相关论文: On the Relationship Between Several Variants of th…

We prove that hashing $n$ balls into $n$ bins via a random matrix over $\mathbf{F}_2$ yields expected maximum load $O(\log n / \log \log n)$. This matches the expected maximum load of a fully random function and resolves an open question…

Let $S\subseteq F_2^u$ have size $n=2^\ell$, and let $h:F_2^u\to F_2^\ell$ be a uniformly random linear map. For $y\in F_2^\ell$, write $Load_h(y):=|h^{-1}(y)\cap S|$, and let $M(S,h):=\max_{y\in F_2^\ell} Load_h(y)$ be the maximum load.…

We consider the hash function $h(x) = ((ax+b) \bmod p) \bmod n$ where $a,b$ are chosen uniformly at random from $\{0,1,\ldots,p-1\}$. We prove that when we use $h(x)$ in hashing with chaining to insert $n$ elements into a table of size $n$…

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…

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…

Linear-probing hash tables have been classically believed to support insertions in time $\Theta(x^2)$, where $1 - 1/x$ is the load factor of the hash table. Recent work by Bender, Kuszmaul, and Kuszmaul (FOCS'21), however, has added a new…

Best-Fit is one of the most prominent and practically used algorithms for the bin packing problem, where a set of items with associated sizes needs to be packed in the minimum number of unit-capacity bins. Kenyon [SODA '96] studied online…

In the (1-dimensional) bin packing problem, we are asked to pack all the given items into bins, each of capacity one, so that the number of non-empty bins is minimized. Zhu~[Chaos, Solitons \& Fractals 2016] proposed an approximation…

The bin packing problem is to find the minimum number of bins of size one to pack a list of items with sizes $a_1,..., a_n$ in $(0,1]$. Using uniform sampling, which selects a random element from the input list each time, we develop a…

Dietzfelbinger and Weidling [DW07] proposed a natural variation of cuckoo hashing where each of $cn$ objects is assigned $k = 2$ intervals of size $\ell$ in a linear (or cyclic) hash table of size $n$ and both start points are chosen…

The monotone minimal perfect hash function (MMPHF) problem is the following indexing problem. Given a set $S= \{s_1,\ldots,s_n\}$ of $n$ distinct keys from a universe $U$ of size $u$, create a data structure $DS$ that answers the following…

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 study a hypothesis testing problem in which data is compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data. The aim is to characterize all achievable encoding rates and…

In the problem of minimal perfect hashing, we are given a size $k$ subset $\mathcal{A}$ of a universe of keys $[n] = \{1,2, \cdots, n\}$, for which we wish to construct a hash function $h: [n] \to [k]$ such that $h(\cdot)$ maps…

The paradigm of many choices has influenced significantly the design of efficient data structures and, most notably, hash tables. Cuckoo hashing is a technique that extends this concept. There,we are given a table with $n$ locations, and we…

The Subset Sum problem asks whether a given set of $n$ positive integers contains a subset of elements that sum up to a given target $t$. It is an outstanding open question whether the $O^*(2^{n/2})$-time algorithm for Subset Sum by…

We study the online bin packing problem under two stochastic settings. In the bin packing problem, we are given n items with sizes in (0,1] and the goal is to pack them into the minimum number of unit-sized bins. First, we study bin packing…

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…

Randomized algorithms and data structures are often analyzed under the assumption of access to a perfect source of randomness. The most fundamental metric used to measure how "random" a hash function or a random number generator is, is its…

We investigate a real-life air cargo loading problem which is a variant of the three-dimensional Variable Size Bin Packing Problem with special bin forms of cuboid and non-cuboid unit load devices (ULDs). Packing is constrained by…