in a finite field. The balls are chosen from a transformed interval. We show that in this setting the expected…

In the cup game, an adversary distributes 1 unit of water among $n$ cups every time step. The player then selects a single cup from which to remove 1 unit of water. In the bamboo trimming problem, the adversary must choose fixed rates for…

In each step of the $p$-processor cup game on $n$ cups, a filler distributes up to $p$ units of water among the cups, subject only to the constraint that no cup receives more than $1$ unit of water; an emptier then removes up to $1$ unit of…

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…

The single- and multi- processor cup games can be used to model natural problems in areas such as processor scheduling, deamortization, and buffer management. At the beginning of the single-processor cup game, $n$ cups are initially empty.…

Suppose we sequentially put $n$ balls into $n$ bins. If we put each ball into a random bin then the heaviest bin will contain ${\sim}\log n/\log\log n$ balls with high probability. However, Azar, Broder, Karlin and Upfal [SIAM J. Comput. 29…

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…

A graph $d$-process starts with an empty graph on $n$ vertices, and adds one edge at each time step, chosen uniformly at random from those pairs which are not yet edges and whose both vertices have current degree less than $d$. If, in the…

Several differential equations usually appearing in mathematical physics are solved through a power series expansion, which reduces in solving difference equations. In this paper a probability problem is presented whose solution follows a…