Related papers: Tight Bounds for Repeated Balls-into-Bins
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…
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…
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…
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 provide a relatively simple proof that the expected gap between the maximum load and the average load in the two choice process is bounded by $(1+o(1))\log \log n$, irrespective of the number of balls thrown. The theorem was first proven…
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…
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…
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 randomly chosen bins, compare their two loads and then place a ball in the least…
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…
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 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…
We estimate the mixing time of the a nonreversible finite Markov chain called Repeated Balls-into-Bins (RBB) process. This process is a discrete time conservative interacting particle system with parallel updates. Place initially in $L$…
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…
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…
We analyze the asymptotic behavior of the average maximal number of balls in a bin obtained by throwing uniformly at random $r$ balls without replacement into $n$ bins, $T$ times. Writing the expected maximum as $\frac{r}{n}T+…
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…
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…
Consider a balls-in-bins process in which each new ball goes into a given bin with probability proportional to f(n), where n is the number of balls currently in the bin and f is a fixed positive function. It is known that these so-called…
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 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…