Computational geometry: an introduction
Computational geometry: an introduction
Art gallery theorems and algorithms
Art gallery theorems and algorithms
Optimal shortest path queries in a simple polygon
SCG '87 Proceedings of the third annual symposium on Computational geometry
Handbook of algorithms and data structures: in Pascal and C (2nd ed.)
Handbook of algorithms and data structures: in Pascal and C (2nd ed.)
Computational geometry in C
Computing minimum length paths of a given homotopy class
Computational Geometry: Theory and Applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Handbook of computational geometry
Handbook of computational geometry
Computing Homotopic Shortest Paths Efficiently
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Computing homotopic shortest paths in the plane
Journal of Algorithms
2D and 3D visibility in discrete geometry: an application to discrete geodesic paths
Pattern Recognition Letters - Special issue: Discrete geometry for computer imagery (DGCI'2002)
Gathering of asynchronous robots with limited visibility
Theoretical Computer Science
Planning Algorithms
Optimal paths for mutually visible agents
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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As computer controlled entities are set to move and explore more complex environments they need to be able to perform navigation tasks, like finding minimal cost routes. Much work has been done on this problem with a single entity in a continuous environment. However these entities may be in teams and their actions may be constrained by the need to consider the actions of other entities. We consider the case of two entities wishing to reach their destinations while travelling the minimum distance and remaining in sight of each other. A version of this problem in continuous space has been addressed previously; however, the problem of minimum length paths does not only exist in continuous space. Robots may have restricted orientations in movement. Also, domains such as circuit design and computer games require discrete movements and restricted orientation. The restricted orientation and the fact that (even in genus zero environments) minimal length paths may not be unique present some challenges. This paper investigates the problem of two entities in a discrete setting, moving to preserve visibility and provides algorithms for computing schedules that minimise the total distance travelled.