Related papers: Chains-into-Bins Processes
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…
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 2-choice allocation problem, $m$ balls are placed into $n$ bins, and each ball must choose between two random bins $i, j \in [n]$ that it has been assigned to. It has been known for more than two decades, that if each ball follows…
We introduce a new class of balanced allocation processes which are primarily characterized by ``filling'' underloaded bins. A prototypical example is the Packing process: At each round we only take one bin sample, if the load is below the…
We give a (strongly) history-independent two-choice balls-and-bins algorithm on $n$ bins that supports both insertions and deletions on a set of up to $m$ balls, while guaranteeing a maximum load of $m / n + O(1)$ with high probability, and…
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,…
Balls are sequentially allocated into $n$ bins as follows: for each ball, an independent, uniformly random bin is generated. An overseer may then choose to either allocate the ball to this bin, or else the ball is allocated to a new…
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…
A fundamental problem in distributed computing is the distribution of requests to a set of uniform servers without a centralized controller. Classically, such problems are modeled as static balls into bins processes, where $m$ balls (tasks)…
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…
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…
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 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 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 this paper, we study the two choice balls and bins process when balls are not allowed to choose any two random bins, but only bins that are connected by an edge in an underlying graph. We show that for $n$ balls and $n$ bins, if the…
Balls-in-bins models describe a random sequential allocation of infinitely many balls into a finite number of bins. In these models a ball is placed into a bin with probability proportional to a given function (feedback function), which…
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…
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…
We study a higher-dimensional 'balls-into-bins' problem. An infinite sequence of i.i.d. random vectors is revealed to us one vector at a time, and we are required to partition these vectors into a fixed number of bins in such a way as to…
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…