Parallel Implementations of Cellular Automata for Traffic Models

The Biham-Middleton-Levine (BML) traffic model is a simple two-dimensional, discrete Cellular Automaton (CA) that has been used to study self-organization and phase transitions arising in traffic flows. From the computational point of view, the BML model exhibits the usual features of discrete CA, where the state of the automaton are updated according to simple rules that depend on the state of each cell and its neighbors. In this paper we study the impact of various optimizations for speeding up CA computations by using the BML model as a case study. In particular, we describe and analyze the impact of several parallel implementations that rely on CPU features, such as multiple cores or SIMD instructions, and on GPUs. Experimental evaluation provides quantitative measures of the payoff of each technique in terms of speedup with respect to a plain serial implementation. Our findings show that the performance gap between CPU and GPU implementations of the BML traffic model can be reduced by clever exploitation of all CPU features

Developing Efficient Discrete Simulations on Multicore and GPU Architectures

In this paper we show how to efficiently implement parallel discrete simulations on multicoreandGPUarchitecturesthrougharealexampleofanapplication: acellularautomatamodel of laser dynamics. We describe the techniques employed to build and optimize the implementations using OpenMP and CUDA frameworks. We have evaluated the performance on two different hardware platforms that represent different target market segments: high-end platforms for scientific computing, using an Intel Xeon Platinum 8259CL server with 48 cores, and also an NVIDIA Tesla V100GPU,bothrunningonAmazonWebServer(AWS)Cloud;and on a consumer-oriented platform, using an Intel Core i9 9900k CPU and an NVIDIA GeForce GTX 1050 TI GPU. Performance results were compared and analyzed in detail. We show that excellent performance and scalability can be obtained in both platforms, and we extract some important issues that imply a performance degradation for them. We also found that current multicore CPUs with large core numbers can bring a performance very near to that of GPUs, and even identical in some cases.Ministerio de Economía, Industria y Competitividad, Gobierno de España (MINECO), and the Agencia Estatal de Investigación (AEI) of Spain, cofinanced by FEDER funds (EU) TIN2017-89842

Quantum Lattice Boltzmann is a quantum walk

Numerical methods for the 1-D Dirac equation based on operator splitting and on the quantum lattice Boltzmann (QLB) schemes are reviewed. It is shown that these discretizations fall within the class of quantum walks, i.e. discrete maps for complex fields, whose continuum limit delivers Dirac-like relativistic quantum wave equations. The correspondence between the quantum walk dynamics and these numerical schemes is given explicitly, allowing a connection between quantum computations, numerical analysis and lattice Boltzmann methods. The QLB method is then extended to the Dirac equation in curved spaces and it is demonstrated that the quantum walk structure is preserved. Finally, it is argued that the existence of this link between the discretized Dirac equation and quantum walks may be employed to simulate relativistic quantum dynamics on quantum computers.Comment: 18 pages, 3 figure

A Comparison of BDD-Based Parity Game Solvers

Parity games are two player games with omega-winning conditions, played on finite graphs. Such games play an important role in verification, satisfiability and synthesis. It is therefore important to identify algorithms that can efficiently deal with large games that arise from such applications. In this paper, we describe our experiments with BDD-based implementations of four parity game solving algorithms, viz. Zielonka's recursive algorithm, the more recent Priority Promotion algorithm, the Fixpoint-Iteration algorithm and the automata based APT algorithm. We compare their performance on several types of random games and on a number of cases taken from the Keiren benchmark set.Comment: In Proceedings GandALF 2018, arXiv:1809.0241