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A Polyhedral Perspective on Tropical Convolutions

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Part of the Lecture Notes in Computer Science book series (LNCS,volume 13889)


Tropical (or min-plus) convolution is a well-studied algorithmic primitive in fine-grained complexity. We exhibit a novel connection between polyhedral formulations and tropical convolution, through which we arrive at a dual variant of tropical convolution. We show this dual operation to be equivalent to primal convolutions. This leads us to considering the geometric objects that arise from dual tropical convolution as a new approach to algorithms and lower bounds for tropical convolutions. In particular, we initiate the study of their extended formulations.

C. Brand was supported by the Austrian Science Fund (FWF, Project Y1329: ParAI). M. Koutecký was partially supported by Charles University project UNCE/SCI/004 and by the project 22-22997S of GA ČR. A. Lassota was supported by the Swiss National Science Foundation within the project Complexity of integer Programming (207365).

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Correspondence to Cornelius Brand .

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Brand, C., Koutecký, M., Lassota, A. (2023). A Polyhedral Perspective on Tropical Convolutions. In: Hsieh, SY., Hung, LJ., Lee, CW. (eds) Combinatorial Algorithms. IWOCA 2023. Lecture Notes in Computer Science, vol 13889. Springer, Cham.

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