Shortest Paths in Graphs of Convex Sets Article Swipe
Tobia Marcucci
,
Jack Umenberger
,
Pablo A. Parrilo
,
Russ Tedrake
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1137/22m1523790
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1137/22m1523790
Given a graph, the shortest-path problem requires finding a sequence of edges\nwith minimum cumulative length that connects a source vertex to a target\nvertex. We consider a variant of this classical problem in which the position\nof each vertex in the graph is a continuous decision variable constrained in a\nconvex set, and the length of an edge is a convex function of the position of\nits endpoints. Problems of this form arise naturally in many areas, from motion\nplanning of autonomous vehicles to optimal control of hybrid systems. The price\nfor such a wide applicability is the complexity of this problem, which is\neasily seen to be NP-hard. Our main contribution is a strong and lightweight\nmixed-integer convex formulation based on perspective operators, that makes it\npossible to efficiently find globally optimal paths in large graphs and in\nhigh-dimensional spaces.\n
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- article
- Language
- en
- Landing Page
- https://doi.org/10.1137/22m1523790
- OA Status
- green
- Cited By
- 44
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All OpenAlex metadata
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https://openalex.org/W3123076862Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1137/22m1523790Digital Object Identifier
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Shortest Paths in Graphs of Convex SetsWork title
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articleOpenAlex work type
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enPrimary language
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2024Year of publication
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2024-02-01Full publication date if available
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Tobia Marcucci, Jack Umenberger, Pablo A. Parrilo, Russ TedrakeList of authors in order
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https://doi.org/10.1137/22m1523790Publisher landing page
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2101.11565Direct OA link when available
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Mathematics, Combinatorics, Convex set, Shortest path problem, Convex analysis, Vertex (graph theory), Mathematical optimization, Discrete mathematics, Regular polygon, Convex optimization, Graph, GeometryTop concepts (fields/topics) attached by OpenAlex
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44Total citation count in OpenAlex
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2025: 23, 2024: 17, 2023: 2, 2021: 2Per-year citation counts (last 5 years)
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105Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| referenced_works_count | 105 |
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