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Journals and Conferences
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.
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 . Using a similar reduction, we… (More)
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)
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.
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)
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)
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.