Connecting a set of circles with minimum sum of radii

Chambers, Erin Wolf; Fekete, Sándor P.; Hoffmann, Hella-Franziska; Marinakis, Dimitri; Mitchell, Joseph S. B.; Srinivasan, Venkatesh; Stege, Ulrike; Whitesides, Sue

doi:10.1016/j.comgeo.2017.06.002

Cited by 2 publications

(1 citation statement)

References 30 publications

(44 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Bar-Noy and Baumer [3] also analyzed non-duty cycling algorithms for Strip Cover with identical batteries. The Connected Range Assignment problem studied by Chambers, et al [9], wherein the goal is to connect a series of points in the plane using circles, is also related. They presented approximation bounds for the case where solutions use a fixed number of circles, which is similar to limiting shift sizes.…”

Section: Motivationmentioning

confidence: 99%

Changing of the guards: Strip cover with duty cycling

Bar-Noy

Baumer

Rawitz

2016

Theoretical Computer Science

View full text Add to dashboard Cite

The notion of duty cycling is common in problems which seek to maximize the lifetime of a wireless sensor network. In the duty cycling model, sensors are grouped into shifts that take turns covering the region in question, and each sensor can belong to at most one shift. We consider the imposition of the duty cycling model upon the Strip Cover problem, where we are given n sensors on a one-dimensional region, and each shift can contain at most k ≤ n sensors. We call the problem of finding the optimal set of shifts so as to maximize the length of time that the entire region can be covered by a wireless sensor network, k-Duty Cycle Strip Cover (k-DutySC). In this paper, we present a polynomial-time algorithm for 2-DutySC. Furthermore, we show that this algorithm is a 35 24 -approximation algorithm for k-DutySC. We also give two lower bounds on the performance of our algorithm: 15 11 , for k ≥ 4, and 6 5 , for k = 3, and provide experimental evidence suggesting that these lower bounds are tight. Finally, we propose a fault tolerance model and find thresholds on the sensor failure rate over which our algorithm has the highest expected performance.

show abstract

Section: Motivationmentioning

confidence: 99%

Changing of the guards: Strip cover with duty cycling

Bar-Noy

Baumer

Rawitz

2016

Theoretical Computer Science

View full text Add to dashboard Cite

show abstract

Range assignment of base-stations maximizing coverage area without interference

Acharyya

Nandy

et al. 2020

Theoretical Computer Science

View full text Add to dashboard Cite

We study the problem of assigning non-overlapping geometric objects centered at a given set of points such that the sum of area covered by them is maximized. If the points are placed on a straight-line and the objects are disks, then the problem is solvable in polynomial time. However, we show that the problem is NP-hard even for simplest objects like disks or squares in R 2 . Eppstein [CCCG, pages 260-265, 2016] proposed a polynomial time algorithm for maximizing the sum of radii (or perimeter) of non-overlapping balls or disks when the points are arbitrarily placed on a plane. We show that Eppstein's algorithm for maximizing sum of perimeter of the disks in R 2 gives a 2-approximation solution for the sum of area maximization problem. We propose a PTAS for our problem. These approximation results are extendible to higher dimensions. All these approximation results hold for the area maximization problem by regular convex polygons with even number of edges centered at the given points.

show abstract

Connecting a set of circles with minimum sum of radii

Cited by 2 publications

References 30 publications

Changing of the guards: Strip cover with duty cycling

Changing of the guards: Strip cover with duty cycling

Range assignment of base-stations maximizing coverage area without interference

Contact Info

Product

Resources

About