Succinct Greedy Geometric Routing in the Euclidean Plane
نویسندگان
چکیده
We show that greedy geometric routing schemes exist for the Euclidean metric in R, for 3-connected planar graphs, with coordinates that can be represented succinctly, that is, with O(log n) bits, where n is the number of vertices in the graph.
منابع مشابه
Succinct Greedy Geometric Routing in R
In greedy geometric routing, messages are passed in a network embedded in a metric space according to the greedy strategy of always forwarding messages to nodes that are closer to the destination. In this paper, we study greedy geometric routing in R, using the standard Euclidean metric. Greedy geometric routing is not always possible in fixed-dimensional Euclidean spaces, of course, as is the ...
متن کاملSuccinct Greedy Graph Drawing in R
In greedy geometric routing, messages are passed in a network embedded in a metric space according to the greedy strategy of always forwarding messages to nodes that are closer to the destination. We show that greedy graph drawing schemes exist for the Euclidean metric in R, for 3-connected planar graphs, with coordinates that can be represented succinctly, that is, with O(log n) bits. Moreover...
متن کاملSuccinct Greedy Drawings May Be Unfeasible
A greedy drawing is a straight-line drawing that contains a distance-decreasing path for every pair of nodes. A path (v0, v1, . . . , vm) is distance-decreasing if d(vi, vm) < d(vi−1, vm), for i = 1, . . . ,m. Greedy drawings easily support geographic greedy routing. Hence, a natural and practical problem is the one of constructing greedy drawings in the plane, using few bits for representing v...
متن کاملSuccinct Greedy Graph Drawing in the Hyperbolic Plane
We describe an efficient method for drawing any n-vertex simple graph G in the hyperbolic plane. Our algorithm produces greedy drawings, which support greedy geometric routing, so that a message M between any pair of vertices may be routed geometrically, simply by having each vertex that receives M pass it along to any neighbor that is closer in the hyperbolic metric to the message’s eventual d...
متن کاملSpatial Analysis in curved spaces with Non-Euclidean Geometry
The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...
متن کامل