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**1 - 2**of**2**### 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 L G 1 (p, q)/L1(p, q), where L G 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 log ..."

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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 L G 1 (p, q)/L1(p, q), where L G 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 log 2 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. 1