DeepAI AI Chat
Log In Sign Up

Computing a rectilinear shortest path amid splinegons in plane

by   Tameem Choudhury, et al.
iit guwahati

We reduce the problem of computing a rectilinear shortest path between two given points s and t in the splinegonal domain to the problem of computing a rectilinear shortest path between two points in the polygonal domain. As part of this, we define a polygonal domain from and transform a rectilinear shortest path computed in to a path between s and t amid splinegon obstacles in . When comprises of h pairwise disjoint splinegons with a total of n vertices, excluding the time to compute a rectilinear shortest path amid polygons in , our reduction algorithm takes O(n + h n) time. For the special case of comprising of concave-in splinegons, we have devised another algorithm in which the reduction procedure does not rely on the structures used in the algorithm to compute a rectilinear shortest path in polygonal domain. As part of these, we have characterized few of the properties of rectilinear shortest paths amid splinegons which could be of independent interest.


page 1

page 2

page 3

page 4


Shortest Paths Among Obstacles in the Plane Revisited

Given a set of pairwise disjoint polygonal obstacles in the plane, findi...

On approximating shortest paths in weighted triangular tessellations

We study the quality of weighted shortest paths when a continuous 2-dime...

Improved Shortest Path Maps with GPU Shaders

We present in this paper several improvements for computing shortest pat...

Shortest Paths in Portalgons

Any surface that is intrinsically polyhedral can be represented by a col...

Bounded Dijkstra (BD): Search Space Reduction for Expediting Shortest Path Subroutines

The shortest path (SP) and shortest paths tree (SPT) problems arise both...

Shortest Paths on Cubes

In 1903, noted puzzle-maker Henry Dudeney published The Spider and the F...

A* shortest string decoding for non-idempotent semirings

The single shortest path algorithm is undefined for weighted finite-stat...