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The Open Algebraic Path Problem

Author Jade Master

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Jade Master
  • Department of Mathematics, University of California, Riverside, CA, USA

Acknowledgements

I would like to thank Mike Shulman, John Baez, Christian Williams, Joe Moeller, Rany Tith, Sarah Rovner-Frydman, Zans Mihejez, Oscar Hernandez, Alex Pokorny and Todd Trimble for their helpful comments and contributions. I would also like to thank everyone in my life who supported me during this time. Your work contributed to this paper as well. This paper was written on Tongva land.

Cite As Get BibTex

Jade Master. The Open Algebraic Path Problem. In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.CALCO.2021.20

Abstract

The algebraic path problem provides a general setting for shortest path algorithms in optimization and computer science. We explain the universal property of solutions to the algebraic path problem by constructing a left adjoint functor whose values are given by these solutions. This paper extends the algebraic path problem to networks equipped with input and output boundaries. We show that the algebraic path problem is functorial as a mapping from a double category whose horizontal composition is gluing of open networks. We introduce functional open matrices, for which the functoriality of the algebraic path problem has a more practical expression.

Subject Classification

ACM Subject Classification
  • Theory of computation → Categorical semantics
  • Theory of computation → Operational semantics
Keywords
  • The Algebraic Path Problem
  • Open Systems
  • Shortest Paths
  • Categorical Semantics
  • Compositionality

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