Evolving labelings of graceful graphs

Luke Branson, Andrew M. Sutton

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publicationGECCO 2022 - Proceedings of the 2022 Genetic and Evolutionary Computation Conference
PublisherAssociation for Computing Machinery, Inc
Pages195-203
Number of pages9
ISBN (Electronic)9781450392372
DOIs
StatePublished - Jul 8 2022
Event2022 Genetic and Evolutionary Computation Conference, GECCO 2022 - Virtual, Online, United States
Duration: Jul 9 2022Jul 13 2022

Publication series

NameGECCO 2022 - Proceedings of the 2022 Genetic and Evolutionary Computation Conference

Conference

Conference2022 Genetic and Evolutionary Computation Conference, GECCO 2022
Country/TerritoryUnited States
CityVirtual, Online
Period7/9/227/13/22

Bibliographical note

Publisher Copyright:
© 2022 ACM.

Keywords

  • Combinatorial optimization
  • graph labeling
  • runtime analysis

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