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
Nearby in the stack
to multi-target scenarios by developing two specialised heuristic functions: the
Intervalheuristic
hv
and the
Targetheuristic
ht
. Though these methods outperform visibility graph algorithms by orders of magnitude in all our experiments they are not robust:
hv
expands many redundant nodes when the set of neighbours is small while
ht
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.