ICS Theory Group

October 17, Fall 2008: Theory Seminar

1:00pm in 253 ICS

Succinct Greedy Graph Drawing in the Hyperbolic Plane

Prof. Michael Goodrich, UC Irvine

Abstract: 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 destination. More importantly, for networking applications, our algorithm produces succinct drawings, in that each of the vertex positions in one of our embeddings can be represented using O(log n) bits and the calculation of which neighbor to send a message to may be performed efficiently using these representations. These properties are useful, for example, for routing in sensor networks, where storage and bandwidth are limited.

Joint work with David Eppstein.