### Abstract

We study a distributed load balancing problem on arbitrary graphs. First Order (F0) and Second Order (SD) schemes are popular local diffusive schedules for this problem. To use them, several parameters have to be chosen carefully. Determining the "optimal" parameters analytically is difficult, and on a practical level, despite the widespread use of these schemes, little is known on how relevant parameters must be set. We employ systematic experiments to engineer the choice of relevant parameters in first and second order schemes. We present a centralized polynomial time algorithm for choosing the "optimal" F0 scheme based on sere[definite programming. Based on the empirical evidence from our implementation of this algorithm, we pose conjectures on the closed-form solution of optimal F0 schemes for various graphs. We also present a heuristic algorithm to locally estimate relevant parameters in the F0 and S0 schemes; our estimates are fairly accurate compared to those based on expensive global communication. Finally, we show that the F0 and S0 schemes that use approximate values rather than the optimal parameters, can be improved using a new iterative scheme that we introduce here; this scheme is of independent interest. The software we have developed for our implementations is available freely, and can serve as a platform for experimental research in this area. Our methods are being included in Paderborn, the Paderborn Finite Element Library [1].

Original language | English (US) |
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Title of host publication | Solving Irregularly Structured Problems in Parallel - 4th International Symposium, IRREGULAR 1997, Proceedings |

Editors | Reinhard Luling, Gianfranco Bilardi, Afonso Ferreira, Gianfranco Bilardi, Jose Rolim |

Publisher | Springer-Verlag |

Pages | 111-122 |

Number of pages | 12 |

ISBN (Print) | 3540631380, 9783540631385 |

State | Published - Jan 1 1997 |

Event | 4th International Symposium on Solving Irregularly Structured Problems in Parallel, IRREGULAR 1997 - Paderborn, Germany Duration: Jun 12 1997 → Jun 13 1997 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1253 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 4th International Symposium on Solving Irregularly Structured Problems in Parallel, IRREGULAR 1997 |
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Country | Germany |

City | Paderborn |

Period | 6/12/97 → 6/13/97 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Solving Irregularly Structured Problems in Parallel - 4th International Symposium, IRREGULAR 1997, Proceedings*(pp. 111-122). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1253). Springer-Verlag.

**Engineering diffusive load balancing algorithms using experiments.** / Diekmann, Ralf; Muthukrishnan, Shanmugavelayutham; Nayakkankuppam, Madhu V.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Solving Irregularly Structured Problems in Parallel - 4th International Symposium, IRREGULAR 1997, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1253, Springer-Verlag, pp. 111-122, 4th International Symposium on Solving Irregularly Structured Problems in Parallel, IRREGULAR 1997, Paderborn, Germany, 6/12/97.

}

TY - GEN

T1 - Engineering diffusive load balancing algorithms using experiments

AU - Diekmann, Ralf

AU - Muthukrishnan, Shanmugavelayutham

AU - Nayakkankuppam, Madhu V.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - We study a distributed load balancing problem on arbitrary graphs. First Order (F0) and Second Order (SD) schemes are popular local diffusive schedules for this problem. To use them, several parameters have to be chosen carefully. Determining the "optimal" parameters analytically is difficult, and on a practical level, despite the widespread use of these schemes, little is known on how relevant parameters must be set. We employ systematic experiments to engineer the choice of relevant parameters in first and second order schemes. We present a centralized polynomial time algorithm for choosing the "optimal" F0 scheme based on sere[definite programming. Based on the empirical evidence from our implementation of this algorithm, we pose conjectures on the closed-form solution of optimal F0 schemes for various graphs. We also present a heuristic algorithm to locally estimate relevant parameters in the F0 and S0 schemes; our estimates are fairly accurate compared to those based on expensive global communication. Finally, we show that the F0 and S0 schemes that use approximate values rather than the optimal parameters, can be improved using a new iterative scheme that we introduce here; this scheme is of independent interest. The software we have developed for our implementations is available freely, and can serve as a platform for experimental research in this area. Our methods are being included in Paderborn, the Paderborn Finite Element Library [1].

AB - We study a distributed load balancing problem on arbitrary graphs. First Order (F0) and Second Order (SD) schemes are popular local diffusive schedules for this problem. To use them, several parameters have to be chosen carefully. Determining the "optimal" parameters analytically is difficult, and on a practical level, despite the widespread use of these schemes, little is known on how relevant parameters must be set. We employ systematic experiments to engineer the choice of relevant parameters in first and second order schemes. We present a centralized polynomial time algorithm for choosing the "optimal" F0 scheme based on sere[definite programming. Based on the empirical evidence from our implementation of this algorithm, we pose conjectures on the closed-form solution of optimal F0 schemes for various graphs. We also present a heuristic algorithm to locally estimate relevant parameters in the F0 and S0 schemes; our estimates are fairly accurate compared to those based on expensive global communication. Finally, we show that the F0 and S0 schemes that use approximate values rather than the optimal parameters, can be improved using a new iterative scheme that we introduce here; this scheme is of independent interest. The software we have developed for our implementations is available freely, and can serve as a platform for experimental research in this area. Our methods are being included in Paderborn, the Paderborn Finite Element Library [1].

UR - http://www.scopus.com/inward/record.url?scp=84947796534&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84947796534&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84947796534

SN - 3540631380

SN - 9783540631385

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 111

EP - 122

BT - Solving Irregularly Structured Problems in Parallel - 4th International Symposium, IRREGULAR 1997, Proceedings

A2 - Luling, Reinhard

A2 - Bilardi, Gianfranco

A2 - Ferreira, Afonso

A2 - Bilardi, Gianfranco

A2 - Rolim, Jose

PB - Springer-Verlag

ER -