Reducing Redundant Work in Jump Point Search

JPS (Jump Point Search) is a state-of-the-art optimal algorithm for online grid-based pathfinding. Widely used in games and other navigation scenarios, JPS nevertheless can exhibit pathological behaviours which are not well studied: (i) it may repeatedly scan the same area of the map to find successors; (ii) it may generate and expand suboptimal search nodes. In this work, we examine the source of these pathological behaviours, show how they can occur in practice, and propose a purely online approach, called Constrained JPS (CJPS), to tackle them efficiently. Experimental results show that CJPS has low overheads and is often faster than JPS in dynamically changing grid environments: by up to 7x in large game maps and up to 14x in pathological scenarios.

Faster and More Robust Mesh-based Algorithms for Obstacle k-Nearest Neighbour

We are interested in the problem of finding $k$ nearest neighbours in the plane and in the presence of polygonal obstacles ($\textit{OkNN}$). 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 $\mathbf{Polyanya}$, 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 $\mathbf{Polyanya}$ to multi-target scenarios by developing two specialised heuristic functions: the $\mathbf{Interval heuristic}$ $h_v$ and the $\mathbf{Target heuristic}$ $h_t$. 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.