The Open Algebraic Path Problem Article Swipe

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Path (computing) Algebraic number Mathematics Algebra over a field Computer science Pure mathematics Mathematical analysis Programming language

Jade Master ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.4230/lipics.calco.2021.20 · OA: W3024851999

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.