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A Coalgebraic Dijkstra Algorithm (Invited Talk)

Authors Takahiro Sanada , Yoàv Montacute , Kittiphon Phalakarn , Ichiro Hasuo

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Subject Classification

ACM Subject Classification
  • Theory of computation → Shortest paths
Keywords
  • Coalgebra
  • Greatest fixed point
  • Dijkstra’s algorithm
  • Shortest path

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Abstract

The Dijkstra algorithm is a classical method for solving the shortest path problem on weighted graphs. There are several variations of the Dijkstra algorithm, including algorithms for the widest path problem and for two-player games. In this paper, we introduce the coalgebraic shortest path problem (CSPP), a unifying framework for a broad class of optimization problems on state-transition systems. This framework encompasses not only the aforementioned problems but also new ones such as the shortest binary tree problem. We further present a coalgebraic Dijkstra algorithm for solving the CSPP efficiently under a suitable condition. Our condition is necessary and sufficient for the algorithm to return correct solutions, thereby providing a precise criterion for when Dijkstra-style acceleration is possible. We also show that the proposed algorithm achieves asymptotic complexity comparable to that of the classical Dijkstra algorithm.

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Takahiro Sanada, Yoàv Montacute, Kittiphon Phalakarn, and Ichiro Hasuo. A Coalgebraic Dijkstra Algorithm (Invited Talk). In 37th International Conference on Concurrency Theory (CONCUR 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 391, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CONCUR.2026.5

Author Details

Takahiro Sanada
  • Fukui Prefectural University, Japan
Yoàv Montacute
  • National Institute of Informatics, Tokyo, Japan
Kittiphon Phalakarn
  • National Institute of Informatics, Tokyo, Japan
Ichiro Hasuo
  • National Institute of Informatics, Tokyo, Japan
  • SOKENDAI (The Graduate University for Advanced Studies), Kanagawa, Japan
  • Imiron Co., Ltd., Tokyo, Japan

Funding

The authors are supported by JST ASPIRE Grant No. JPMJAP2301.
  • Sanada, Takahiro: Supported by JSPS KAKENHI Grant No. JP24K23867.
  • Montacute, Yoàv: Supported by JST ACT-X Grant No. JPMJAX24CR.

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