Paper Info
Title
A Search Algorithm for Simplicial Complexes.
Abstract
We present the `Basic S*u0027 algorithm for computing shortest path through a metric simplicial complex. In particular, given a metric graph, $G$, which is constructed as a discrete representation of an underlying configuration space (a larger space/manifold typically of dimension greater than one), we consider the Rips complex, $mathcal{R}(G)$, associated with it. Such a complex, and hence shortest paths in it, represent the underlying metric space more closely than what the graph does. While discrete graph representations of continuous spaces is convenient for motion planning in configuration spaces of robotic systems, the metric induced in them by the ambient configuration space is significantly different from the metric of the configuration space itself. We remedy this problem using the simplicial complex representation. Our algorithm requires only an abstract graph, $G=(V,E)$, and a cost/length function, $d:Erightarrow mathbb{R}_+$, as inputs, and no global information such as an embedding or a global coordinate chart is required. The complexity of the Basic S* algorithm is comparable to that of Dijkstrau0027s search, but, as the results presented in this paper demonstrate, the shortest paths obtained using the proposed algorithm represent/approximate the geodesic paths in the original metric space significantly more closely.
Year
Venue
Field
2016
arXiv: Discrete Mathematics
Discrete mathematics,Any-angle path planning,Fisher information metric,Combinatorics,Convex metric space,Metric (mathematics),Intrinsic metric,Word metric,Metric space,Mathematics,Injective metric space
DocType
Volume
Citations 
Journal
abs/1607.07009
0
PageRank 
References 
Authors
0.34
13
1
Name
Order
Citations
PageRank
Subhrajit Bhattacharya146236.93