相关论文: The devil's staircase for chip-firing on random gr…

We study the problem of finding the maximum of a function defined on the nodes of a connected graph. The goal is to identify a node where the function obtains its maximum. We focus on local iterative algorithms, which traverse the nodes of…

Thread-level parallelism in irregular applications with mutable data dependencies presents challenges because the underlying data is extensively modified during execution of the algorithm and a high degree of parallelism must be realized…

In this paper we solve on GPUs massive problems with large amount of data, which are not appropriate for solution with the SIMD technology. For the given problem we consider a three-level parallelization. The multithreading of CPU is used…

In this paper we describe a physical problem, based on electromagnetic fields, whose topological constraints are higher dimensional versions of Kirchhoff's laws, involving $2-$ simplicial complexes embedded in $\mathbb{R} ^3$ rather than…

We consider a cascade model of $N$ different processors performing a distributed parallel simulation. The main goal of the study is to show that the long-time dynamics of the system has a cluster behavior. To attack this problem we combine…

We consider a continuous-time quantum walk on a triple graph and investigate the influence of the side chain on the propagation in the main chain. Calculating the interchange of the probabilities between the two parts of the main chain, we…

This paper improves algorithms given in math.CO/0012036. Although the graph (digraph) becomes non-random as the algorithm proceeds, the probability for success stays the same. We also give examples.

We study a discrete time self interacting random process on graphs, which we call Greedy Random Walk. The walker is located initially at some vertex. As time evolves, each vertex maintains the set of adjacent edges touching it that have not…

In this paper we show that many sequential randomized incremental algorithms are in fact parallel. We consider algorithms for several problems including Delaunay triangulation, linear programming, closest pair, smallest enclosing disk,…

We study the cutoff phenomenon for generalized riffle shuffles where, at each step, the deck of cards is cut into a random number of packs of multinomial sizes which are then riffled together.

We prove a metric space scaling limit for a critical random graph with independent and identically distributed degrees having power-law tail behaviour with exponent $\alpha+1$, where $\alpha \in (1,2)$. The limiting components are…

We study the algebraic decay of the survival probability in open hierarchical graphs. We present a model of a persistent random walk on a hierarchical graph and study the spectral properties of the Frobenius-Perron operator. Using a…

A number of problems in parallel computing require reasoning about the dependency structure in parallel programs. For example, dynamic race detection relies on efficient "on-the-fly" determination of dependencies between sequential and…

We consider a general interacting particle system with interactions on a random graph, and study the large population limit of this system. When the sequence of underlying graphs converges to a graphon, we show convergence of the…

The \emph{graph realization problem} is to find for given nonnegative integers $a_1,\dots,a_n$ a simple graph (no loops or multiple edges) such that each vertex $v_i$ has degree $a_i.$ Given pairs of nonnegative integers…

The spread of an infection, a contagion, meme, emotion, message and various other spreadable objects have been discussed in several works. Burning and firefighting have been discussed in particular on static graphs. Graph burning simulates…

In card-based cryptography, a deck of physical cards is used to achieve secure computation. A shuffle, which randomly permutes a card-sequence along with some probability distribution, ensures the security of a card-based protocol. The…

We investigate the random dynamics of polynomial maps on the Riemann sphere and the dynamics of semigroups of polynomial maps on the Riemann sphere. In particular, the dynamics of a semigroup $G$ of polynomials whose planar postcritical set…

We observe a network scenario where parts of a secret are distributed among its nodes. Within the network, a group of attackers is actively trying to obtain the complete secret, while there is also the issue of some nodes malfunctioning or…

The scalability of massively parallel algorithms is a fundamental question in computer science. We study the scalability and the efficiency of a conservative massively parallel algorithm for discrete-event simulations where the discrete…