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Is Prüfer Code Encoding Always a Bad Idea?

  • H. HildmannEmail author
  • D. Y. Atia
  • D. Ruta
  • A. F. Isakovic
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Part of the Studies in Computational Intelligence book series (SCI, volume 795)

Abstract

Real world problems are often of a complexity that renders deterministic approaches intractable. In the area of applied optimization, heuristics can offer a viable alternative. While potentially forfeiting on finding the most optimal solution, these techniques return good solutions in a short time. To do so, a suitable modelling of the problem as well as an efficient mapping of the problem’s solutions into a so-called solution space is required. Since it is very common to represent solutions as graphs, algorithms that efficiently map graphs into a heuristic-friendly solutions-space are of general interest to community. For a special type of graph, namely trees (i.e., undirected, connected and acyclic graphs such as Cayley in Phil Mag 13:172–176 (1857) [13]) Prüfer Code (Prüfer in Archiv der Mathematik und Physik 27:742–744 (1918) [43]) (PC) offers a bijective encoding process that comes at a low complexity (algorithms of \(\varTheta (n)\)-complexity are known Micikevičius et al. in Linear-time algorithms for encoding trees as sequences of node labels (2007) [37]) and facilitates mapping to \(n-2\) dimensional Euclidean space. However, this encoding does not preserve properties such as e.g., locality and has therefore been shown to be sub-optimal for entire classes of problems (Gottlieb et al. in Prüfer numbers: a poor representation of spanning trees for evolutionary search (2001) [24]). We argue that Prüfer Code does preserve some characterizing properties (e.g., degree of branching and branching vertices) and that these are sufficiently relevant for certain types of problems to motivate encoding them in PC. We present our investigations and provide an example problem where PC encoding worked very well.

Keywords

Encryption Code Branching Vertex Solution Space Branch Vertices Branching Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes

Acknowledgements

The authors are grateful for the support from the UAE ICT-Fund on the project “Biologically Inspired Network Services”. We acknowledge K. Poon (EBTIC, KUST) for bringing the I-DAS problem to our attention. HH acknowledges the hospitality of the EBTIC Institute and F. Saffre (EBTIC, KUST) during his fellowship 2017.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • H. Hildmann
    • 1
    Email author
  • D. Y. Atia
    • 2
  • D. Ruta
    • 3
  • A. F. Isakovic
    • 4
  1. 1.Dep. de Ingeniería de Sistemas y AutomáticaUniversidad Carlos III de Madrid (UC3M)LéganesSpain
  2. 2.Khalifa University of Science and TechnologyAbu DhabiUAE
  3. 3. EBTICKhalifa University of Science and TechnologyAbu DhabiUAE
  4. 4.Physics DepartmentKhalifa University of Science and TechnologyAbu DhabiUAE

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