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- Mark Lanthier, Anil Maheshwari, Jörg-Rüdiger Sack
- Symposium on Computational Geometry
- 1997

Mark Lanthier, Anil Maheshwari and Jorg-Rudiger Sack School of Computer Science Carleton University 1125 Colonel By Drive Ottawa, ON, CANADA KIS 5B6 E-mail: {lanthier,maheshwa, sack} @scs.carleton.ca Consider a simple polyhedron T, possibly non-convex, composed of n triangular regions (faces), in which each region has an associated positive weight. The cost… (More)

- Lyudmil Aleksandrov, Anil Maheshwari, Jörg-Rüdiger Sack
- J. ACM
- 2005

In this article, we present an approximation algorithm for solving the single source shortest paths problem on weighted polyhedral surfaces. We consider a polyhedral surface <i>P</i> as consisting of <i>n</i> triangular faces, where each face has an associated positive weight. The cost of travel through a face is the Euclidean distance traveled, multiplied… (More)

We consider the classical geometric problem of determining a shortest path through a weighted domain. We present approximation algorithms that compute e-short paths, i.e., paths whose costs are within a factor of 1 + e of the shortest path costs, for an arbitrary constant e > O, for the following geometric configurations: S P P S P r o b l e m : We are… (More)

- Mike D. Atkinson, Jörg-Rüdiger Sack, Nicola Santoro, Thomas Strothotte
- Commun. ACM
- 1986

A simple implementation of double-ended priority queues is presented. The proposed structure, called a min-max heap, can be built in linear time; in contrast to conventional heaps, it allows both</italic> FindMin <italic>and</italic> FindMax <italic>to be performed in constant time;</italic> Insert, DeleteMin, <italic>and</italic> DeleteMax… (More)

- Mike D. Atkinson, Jörg-Rüdiger Sack
- Inf. Process. Lett.
- 1992

Atkinson, M.D. and J.-R. Sack, Generating binary trees at random, Information Processing Letters 41 (1992) 21-23. We give a new constructive proof of the Chung-Feller theorem. Our proof provides a new and simple linear-time algorithm for generating random binary trees on n nodes; the algorithm uses integers no larger than 212.

Given a point set S and a polygonal curve P in R, we study the problem of finding a polygonal curve through S, which has a minimum Fréchet distance to P . We present an efficient algorithm to solve the decision version of this problem in O(nk) time, where n and k represent the sizes of P and S, respectively. A curve minimizing the Fréchet distance can be… (More)

- Mark Lanthier, Anil Maheshwari, Jörg-Rüdiger Sack
- ICALP
- 1999

We discuss the problem of computing shortest an-isotropic paths on terrains. Anisotropic path costs take into account the length of the path traveled, possibly weighted, and the direction of travel along the faces of the terrain. Considering faces to be weighted has added realism to the study of (pure) Euclidean shortest paths. Parameters such as the varied… (More)

- Masoud T. Omran, Jörg-Rüdiger Sack, Hamid Zarrabi-Zadeh
- J. Comb. Optim.
- 2011

Motivated by a security problem in geographic information systems, we study the following graph theoretical problem: given a graph G, two special nodes s and t in G, and a number k, find k paths from s to t in G so as to minimize the number of edges shared among the paths. This is a generalization of the well-known disjoint paths problem. While disjoint… (More)

- Frank Dehne, Jörg-Rüdiger Sack
- The Visual Computer
- 1987

We consider the problem of separating a set of polygons by a sequence of translations (one such collision-free translation motion for each polygon). If all translations are performed in a common direction the separability problem so obtained has been referred to as the uni-directional separability problem; for different translation directions, the more… (More)