Anil Maheshwari School of Computer Science Carleton

Approximating Geometric Bottleneck Shortest Paths

In a geometric bottleneck shortest path problem, we are given a set S of n points in the plane, and want to answer queries of the following type: Given two points p and q of S and a real number L, compute (or approximate) a shortest path between p and q in the subgraph of the complete graph on S consisting of all edges whose lengths are less than or equal to L. We present efficient algorithms f...

Low-interference networks in metric spaces of bounded doubling dimension

Let S be a set of n points in a metric space, let R = {Rp : p ∈ S} be a set of positive real numbers, and let GR be the undirected graph with vertex set S in which {p, q} is an edge if and only if |pq| ≤ min(Rp, Rq). The interference of a point q of S is defined to be the number of points p ∈ S \ {q} with |pq| ≤ Rp. For the case when S is a subset of the Euclidean space R, Halldórsson and Tokuy...

Lecture Notes on Algorithms

These notes extensively use material from course notes of Lars Arge, David Mount, COMP 2805/3803 Notes of myself and Michiel Smid [10], CLRS book [3], Knuth’s Art of Computer Programming [8], Kleinberg and Tardos Algorithms book [7], Ullman et al’s book on Algorithms for Massive Data Sets [13]. They are updated occasionally. I have used part of this material for graduate course COMP 5703 on Alg...

External Memory Algorithms for Outerplanar Graphs

Geometric Spanners

Geometric Spanners Name: Joachim Gudmundsson, Giri Narasimhan, Michiel Smid Affil./Addr. 1: School of Information Technologies, The University of Sydney, NSW, Australia Affil./Addr. 2: School of Computing & Information Sciences Florida International University, FL, USA Affil./Addr. 3: School of Computer Science Carleton University, ON, Canada