Computing the Stretch Factor of Paths, Trees, and Cycles in Weighted Fixed Orientation Metrics

Let G be a graph embedded in the L1-plane. The stretch factor of G is the maximum over all pairs of distinct vertices p and q of G of the ratio LG 1 (p, q)/L1(p, q), where LG 1 (p, q) is the L1-distance in G between p and q. We show how to compute the stretch factor of an n-vertex path in O(n log2 n) worst-case time and O(n) space and we mention generalizations to trees and cycles, to general weighted fixed orientation metrics, and to higher dimensions.

• Type: Conference
• Year: 2008
• Where: CCCG
• Authors: Christian Wulff-Nilsen
• Keywords: CCCG 2008, Computational Geometry, Distinct Vertices, Ratio Lg, Stretch Factor