1,360 research outputs found
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Improved Analysis of Deterministic Load-Balancing Schemes
We consider the problem of deterministic load balancing of tokens in the
discrete model. A set of processors is connected into a -regular
undirected network. In every time step, each processor exchanges some of its
tokens with each of its neighbors in the network. The goal is to minimize the
discrepancy between the number of tokens on the most-loaded and the
least-loaded processor as quickly as possible.
Rabani et al. (1998) present a general technique for the analysis of a wide
class of discrete load balancing algorithms. Their approach is to characterize
the deviation between the actual loads of a discrete balancing algorithm with
the distribution generated by a related Markov chain. The Markov chain can also
be regarded as the underlying model of a continuous diffusion algorithm. Rabani
et al. showed that after time , any algorithm of their
class achieves a discrepancy of , where is the spectral
gap of the transition matrix of the graph, and is the initial load
discrepancy in the system.
In this work we identify some natural additional conditions on deterministic
balancing algorithms, resulting in a class of algorithms reaching a smaller
discrepancy. This class contains well-known algorithms, eg., the Rotor-Router.
Specifically, we introduce the notion of cumulatively fair load-balancing
algorithms where in any interval of consecutive time steps, the total number of
tokens sent out over an edge by a node is the same (up to constants) for all
adjacent edges. We prove that algorithms which are cumulatively fair and where
every node retains a sufficient part of its load in each step, achieve a
discrepancy of in time . We
also show that in general neither of these assumptions may be omitted without
increasing discrepancy. We then show by a combinatorial potential reduction
argument that any cumulatively fair scheme satisfying some additional
assumptions achieves a discrepancy of almost as quickly as the
continuous diffusion process. This positive result applies to some of the
simplest and most natural discrete load balancing schemes.Comment: minor corrections; updated literature overvie
Stability of JSQ in queues with general server-job class compatibilities
We consider Poisson streams of exponentially distributed jobs arriving at each edge of a hypergraph of queues. Upon arrival, an incoming job is routed to the shortest queue among the corresponding vertices. This generalizes many known models such as power-of-d load balancing and JSQ (join the shortest queue) on generic graphs. We prove that stability in this model is achieved if and only if there exists a stable static routing policy. This stability condition is equivalent to that of the JSW (join the shortest workload) policy. We show that some graph topologies lead to a loss of capacity, implying more restrictive stability conditions than in, for example, complete graphs.Fil: Cruise, James. Heriot-watt University; Reino UnidoFil: Jonckheere, Matthieu Thimothy Samson. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Shneer, Seva. Heriot-watt University; Reino Unid
Discrete Load Balancing in Heterogeneous Networks with a Focus on Second-Order Diffusion
In this paper we consider a wide class of discrete diffusion load balancing
algorithms. The problem is defined as follows. We are given an interconnection
network and a number of load items, which are arbitrarily distributed among the
nodes of the network. The goal is to redistribute the load in iterative
discrete steps such that at the end each node has (almost) the same number of
items. In diffusion load balancing nodes are only allowed to balance their load
with their direct neighbors.
We show three main results. Firstly, we present a general framework for
randomly rounding the flow generated by continuous diffusion schemes over the
edges of a graph in order to obtain corresponding discrete schemes. Compared to
the results of Rabani, Sinclair, and Wanka, FOCS'98, which are only valid
w.r.t. the class of homogeneous first order schemes, our framework can be used
to analyze a larger class of diffusion algorithms, such as algorithms for
heterogeneous networks and second order schemes. Secondly, we bound the
deviation between randomized second order schemes and their continuous
counterparts. Finally, we provide a bound for the minimum initial load in a
network that is sufficient to prevent the occurrence of negative load at a node
during the execution of second order diffusion schemes.
Our theoretical results are complemented with extensive simulations on
different graph classes. We show empirically that second order schemes, which
are usually much faster than first order schemes, will not balance the load
completely on a number of networks within reasonable time. However, the maximum
load difference at the end seems to be bounded by a constant value, which can
be further decreased if first order scheme is applied once this value is
achieved by second order scheme.Comment: Full version of paper submitted to ICDCS 201
Designing a scalable dynamic load -balancing algorithm for pipelined single program multiple data applications on a non-dedicated heterogeneous network of workstations
Dynamic load balancing strategies have been shown to be the most critical part of an efficient implementation of various applications on large distributed computing systems. The need for dynamic load balancing strategies increases when the underlying hardware is a non-dedicated heterogeneous network of workstations (HNOW). This research focuses on the single program multiple data (SPMD) programming model as it has been extensively used in parallel programming for its simplicity and scalability in terms of computational power and memory size.;This dissertation formally defines and addresses the problem of designing a scalable dynamic load-balancing algorithm for pipelined SPMD applications on non-dedicated HNOW. During this process, the HNOW parameters, SPMD application characteristics, and load-balancing performance parameters are identified.;The dissertation presents a taxonomy that categorizes general load balancing algorithms and a methodology that facilitates creating new algorithms that can harness the HNOW computing power and still preserve the scalability of the SPMD application.;The dissertation devises a new algorithm, DLAH (Dynamic Load-balancing Algorithm for HNOW). DLAH is based on a modified diffusion technique, which incorporates the HNOW parameters. Analytical performance bound for the worst-case scenario of the diffusion technique has been derived.;The dissertation develops and utilizes an HNOW simulation model to conduct extensive simulations. These simulations were used to validate DLAH and compare its performance to related dynamic algorithms. The simulations results show that DLAH algorithm is scalable and performs well for both homogeneous and heterogeneous networks. Detailed sensitivity analysis was conducted to study the effects of key parameters on performance
Analysis of Various Decentralized Load Balancing Techniques with Node Duplication
Experience in parallel computing is an increasingly necessary skill for today’s upcoming computer scientists as processors are hitting a serial execution performance barrier and turning to parallel execution for continued gains. The uniprocessor system has now reached its maximum speed limit and, there is very less scope to improve the speed of such type of system. To solve this problem multiprocessor system is used, which have more than one processor. Multiprocessor system improves the speed of the system but it again faces some problems like data dependency, control dependency, resource dependency and improper load balancing. So this paper presents a detailed analysis of various decentralized load balancing techniques with node duplication to reduce the proper execution time
- …