Dynamic Averaging Load Balancing on Arbitrary Graphs

In this paper we study dynamic averaging load balancing on general graphs. We consider infinite time and dynamic processes, where in every step new load items are assigned to randomly chosen nodes. A matching is chosen, and the load is averaged over the edges of that matching. We analyze the discrete case where load items are indivisible, moreover our results also carry over to the continuous case where load items can be split arbitrarily. For the choice of the matchings we consider three different models, random matchings of linear size, random matchings containing only single edges, and deterministic sequences of matchings covering the whole graph. We bound the discrepancy, which is defined as the difference between the maximum and the minimum load. Our results cover a broad range of graph classes and, to the best of our knowledge, our analysis is the first result for discrete and dynamic averaging load balancing processes. As our main technical contribution we develop a drift result that allows us to apply techniques based on the effective resistance in an electrical network to the setting of dynamic load balancing

PPF - A Parallel Particle Filtering Library

We present the parallel particle filtering (PPF) software library, which enables hybrid shared-memory/distributed-memory parallelization of particle filtering (PF) algorithms combining the Message Passing Interface (MPI) with multithreading for multi-level parallelism. The library is implemented in Java and relies on OpenMPI's Java bindings for inter-process communication. It includes dynamic load balancing, multi-thread balancing, and several algorithmic improvements for PF, such as input-space domain decomposition. The PPF library hides the difficulties of efficient parallel programming of PF algorithms and provides application developers with the necessary tools for parallel implementation of PF methods. We demonstrate the capabilities of the PPF library using two distributed PF algorithms in two scenarios with different numbers of particles. The PPF library runs a 38 million particle problem, corresponding to more than 1.86 GB of particle data, on 192 cores with 67% parallel efficiency. To the best of our knowledge, the PPF library is the first open-source software that offers a parallel framework for PF applications.Comment: 8 pages, 8 figures; will appear in the proceedings of the IET Data Fusion & Target Tracking Conference 201

Tight Bounds for Randomized Load Balancing on Arbitrary Network Topologies

We consider the problem of balancing load items (tokens) in networks. Starting with an arbitrary load distribution, we allow nodes to exchange tokens with their neighbors in each round. The goal is to achieve a distribution where all nodes have nearly the same number of tokens. For the continuous case where tokens are arbitrarily divisible, most load balancing schemes correspond to Markov chains, whose convergence is fairly well-understood in terms of their spectral gap. However, in many applications, load items cannot be divided arbitrarily, and we need to deal with the discrete case where the load is composed of indivisible tokens. This discretization entails a non-linear behavior due to its rounding errors, which makes this analysis much harder than in the continuous case. We investigate several randomized protocols for different communication models in the discrete case. As our main result, we prove that for any regular network in the matching model, all nodes have the same load up to an additive constant in (asymptotically) the same number of rounds as required in the continuous case. This generalizes and tightens the previous best result, which only holds for expander graphs, and demonstrates that there is almost no difference between the discrete and continuous cases. Our results also provide a positive answer to the question of how well discrete load balancing can be approximated by (continuous) Markov chains, which has been posed by many researchers.Comment: 74 pages, 4 figure

Dynamic load balancing of parallel road traffic simulation

The objective of this research was to investigate, develop and evaluate dynamic load-balancing strategies for parallel execution of microscopic road traffic simulations. Urban road traffic simulation presents irregular, and dynamically varying distributed computational load for a parallel processor system. The dynamic nature of road traffic simulation systems lead to uneven load distribution during simulation, even for a system that starts off with even load distributions. Load balancing is a potential way of achieving improved performance by reallocating work from highly loaded processors to lightly loaded processors leading to a reduction in the overall computational time. In dynamic load balancing, workloads are adjusted continually or periodically throughout the computation. In this thesis load balancing strategies were evaluated and some load balancing policies developed. A load index and a profitability determination algorithms were developed. These were used to enhance two load balancing algorithms. One of the algorithms exhibits local communications and distributed load evaluation between the neighbour partitions (diffusion algorithm) and the other algorithm exhibits both local and global communications while the decision making is centralized (MaS algorithm). The enhanced algorithms were implemented and synthesized with a research parallel traffic simulation. The performance of the research parallel traffic simulator, optimized with the two modified dynamic load balancing strategies were studied

Dynamic load balancing of parallel road traffic simulation

The objective of this research was to investigate, develop and evaluate dynamic load-balancing strategies for parallel execution of microscopic road traffic simulations. Urban road traffic simulation presents irregular, and dynamically varying distributed computational load for a parallel processor system. The dynamic nature of road traffic simulation systems lead to uneven load distribution during simulation, even for a system that starts off with even load distributions. Load balancing is a potential way of achieving improved performance by reallocating work from highly loaded processors to lightly loaded processors leading to a reduction in the overall computational time. In dynamic load balancing, workloads are adjusted continually or periodically throughout the computation. In this thesis load balancing strategies were evaluated and some load balancing policies developed. A load index and a profitability determination algorithms were developed. These were used to enhance two load balancing algorithms. One of the algorithms exhibits local communications and distributed load evaluation between the neighbour partitions (diffusion algorithm) and the other algorithm exhibits both local and global communications while the decision making is centralized (MaS algorithm). The enhanced algorithms were implemented and synthesized with a research parallel traffic simulation. The performance of the research parallel traffic simulator, optimized with the two modified dynamic load balancing strategies were studied.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Communication Patterns for Randomized Algorithms

Examples of large scale networks include the Internet, peer-to-peer networks, parallel computing systems, cloud computing systems, sensor networks, and social networks. Efficient dissemination of information in large networks such as these is a funda- mental problem. In many scenarios the gathering of information by a centralised controller can be impractical. When designing and analysing distributed algorithms we must consider the limitations imposed by the heterogeneity of devices in the networks. Devices may have limited computational ability or space. This makes randomised algorithms attractive solutions. Randomised algorithms can often be simpler and easier to implement than their deterministic counterparts. This thesis analyses the effect of communication patterns on the performance of distributed randomised algorithms. We study randomized algorithms with application to three different areas. Firstly, we study a generalization of the balls-into-bins game. Balls into bins games have been used to analyse randomised load balancing. Under the Greedy[d] allocation scheme each ball queries the load of d random bins and is then allocated to the least loaded of them. We consider an infinite, parallel setting where expectedly λn balls are allocated in parallel according to the Greedy[d] allocation scheme in to n bins and subsequently each non-empty bin removes a ball. Our results show that for d = 1,2, the Greedy[d] allocation scheme is self-stabilizing and that in any round the maximum system load for high arrival rates is exponentially smaller for d = 2 compared to d = 1 (w.h.p). Secondly, we introduce protocols that solve the plurality consensus problem on arbitrary graphs for arbitrarily small bias. Typically, protocols depend heavily on the employed communication mechanism. Our protocols are based on an interest- ing relationship between plurality consensus and distributed load balancing. This relationship allows us to design protocols that are both time and space efficient and generalize the state of the art for a large range of problem parameters. Finally, we investigate the effect of restricting the communication of the classical PULL algorithm for randomised rumour spreading. Rumour spreading (broadcast) is a fundamental task in distributed computing. Under the classical PULL algo- rithm, a node with the rumour that receives multiple requests is able to respond to all of them in a given round. Our model restricts nodes such that they can re- spond to at most one request per round. Our results show that the restricted PULL algorithm is optimal for several graph classes such as complete graphs, expanders, random graphs and several Cayley graphs