Faster and More Robust Mesh-based Algorithms for Obstacle k-Nearest Neighbour
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We are interested in the problem of finding k nearest neighbours in the plane and in the presence of polygonal obstacles (OkNN). Widely used algorithms for OkNN are based on incremental visibility graphs, which means they require costly and online visibility checking and have worst-case quadratic running time. Recently Polyanya, a fast point-to-point pathfinding algorithm was proposed which avoids the disadvantages of visibility graphs by searching over an alternative data structure known as a navigation mesh. Previously, we adapted Polyanya to multi-target scenarios by developing two specialised heuristic functions: the Interval heuristic h_v and the Target heuristic h_t. Though these methods outperform visibility graph algorithms by orders of magnitude in all our experiments they are not robust: h_v expands many redundant nodes when the set of neighbours is small while h_t performs poorly when the set of neighbours is large. In this paper, we propose new algorithms and heuristics for OkNN which perform well regardless of neighbour density.
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