2026-07-30T21:42:18Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:15375 2024-03-06T10:55:15Z ddc:004 open_access

The Open Algebraic Path Problem Master, Jade The Algebraic Path Problem Open Systems Shortest Paths Categorical Semantics Compositionality 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jade Master 2021 Is Part Of LIPIcs, Volume 211, 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CALCO.2021.20 urn:nbn:de:0030-drops-153754 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.20 eng https://creativecommons.org/licenses/by/4.0/legalcode