Autonomous Unmanned Aerial Vehicles (UAVs) have gained popularity due to their many potential application fields. Alongside sophisticated sensors, UAVs can be equipped with communication adaptors aimed for inter-UAV communication. Inter-communication of UAVs to form a UAV swarm raises questions on how to manage its communication structure and mobility. In this paper, we consider therefore the problem of establishing an efficient swarm movement model and a network topology between a collection of UAVs, which are specifically deployed for the scenario of high-quality forest-mapping.
Existing approaches for optimizing formation acquisition and maintenance mostly focus on @cite_18 @cite_3 . A variant of the coverage problem is the , where packing of a maximum number of circles is required. For the two dimensional case the problem has a polynomial time solution @cite_5 .
@cite_5 @cite_18 @cite_3
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In this paper we address the problem of persistent coverage of a given convex polygonal region in the plane. We present an algorithmic solution for this problem that takes into account the limitations in the communication and sensing ranges of the agents. We show that our algorithm provides a persistent coverage period that is bounded away by a constant factor from a minimal tour among the centers of an optimal static cover, which is comprised of circles having the same radius as the sensing radius of the agents. A simulation is provided that illustrates the algorithm. We study the following packing problem: Given a collection of d-dimensional rectangles of specified sizes, pack them into the minimum number of unit cubes. We show that unlike the one-dimensional case, the two-dimensional packing problem cannot have an asymptotic polynomial time approximation scheme (APTAS), unless PNP. On the positive side, we give an APTAS for the special case of packing d-dimensional cubes into the minimum number of unit cubes. Second, we give a polynomial time algorithm for packing arbitrary two-dimensional rectangles into at most OPT square bins with sides of length 1 , where OPT denotes the minimum number of unit bins required to pack these rectangles. Interestingly, this result has no additive constant term, i.e., is not an asymptotic result. As a corollary, we obtain the first approximation scheme for the problem of placing a collection of rectangles in a minimum-area encasing rectangle. In this paper we consider the Online Bin Packing Problem in three variants: Circles in Squares, Circles in Isosceles Right Triangles, and Spheres in Cubes. The two first ones receive an online sequence of circles (items) of different radii while the third one receive an online sequence of spheres (items) of different radii, and they want to pack the items into the minimum number of unit squares, isosceles right triangles of leg length one, and unit cubes, respectively. For Online Circle Packing in Squares, we improve the previous best-known competitive ratio for the bounded space version, when at most a constant number of bins can be open at any given time, from 2.439 to 2.3536. For Online Circle Packing in Isosceles Right Triangles and Online Sphere Packing in Cubes we show bounded space algorithms of asymptotic competitive ratios 2.5490 and 3.5316, respectively, as well as lower bounds of 2.1193 and 2.7707 on the competitive ratio of any online bounded space algorithm for these two problems. We also considered the online unbounded space variant of these three problems which admits a small reorganization of the items inside the bin after their packing, and we present algorithms of competitive ratios 2.3105, 2.5094, and 3.5146 for Circles in Squares, Circles in Isosceles Right Triangles, and Spheres in Cubes, respectively. We study a geometric version of the Red-Blue Set Cover problem originally proposed by (2000) 1: given a red point set, a blue point set, and a set of objects, we want to choose a subset of objects to cover all the blue points, while minimizing the number of red points covered. We prove that the problem is NP-hard even when the objects are unit squares in 2D, and we give the first polynomial-time approximation scheme (PTAS) for this case. The technique we use simplifies and unifies previous PTASs for the weighted geometric set cover problem and the unique maximum coverage problem for 2D unit squares.