### Abstract

There is given a graph, that models a communication network of a multiprocessor system, and there are tokens (jobs) allocated to nodes of the graph. The task is to distribute the tokens evenly, subject to the constraint that they may be moved only along the edges of the graph. The cost of a distribution strategy is measured as the total number of operations of moving a token along an edge. An algorithm for general graphs is developed, by reduction to a maximum-flow minimum-cost problem, that finds a cost-optimal distribution strategy, given a graph and an initial token allocation. The main result is an algorithm for graphs that are lines of nodes; it finds the distribution strategy in time O(n), for a line of n nodes.

Original language | English (US) |
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Pages (from-to) | 313-328 |

Number of pages | 16 |

Journal | Fundamenta Informaticae |

Volume | 32 |

Issue number | 3-4 |

DOIs | |

State | Published - Jan 1 1997 |

Externally published | Yes |

### Keywords

- Graph
- Line of nodes
- Optimal distribution
- Token

### ASJC Scopus subject areas

- Theoretical Computer Science
- Algebra and Number Theory
- Information Systems
- Computational Theory and Mathematics

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## Cite this

*Fundamenta Informaticae*,

*32*(3-4), 313-328. https://doi.org/10.3233/FI-1997-323406