Euclidean Pathfinding with Compressed Path Databases

We consider optimal and anytime algorithms for the Euclidean Shortest Path Problem (ESPP) in two dimensions. Our approach leverages ideas from two recent works: Polyanya, a mesh-based ESPP planner which we use to represent and reason about the environment, and Compressed Path Databases, a speedup technique for pathfinding on grids and spatial networks, which we exploit to compute fast candidate paths. In a range of experiments and empirical comparisons we show that: (i) the auxiliary data structures required by the new method are cheap to build and store; (ii) for optimal search, the new algorithm is faster than a range of recent ESPP planners, with speedups ranging from several factors to over one order of magnitude; (iii) for anytime search, where feasible solutions are needed fast, we report even better runtimes.

A New Algorithm for Euclidean Shortest Path of Visiting Segments in a Polygon

Let s and t be two points on the boundary of a simple polygon, how to compute the Euclidean shortest path between s and t which visits a sequence of segments given in the simple polygon is the problem to be discussed, especially, the situation of the adjacent segments intersect is the focus of our study. In this paper, we first analyze the degeneration applying rubber-band algorithm to solve the problem. Then based on rubber-band algorithm, we present an improved algorithm which can solve the degeneration by the method of crossing over two segments to deal with intersection and in our algorithm the adjacent segments order can be changed when they intersect. Particularly, we have implemented the algorithm and have applied a large of test data to test it. The experiments demonstrate that our algorithm is correct and efficient, and it has the same time complexity as the rubber-band algorithm.

Approximate Euclidean Shortest Paths in 3-Space

Papadimitriou's approximation approach to the Euclidean shortest path (ESP) in 3-space is revisited. As this problem is NP-hard, his approach represents an important step towards practical algorithms. However, there are several gaps in the original description. Besides giving a complete treatment in the framework of bit complexity, we also improve on his subdivision method. Among the tools needed are root-separation bounds and nontrivial applications of Brent's complexity bounds on evaluation of elementary functions using floating point numbers.