Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Computer Networks
Geographic routing without location information
Proceedings of the 9th annual international conference on Mobile computing and networking
Topological hole detection in wireless sensor networks and its applications
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
On a conjecture related to geometric routing
Theoretical Computer Science - Algorithmic aspects of wireless sensor networks
Convex Drawings of 3-Connected Plane Graphs
Algorithmica
Distributed computation of virtual coordinates
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
A Distributed Geometric Routing Algorithm for Ad HocWireless Networks
ITNG '07 Proceedings of the International Conference on Information Technology
Schnyder Woods and Orthogonal Surfaces
Discrete & Computational Geometry
Schnyder Woods for Higher Genus Triangulated Surfaces, with Applications to Encoding
Discrete & Computational Geometry - Special Issue: 24th Annual Symposium on Computational Geometry
Succinct Greedy Geometric Routing in the Euclidean Plane
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Greedy Drawings of Triangulations
Discrete & Computational Geometry
On the efficiency of a local iterative algorithm to compute Delaunay realizations
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Some Results on Greedy Embeddings in Metric Spaces
Discrete & Computational Geometry
A generalized greedy routing algorithm for 2-connected graphs
Theoretical Computer Science
Distributed computation of virtual coordinates for greedy routing in sensor networks
Discrete Applied Mathematics
On succinct convex greedy drawing of 3-connected plane graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Succinct greedy drawings do not always exist
GD'09 Proceedings of the 17th international conference on Graph Drawing
Hi-index | 5.23 |
Geometric routing is an elegant way for solving network routing problems. The essence of this routing scheme is the following: When an origin vertex u wants to send a message to a destination vertex w, it forwards the message to a neighbor t, solely based on the location information of u,w and the neighbors of u. In its simplest form, greedy routing, a message is simply forwarded to a neighbor that is closer to the destination. A greedy drawing of a graph G is an embedding of G for which the greedy routing algorithm works. Recently, Leighton and Moitra (2010) [18] found an algorithm that produces an embedding of any 3-connected planar graph in R^2 that supports greedy routing. A similar result was independently found by Angelini et al. (2010) [2]. One main drawback of these algorithms is that they need @W(nlogn) bits to represent the coordinates of the vertex locations. This is the same space usage as traditional routing table approaches, and hence makes greedy routing infeasible in applications. In the greedy routing scheme, the routing decision is based on decreasing distances between vertex locations. For this idea to work, however, the routing decision does not have to be based on decreasing distances. As long as the routing decision is solely based on the location information of the source, the destination, and the neighbors of the source, the geometric routing scheme will work fine. In this paper, we introduce a new model of geometric routing. Instead of relying on decreasing distance for routing decisions, our algorithm uses other criterion to determine the routing path, solely based on location information. Our routing algorithms are based on Schnyder coordinates which are derived from Schnyder realizers for plane triangulations and Schnyder woods for 3-connected plane graphs. The coordinates of vertex locations consist of three integers between 0 and 2n, hence the representation only needs O(logn) bits. In order to send a message from the origin u to the destination w, our routing algorithm determines the routing path from the Schnyder coordinates of u, w and all neighbors of u. The algorithms are natural and simple to implement.