Randomly removing g handles at once

It was shown in [11] that any orientable graph of genus g can be probabilistically embedded into a graph of genus g − 1 with constant distortion. Removing handles one by one gives an embedding into a distribution over planar graphs with distortion 2O(g) . By removing all g handles at once, we present a probabilistic embedding with distortion O(g2 ) for both orientable and non-orientable graphs. Our result is obtained by showing that the minimum-cut graph of [6] has low dilation, and then randomly cutting this graph out of the surface using the Peeling Lemma from [13]. Categories and Subject Descriptors F.2 [Analysis of Algorithms and Problem Complexity]: General General Terms Algorithms Theory Keywords Embeddings, Probablistic Approximation, Bounded Genus Graphs, Planar Graphs

• Type: Conference
• Year: 2009
• Where: COMPGEOM
• Authors: Glencora Borradaile, James R. Lee, Anastasios Sidiropoulos
• Keywords: COMPGEOM 2009, Constant Distortion, Discrete Geometry, Orientable Graph, Planar Graphs