Related papers: Concentration Independent Random Number Generation…
We present an alternate formulation of the partial assignment problem as matching random clique complexes, that are higher-order analogues of random graphs, designed to provide a set of invariants that better detect higher-order structure.…
Randomisation is a critical tool in designing distributed systems. The common coin primitive, enabling the system members to agree on an unpredictable random number, has proven to be particularly useful. We observe, however, that it is…
$ \renewcommand{\tilde}{\widetilde} $We present an $\tilde{O}(\log^2 n)$ round deterministic distributed algorithm for the maximal independent set problem. By known reductions, this round complexity extends also to maximal matching,…
We report upon a novel principle for realization of a fast nondeterministic random number generator whose randomness relies on intrinsic randomness of the quantum physical processes of photonic emission in semiconductors and subsequent…
In the field of algorithmic self-assembly, a long-standing unproven conjecture has been that of the NP-hardness of binary pattern tile set synthesis (2-PATS). The $k$-PATS problem is that of designing a tile assembly system with the…
The assembly of molecular networks into structures such as random tilings and glasses has recently been demonstrated for a number of two-dimensional systems. These structures are dynamically-arrested on experimental timescales so the…
Let $M$ be a $3\times 3$ integer matrix which is expanding in the sense that each of its eigenvalues is greater than $1$ in modulus and let $\mathcal{D} \subset \mathbb{Z}^3$ be a digit set containing $|\det M|$ elements. Then the unique…
We study the statistical properties of the generation of random graphs according the configuration model, where one assigns randomly degrees to nodes. This model is often used, e.g., for the scale-free degree distribution ~d^gamma. For the…
Arbitrary pattern formation (\textsc{Apf}) is a well-studied problem in swarm robotics. To the best of our knowledge, the problem has been considered in two different settings: one in a euclidean plane and another in an infinite grid. This…
We consider low-space algorithms for the classic Element Distinctness problem: given an array of $n$ input integers with $O(\log n)$ bit-length, decide whether or not all elements are pairwise distinct. Beame, Clifford, and Machmouchi [FOCS…
We consider the distinct elements problem, where the goal is to estimate the number of distinct colors in an urn containing $ k $ balls based on $n$ samples drawn with replacements. Based on discrete polynomial approximation and…
Amorphous (disordered) materials are solids that have shown great potential in various domains, including energy storage, thermal management, and advanced materials. Unlike crystalline materials that can be described by unit cells…
We study a variant of the \emph{generalized assignment problem} ({\sf GAP}) with group constraints. An instance of {\sf Group GAP} is a set $I$ of items, partitioned into $L$ groups, and a set of $m$ uniform (unit-sized) bins. Each item $i…
Genuine random numbers can be produced beyond a shadow of doubt through the intrinsic randomness provided by quantum mechanics theory. While many degrees of freedom have been investigated for randomness generation, not adequate attention…
Maximal Independent Set selection is a fundamental problem in distributed computing. A novel probabilistic algorithm for this problem has recently been proposed by Afek et al, inspired by the study of the way that developing cells in the…
Due to the significant process variations, designers have to optimize the statistical performance distribution of nano-scale IC design in most cases. This problem has been investigated for decades under the formulation of stochastic…
In this article we study domino tilings of a family of finite regions called Aztec diamonds. Every such tiling determines a partition of the Aztec diamond into five sub-regions; in the four outer sub-regions, every tile lines up with nearby…
We present a random number generator based on quantum effects in photonic emission and detection. It is unique in simultaneous use of both spatial and temporal quantum information contained in the system which makes it resilient to hardware…
We introduce probabilistic frames to study finite frames whose elements are chosen at random. While finite tight frames generalize orthonormal bases by allowing redundancy, independent, uniformly distributed points on the sphere…
In this note we study the right large deviation of the top eigenvalue (or singular value) of the sum or product of two random matrices $\mathbf{A}$ and $\mathbf{B}$ as their dimensions goes to infinity. The matrices $\mathbf{A}$ and…