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- Takahisa Toda, Ivo Vigan
- Discrete Mathematics
- 2013

Let S be a set of n points in the plane. We present data structures that solve range-aggregate query problems on three geometric extent measure problems. Using these data structures, we can report , for any axis-parallel query rectangle Q, the area/perimeter of the convex hull, the width, and the radius of the smallest enclosing disk of the points in S ∩ Q.

- Rainer Penninger, Ivo Vigan
- ArXiv
- 2012

We consider the situation where one is given a set S of points in the plane and a collection D of unit disks embedded in the plane. We show that finding a minimum cardinality subset of D such that any path between any two points in S is intersected by at least one disk is NP-complete. This settles an open problem raised in [1]. Using a similar reduction, we… (More)

- Ivo Vigan
- ArXiv
- 2013

Given a polygon P , for two points s and t contained in the polygon, their geodesic distance is the length of the shortest st-path within P. A geodesic disk of radius r centered at a point v ∈ P is the set of points in P whose geo-desic distance to v is at most r. We present a polynomial time 2-approximation algorithm for finding a densest geodesic unit… (More)

- Ning Xu, Peter Brass, Ivo Vigan
- 2012

- Peter Braß, Ivo Vigan, Ning Xu
- 2014 13th International Conference on Control…
- 2014

In this paper, we present an algorithm for exploring an unknown graph with opaque edges by multiple robots. We show that this algorithm is near optimal on graphs with n vertices and superlinear number of edges (i.e., ω(n) edges), and give an adversarial construction to show that the algorithm does not perform well on cyclic graphs with O(n) edges.

- Amotz Bar-Noy, David Peleg, George Rabanca, Ivo Vigan
- ESA
- 2015

- Peter Braß, Ivo Vigan, Ning Xu
- Comput. Geom.
- 2015

- Ivo Vigan
- 2015

I, Ivo Vigan, declare that this thesis titled, 'Geometric Separation and Packing Problems' and the work presented in it are my own. I confirm that: This work was done wholly or mainly while in candidature for a research degree at this University. Where any part of this thesis has previously been submitted for a degree or any other qualification at this… (More)