The Order/degree Problem Competition

Find a graph that has smallest diameter & average shortest path length given an order and a degree.

- 2017-03-06: The 2017 competition opens!

Update 2017-03-06

Will be announced after 2017-06-26. Show baseline

Order | Degree | Length | Diameter | ASPL | ASPL Gap | |
---|---|---|---|---|---|---|

32 | 5 | 4 | 2.280 | 12.202% | list | |

256 | 18 | 3 | 2.188 | 13.407% | list | |

576 | 30 | 3 | 2.141 | 9.920% | list | |

1344 | 30 | 3 | 2.483 | 7.586% | list | |

4896 | 24 | 4 | 2.949 | 2.486% | list | |

9344 | 10 | 6 | 4.311 | 7.422% | list | |

88128 | 12 | 7 | 4.911 | 2.724% | list | |

98304 | 10 | 7 | 5.383 | 4.410% | list | |

100000 | 32 | 5 | 3.717 | 1.240% | list | |

100000 | 64 | 4 | 3.035 | 2.580% | list | |

16 | 3 | 2 | 9 | 3.792 | 72.348% | list |

256 | 3 | 3 | 22 | 8.583 | 53.596% | list |

256 | 3 | 4 | 18 | 7.890 | 41.194% | list |

256 | 3 | 15 | 13 | 6.274 | 12.275% | list |

256 | 6 | 3 | 13 | 5.319 | 71.254% | list |

256 | 6 | 4 | 10 | 4.550 | 46.480% | list |

256 | 6 | 15 | 5 | 3.396 | 9.356% | list |

256 | 15 | 3 | 10 | 4.199 | 103.938% | list |

256 | 15 | 4 | 8 | 3.465 | 68.298% | list |

256 | 15 | 15 | 4 | 2.374 | 15.290% | list |

10000 | 3 | 6 | 59 | 23.753 | 120.449% | list |

10000 | 3 | 18 | 26 | 13.147 | 22.017% | list |

10000 | 3 | 33 | 19 | 11.677 | 8.367% | list |

10000 | 9 | 6 | 36 | 13.570 | 208.503% | list |

10000 | 9 | 18 | 14 | 6.175 | 40.384% | list |

10000 | 9 | 33 | 9 | 4.924 | 11.937% | list |

10000 | 28 | 6 | 34 | 11.826 | 305.154% | list |

10000 | 28 | 18 | 12 | 4.821 | 65.188% | list |

10000 | 28 | 33 | 7 | 3.534 | 21.067% | list |

Graph design has a rich variety of application fields of computer systems. In particular, it is just meeting a network design of future supercomputers and future high-end datacenters in terms of hop counts, since their networks are topologically modeled as undirected regular graphs. Low latency is preconditioned on small hop counts, but existing network topologies have hop counts much larger than theoretical lower bounds. Therefore, computer network designers desire to find a graph that has a small number of hops between any pair of nodes. How to minimize the diameter and the average shortest path length (ASPL) of a graph given the order (the number of nodes) and the degree (the number of edges at each node)?

Graph Golf is an international competition of the order/degree problem since 2015. It is conducted with the goal of making a catalog of smallest-diameter graphs for every order/degree pair. Anyone in the world can take part in the competition by submitting a graph. Outstanding authors were awarded in CANDAR'17, an international conference held in Aomori, Japan, in November 2017.

You're welcome! Go to the submission page and follow the instructions.