#### Filter Results:

- Full text PDF available (7)

#### Publication Year

2012

2016

- This year (0)
- Last 5 years (13)
- Last 10 years (13)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

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 geodesic distance to v is at most r. We present a polynomial time 2-approximation algorithm for finding a densest geodesic unit… (More)

- 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.

- Ning Xu, Peter Brass, Ivo Vigan
- 2012

There is vast amount of literature focusing on motion planning for general robots. However, the same studies for tethered robots have not been investigated much. While a robot navigates in an environment with obstacles, it may meet some problems, such as a lack of power supply, or losing its wireless communication connection. If a robot is attached to a… (More)

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

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

- Takahisa Toda, Ivo Vigan
- Discrete Mathematics
- 2013

We focus on families of bipartitions, i.e. set partitions consisting of atmost two components. A family of bipartitions is a separating family for a set if every two elements in the set are separated by some bipartition. In this paper we enumerate separating families of arbitrary size. We furthermore enumerate inclusion-wise minimal separating families of… (More)

- George Rabanca, Ivo Vigan
- ArXiv
- 2014

We present an O(n log n) time 2-approximation algorithm for computing the number of geodesic unit disks needed to cover the boundary of a simple polygon on n vertices. The running time thus only depends on the number of vertices and not on the number of disks; the disk centers can be computed in additional time proportional to the number of disks.