## Abstract

A graceful labeling of a graph G = (V, E) is an assignment of labels to the vertices V of G subject to constraints arising from the structure of the graph. A graph is called graceful if it admits a graceful labeling. As a combinatorial problem, it has applications in coding theory, communications networks, and optimizing circuit layouts. Several different approaches, both heuristic and complete, for finding graceful labelings have been developed and analyzed empirically. Most such algorithms have been established in the context of verifying the conjecture that trees are graceful. In this paper, we present the first rigorous running time analysis of a simple evolutionary algorithm applied to finding labelings of graceful graphs. We prove that an evolutionary algorithm can find a graceful labeling in polynomial time for all paths, stars, and complete bipartite graphs with a constant-sized partition. We also empirically compare the running time of a simple evolutionary algorithm against a complete constraint solver.

Original language | English (US) |
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Title of host publication | GECCO 2022 - Proceedings of the 2022 Genetic and Evolutionary Computation Conference |

Publisher | Association for Computing Machinery, Inc |

Pages | 195-203 |

Number of pages | 9 |

ISBN (Electronic) | 9781450392372 |

DOIs | |

State | Published - Jul 8 2022 |

Event | 2022 Genetic and Evolutionary Computation Conference, GECCO 2022 - Virtual, Online, United States Duration: Jul 9 2022 → Jul 13 2022 |

### Publication series

Name | GECCO 2022 - Proceedings of the 2022 Genetic and Evolutionary Computation Conference |
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### Conference

Conference | 2022 Genetic and Evolutionary Computation Conference, GECCO 2022 |
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Country/Territory | United States |

City | Virtual, Online |

Period | 7/9/22 → 7/13/22 |

### Bibliographical note

Publisher Copyright:© 2022 ACM.

## Keywords

- Combinatorial optimization
- graph labeling
- runtime analysis