### Abstract

The problem of scheduling task graphs on multiprocessor systems is known to be NP-complete in its general form as well as many restricted cases. Few polynomial algorithms have been developed for solving special cases of this problem when the communication cost is ignored. The complexity of the problem rises even further when communication among tasks is considered. Several different models have been used by researchers to compute the communication cost. The complexity of the problem changes based on which cost model is used to estimate the communication cost. Several versions of the scheduling problem with communication were proven to be NP-complete using different models [10, 11]. In this paper, we first survey the different communication models. Focusing on one of these models, we study the effect of considering communication on the relationship between the two-processor scheduling problem and the problem of finding maximum matching in the complement of the task graph. We introduce the idea of augmented task graphs and show that in some cases scheduling an augmented graph without considering communication is equivalent to scheduling the original task graph with communication. We show that the problem of scheduling an arbitrary task graph with communication on two processors can be reduced to the problem of constructing an augmented graph. We introduce a polynomial algorithm to optimally schedule a tree-structured task graph with communication on two processors by the construction of its augmented graph. We also prove the optimality of the introduced algorithm.

Original language | English (US) |
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Pages (from-to) | 177-191 |

Number of pages | 15 |

Journal | Parallel Algorithms and Applications |

Volume | 3 |

Issue number | 3-4 |

DOIs | |

State | Published - Jan 1 1994 |

### Keywords

- Augmented task graphs
- Communication models
- Maximum matching
- Parallel and distributed computers
- Scheduling algorithms
- Task graphs
- Tree-structured graphs
- Two-processor scheduling

### ASJC Scopus subject areas

- Computer Science(all)

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## Cite this

*Parallel Algorithms and Applications*,

*3*(3-4), 177-191. https://doi.org/10.1080/10637199408962536