Constant-Work-Space Algorithms for Shortest Paths in Trees and Simple Polygons

Constant-Work-Space Algorithms for Shortest Paths in Trees and Simple Polygons

Constant-work-space algorithms model computation when space is at a premium: the input is given as a read-only array that allows random access to its entries, and the algorithm may use constantly many additional registers of O(logn) bits each, where n denotes the input size. We present such algorithms for two restricted variants of the shortest path problem. First, we describe how to report a s...

Shortest paths in convex and simple weighted polygons

Single-Point Visibility Constraint Minimum Link Paths in Simple Polygons

We address the following problem: Given a simple polygon $P$ with $n$ vertices and two points $s$ and $t$ inside it, find a minimum link path between them such that a given target point $q$ is visible from at least one point on the path. The method is based on partitioning a portion of $P$ into a number of faces of equal link distance from a source point. This partitioning is essentially a shor...

Shortest paths in simple polygons with polygon-meet constraints

We study a constrained version of the shortest path problem in simple polygons, in which the path must visit a given target polygon. We provide a worst-case optimal algorithm for this problem and also present a method to construct a subdivision of the simple polygon to efficiently answer queries to retrieve the shortest polygon-meeting paths from a single-source to the query point. The algorith...

Query-point visibility constrained shortest paths in simple polygons

In this paper, we study the problem of finding the shortest path between two points inside a simple polygon such that there is at least one point on the path fromwhich a query point is visible. We provide an algorithmwhich preprocesses the input in O(n2+nK ) time and space and provides logarithmic query time. The input polygon has n vertices and K is a parameter dependent on the input polygon w...