## Analysis of The Generalized Dimension Exchange Method for Dynamic Load Balancing (1992)

Venue: | Journal of Parallel and Distributed Computing |

Citations: | 42 - 7 self |

### BibTeX

@ARTICLE{Xu92analysisof,

author = {C. Z. Xu and F. C. M. Lau},

title = {Analysis of The Generalized Dimension Exchange Method for Dynamic Load Balancing},

journal = {Journal of Parallel and Distributed Computing},

year = {1992},

volume = {16},

pages = {385--393}

}

### Years of Citing Articles

### OpenURL

### Abstract

The dimension exchange method is a distributed load balancing method for point-to-point networks. We add a parameter, called the exchange parameter, to the method to control the splitting of load between a pair of directly connected processors, and call this parameterized version the generalized dimension exchange (GDE) method. The rationale for the introduction of this parameter is that splitting the workload into equal halves does not necessarily lead to an optimal result (in terms of the convergence rate) for certain structures. We carry out an analysis of this new method, emphasizing on its termination aspects and potential efficiency. Given a specific structure, one needs to determine a value to use for the exchange parameter that would lead to an optimal result. To this end, we first derive a sufficient and necessary condition for the termination of the method. We then show that equal splitting, proposed originally by others as a heuristic strategy, indeed yields optimal efficie...

### Citations

4697 |
Topics in Matrix Analysis
- Horn, Johnson
- 1991
(Show Context)
Citation Context ...cause the eigenvalues of M() are just the zeros of its characteristic polynomial, they are continuously dependent on the coefficients of the polynomial according to the fundamental theorem of algebra =-=[12]-=-. Given also the fact that the coefficients of the characteristic polynomial of a square real matrix are continuous functions of the elements of the matrix, it follows that the eigenvalues of M() are ... |

1004 |
The contract net protocol: high-level communication and control in a distributed problem solver,” in
- Smith
- 1980
(Show Context)
Citation Context ...of load balancing in distributed systems can be found in [11, 3]. In the past, numerous dynamic load balancing schemes with different characteristics have been proposed, such as the bidding algorithm =-=[9, 21, 23]-=-, the drafting algorithm [18], and the gradientmodel algorithm [16, 17]. Most of them were evaluated using simulation in which the performance of the proposed algorithm is dependent upon a number of p... |

625 | Tsitsiklis. Parallel and Distributed Computation: Numerical Methods - Bertsekas, N - 1989 |

386 |
Dynamic Load Sharing in Homogeneous Distributed Systems
- EAGER, LAZOWSKA, et al.
- 1986
(Show Context)
Citation Context ...ional model. To thoroughly evaluate and compare these algorithms requires a careful selection of a number of combinations of values for these parameters, which could turn out to be a non-trivial task =-=[5, 15, 8]-=-. Therefore, simulation alone is not sufficient for a thorough understanding of a load balancing policy, especially of its more fundamental properties. In fact, the fundamental properties, such as ter... |

260 |
Nonnegative matrices in the mathematical sciences
- Berman, Plemmons
- 1979
(Show Context)
Citation Context ...nsecutive exchange operations. As such, the processor interacts with all of its neighbors one at a time in each sweep. In order to guarantee ws0, the domain of the exchange parametersis restricted to =-=[0,1]-=-. By choosings= 1/2, the GDE method is equivalent to the original dimension exchange method. Two issues need to be addressed. One is the termination condition under which the algorithm would terminate... |

250 | A taxonomy of scheduling in general-purpose distributed computing systems
- Casavant, Kuhl
- 1988
(Show Context)
Citation Context ...tter results. With dynamic load balancing, workload may migrate from one processor to another during runtime. Detailed discussions and surveys of load balancing in distributed systems can be found in =-=[11, 3]-=-. In the past, numerous dynamic load balancing schemes with different characteristics have been proposed, such as the bidding algorithm [9, 21, 23], the drafting algorithm [18], and the gradientmodel ... |

128 |
The Gradient Model Load Balancing Method
- Lin, Keller
- 1987
(Show Context)
Citation Context ...ast, numerous dynamic load balancing schemes with different characteristics have been proposed, such as the bidding algorithm [9, 21, 23], the drafting algorithm [18], and the gradientmodel algorithm =-=[16, 17]-=-. Most of them were evaluated using simulation in which the performance of the proposed algorithm is dependent upon a number of parameters that characterize the underlying system and computational mod... |

95 |
The Influence of Different Workload Descriptions on a Heuristic Load Balancing Scheme
- KUNZ
- 1991
(Show Context)
Citation Context ...ional model. To thoroughly evaluate and compare these algorithms requires a careful selection of a number of combinations of values for these parameters, which could turn out to be a non-trivial task =-=[5, 15, 8]-=-. Therefore, simulation alone is not sufficient for a thorough understanding of a load balancing policy, especially of its more fundamental properties. In fact, the fundamental properties, such as ter... |

79 |
Edge-Colouring of Graphs
- Fiorini, Wilson
- 1977
(Show Context)
Citation Context ...note the degree of a vertex i in G and ffi(G) denote the maximum of the degrees of G's vertices. It is known that the minimum number of colors k is strictly bounded by ffi(G), and ffi(G)sksffi(G) + 1 =-=[10]-=-. We index the colors in a given k-color graph with integers from 1 to k. Consequently, the k-color graph can be represented as G k = (V; E k ), of which E k is a set of 3-tuples of the form (i; j; c)... |

58 |
A Distributed Drafting Algorithm for Load Balancing
- Ni, Xu, et al.
- 1985
(Show Context)
Citation Context ...tems can be found in [11, 3]. In the past, numerous dynamic load balancing schemes with different characteristics have been proposed, such as the bidding algorithm [9, 21, 23], the drafting algorithm =-=[18]-=-, and the gradientmodel algorithm [16, 17]. Most of them were evaluated using simulation in which the performance of the proposed algorithm is dependent upon a number of parameters that characterize t... |

40 | Load balancing in large networks: a comparative study
- Lüling, Monien, et al.
- 1991
(Show Context)
Citation Context ...ast, numerous dynamic load balancing schemes with different characteristics have been proposed, such as the bidding algorithm [9, 21, 23], the drafting algorithm [18], and the gradientmodel algorithm =-=[16, 17]-=-. Most of them were evaluated using simulation in which the performance of the proposed algorithm is dependent upon a number of parameters that characterize the underlying system and computational mod... |

36 |
Optimal dynamic remapping of data parallel computations
- Nicol, Reynolds
- 1990
(Show Context)
Citation Context ...ism for the termination detection of load balancing based on the method [25]. We are also in the process of incorporating the GDE load balancing algorithm into remapping of data parallel computations =-=[19]-=-. Finally, we should point out that the GDE method is based on the assumption of a synchronous model in which migration of workload across an edge can be treated as instantaneous. In asynchronous mode... |

33 |
Analysis of a graph coloring based distributed load balancing algorithm
- Hosseini, Litow, et al.
- 1990
(Show Context)
Citation Context ...perties of a load balancing policy, which are the properties we are most interested in. In this study, we concentrate on the dimension exchange method and its analysis in a fashion similar to that of =-=[6, 13]-=-. In the dimension exchange method [20, 6, 13], load balancing happens in one dimension at a time, where a dimension corresponds to some subset of all pairs of directly connected processors, and the r... |

33 | Clustering on a Hypercube Multicomputer
- Ranka, Sahni
- 1991
(Show Context)
Citation Context ...are the properties we are most interested in. In this study, we concentrate on the dimension exchange method and its analysis in a fashion similar to that of [6, 13]. In the dimension exchange method =-=[20, 6, 13]-=-, load balancing happens in one dimension at a time, where a dimension corresponds to some subset of all pairs of directly connected processors, and the result is an equal distribution of workload bet... |

32 |
Stability and Distributed Scheduling Algorithms
- Stankovic
- 1985
(Show Context)
Citation Context ...ich is a combination of finite automata and directed graphs, to formally model the general behavior of distributed scheduling [4]. Stankovic addressed the issue of stability of distributed scheduling =-=[22]-=-. Among them, Cybenko's matrix iterative approach stands out as being most suited for analyzing the efficiency and termination properties of a load balancing policy, which are the properties we are mo... |

23 |
The greedy load sharing algorithm
- Chowdhury
- 1990
(Show Context)
Citation Context ...ional model. To thoroughly evaluate and compare these algorithms requires a careful selection of a number of combinations of values for these parameters, which could turn out to be a non-trivial task =-=[5, 15, 8]-=-. Therefore, simulation alone is not sufficient for a thorough understanding of a load balancing policy, especially of its more fundamental properties. In fact, the fundamental properties, such as ter... |

21 |
An adaptive bidding algorithm for processes, clusters and distributed groups
- Stankovic, Sidhu
- 1984
(Show Context)
Citation Context ...of load balancing in distributed systems can be found in [11, 3]. In the past, numerous dynamic load balancing schemes with different characteristics have been proposed, such as the bidding algorithm =-=[9, 21, 23]-=-, the drafting algorithm [18], and the gradientmodel algorithm [16, 17]. Most of them were evaluated using simulation in which the performance of the proposed algorithm is dependent upon a number of p... |

13 |
A communicating finite automata approach to modeling distributed computation and its application to distributed decision making
- CASAVANT, KUHL
- 1990
(Show Context)
Citation Context ... [14]. Casavant developed a tool, called communicating finite automata, which is a combination of finite automata and directed graphs, to formally model the general behavior of distributed scheduling =-=[4]-=-. Stankovic addressed the issue of stability of distributed scheduling [22]. Among them, Cybenko's matrix iterative approach stands out as being most suited for analyzing the efficiency and terminatio... |

5 |
Load Balancing Algorithms in Loosely-Coupled Distributed Systems: A Survey
- Harget, Johnson
- 1990
(Show Context)
Citation Context ...tter results. With dynamic load balancing, workload may migrate from one processor to another during runtime. Detailed discussions and surveys of load balancing in distributed systems can be found in =-=[11, 3]-=-. In the past, numerous dynamic load balancing schemes with different characteristics have been proposed, such as the bidding algorithm [9, 21, 23], the drafting algorithm [18], and the gradientmodel ... |

4 |
The generalized dimension exchange method on some specific structures
- Xu, Lau
- 1992
(Show Context)
Citation Context ...sb (MR 2n ()) =sb (MT 2n 1 ;2n 2 ()) =sb (MC n ()) =sb (MM n 1 ;n 2 ()) (5) which is equal to 2\Gamma p 2(1\Gammacos(2��=n)) 1+cos(2��=n) . The complete detailed proof can be found in a relate=-=d paper [24]-=-. 4 Extension and Comparison with The Diffusion Scheme An obvious extension of the method is to relax the restriction of a single parameter and to allow different values of the exchange parameter to b... |

2 | N.: Probabilistic analysis of the optimal efficiency of the multi-level dynamic 449 | P a g e - Kimura, Ichiyosi - 1991 |

1 |
Load balancing for distributed memeory multiprocessors
- Cybenko
- 1989
(Show Context)
Citation Context ...two methods for dynamic load balancing, the diffusion method and the dimension exchange method, using matrix iterative approach, and derived a sufficient and necessary condition for their termination =-=[6, 2]-=-. Kimura and Ichiyoshi investigated the optimal efficiency of a multi-level schemes for OR-parallel programs using probablity theory [14]. Casavant developed a tool, called communicating finite automa... |

1 |
Circulant matrices
- David
- 1979
(Show Context)
Citation Context ... (MC 4 ()) is somewhere between 0.55 and 0.65; in the chain of 8 vertices,sb (MC 8 ()) is between 0.7 and 0.8. Furthermore, through closely analyzing these GDE matrices using block circulant matrices =-=[7], we deriv-=-ed the optimal exchange parameters for the "even" case of these structures and uncovered the relationships between their convergence rates. Suppose n 1 , n 2 are even, and n = maxfn 1 ; n 2 ... |

1 |
The distributed computing systems
- Faber
- 1973
(Show Context)
Citation Context ...of load balancing in distributed systems can be found in [11, 3]. In the past, numerous dynamic load balancing schemes with different characteristics have been proposed, such as the bidding algorithm =-=[9, 21, 23]-=-, the drafting algorithm [18], and the gradientmodel algorithm [16, 17]. Most of them were evaluated using simulation in which the performance of the proposed algorithm is dependent upon a number of p... |

1 |
Termination detection for synchronous parallel iterative computations
- Xu, Lau
(Show Context)
Citation Context ... load migration would take place in the second stage. To complement the GDE method, we have developed a fully distributed mechanism for the termination detection of load balancing based on the method =-=[25]-=-. We are also in the process of incorporating the GDE load balancing algorithm into remapping of data parallel computations [19]. Finally, we should point out that the GDE method is based on the assum... |