On Two Problems Regarding Farthest Distances in Continuous Networks

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  • Consider the continuum of points along the edges of a network, i.e., a connected, undirected graph with positive edge weights. We measure the distance between these points in terms of the network distance, i.e., the weighted shortest path distance. The continuous diameter of a network is the largest network distance between any two points on the network. We study two intertwined problems within this metric space: The first problem is to minimize the continuous diameter of a geometric network by introducing one or more shortcuts that may connect any two points along the network. The second problem is to develop efficient data structures that support queries for the farthest points from a query point along a network.

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  • Copyright © 2018 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
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  • 2018


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