Related papers: Unbalanced Allocations
We consider several extensions of the fractional bin packing problem, a relaxation of the traditional bin packing problem where the objects may be split across multiple bins. In these extensions, we introduce load-balancing constraints…
We study the binary choice problem in a data-rich environment with asymmetric loss functions. The econometrics literature covers nonparametric binary choice problems but does not offer computationally attractive solutions in data-rich…
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…
Mechanism design is addressed in the context of fair allocations of indivisible goods with monetary compensation. Motivated by a real-world social choice problem, mechanisms with verification are considered in a setting where (i) agents'…
Finding a counterfeit coin with the different weight from a set of visually identical coin using a balance, usually a two-armed balance, known as the balance question, is an intersting and inspiring question. Its variants involve…
We study different online optimization problems in the random-order model. There is a finite set of bins with known capacity and a finite set of items arriving in a random order. Upon arrival of an item, its size and its value for each of…
The stable allocation problem is a many-to-many generalization of the well-known stable marriage problem, where we seek a bipartite assignment between, say, jobs (of varying sizes) and machines (of varying capacities) that is "stable" based…
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…
We study d-way balanced allocation, which assigns each incoming job to the lightest loaded among d randomly chosen servers. While prior work has extensively studied the performance of the basic scheme, there has been less published work on…
We study the problem of mechanism design for allocating a set of indivisible items among agents with private preferences on items. We are interested in such a mechanism that is strategyproof (where agents' best strategy is to report their…
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…
Distributed optimization for resource allocation problems is investigated and a sub-optimal continuous-time algorithm is proposed. Our algorithm has lower order dynamics than others to reduce burdens of computation and communication, and is…
The proportional fair resource allocation problem is a major problem studied in flow control of networks, operations research, and economic theory, where it has found numerous applications. This problem, defined as the constrained…
In the balls-into-bins setting, $n$ balls are thrown uniformly at random into $n$ bins. The na\"{i}ve way to generate the final load vector takes $\Theta(n)$ time. However, it is well-known that this load vector has with high probability…
Motivated by a transit line planning problem in transportation systems, we investigate the following capacitated assignment problem under a budget constraint. Our model involves $L$ bins and $P$ items. Each bin $l$ has a utilization cost…
In this paper, we study the maximum loads of explicit hash families in the $d$-choice schemes when allocating sequentially $n$ balls into $n$ bins. We consider the \emph{Uniform-Greedy} scheme, which provides $d$ independent bins for each…
Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems,…
This paper proposes an optimal allocation problem with ramified transport technology in a spatial economy. Ramified transportation is used to model the transport economy of scale in group transportation observed widely in both nature and…
Contrary to traditional deterministic notions of algorithmic fairness, this paper argues that fairly allocating scarce resources using machine learning often requires randomness. We address why, when, and how to randomize by proposing…