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Let S be a subdivision of the plane into polygonal regions, where each region has an associated positive weight. The weighted region shortest path problem is to determine a shortest path in S between two points s, t ∈ R 2 , where the distances are measured according to the weighted Euclidean metric—the length of a path is defined to be the weighted sum of… (More)

- Prosenjit Bose, Kai Dannies, Jean-Lou De Carufel, Christoph Doell, Carsten Grimm, Anil Maheshwari +2 others
- JoCG
- 2013

Consider the continuum of points along the edges of a network, i.e., an undirected graph with positive edge weights. We measure distance between these points in terms of the shortest path distance along the network, known as the network distance. Within this metric space, we study farthest points. We introduce network farthest-point diagrams, which capture… (More)

Consider the continuum of points on 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 weighted shortest path distance, called the network distance. Within this metric space, we study farthest points and farthest distances. We introduce optimal data structures… (More)

Consider the continuum of points along the edges of a network, an embedded undirected graph with positive edge weights. Distance between these points can be measured as shortest path distance along the edges of the network. We introduce two new concepts to capture farthest-point information in this metric space. The first, eccentricity diagrams, are used to… (More)

We seek to augment a geometric network in the Euclidean plane with shortcuts to minimize its continuous diameter, i.e., the largest network distance between any two points on the augmented network. Unlike in the discrete setting where a shortcut connects two vertices and the diameter is measured between vertices, we take all points along the edges of the… (More)

We seek to perform efficient queries for the predecessor among n values stored in k sorted arrays. Evading the Ω(n log k) lower bound from merging k arrays, we support predecessor queries in O(log n) time after O(n log(k log n)) construction time. By applying Ben-Or's technique, we establish that this is optimal for strict predecessor queries, i.e., every… (More)

- Carsten Grimm
- WG
- 2015

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 weighted shortest path distance, called the network distance. Within this metric space, we study farthest points and farthest distances. We introduce a data structure… (More)

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