scholarly journals A linear approximation algorithm for bin packing with absolute approximation factor 32

2003 ◽  
Vol 48 (1) ◽  
pp. 67-80 ◽  
Author(s):  
Rudolf Berghammer ◽  
Florian Reuter
Keyword(s):  
Approximation Algorithm ◽  
Linear Approximation ◽  
Bin Packing ◽  
Approximation Factor

When a worse approximation factor gives better performance: a 3-approximation algorithm for the vertex k-center problem

2017 ◽  
Vol 23 (5) ◽  
pp. 349-366 ◽  
Author(s):  
Jesus Garcia-Diaz ◽  
Jairo Sanchez-Hernandez ◽  
Ricardo Menchaca-Mendez ◽  
Rolando Menchaca-Mendez
Keyword(s):  
Approximation Algorithm ◽  
Center Problem ◽  
Approximation Factor

scholarly journals Approximation Algorithms for Barrier Sweep Coverage

2019 ◽  
Vol 30 (03) ◽  
pp. 425-448 ◽  
Author(s):  
Barun Gorain ◽  
Partha Sarathi Mandal
Keyword(s):  
Energy Source ◽  
Approximation Algorithm ◽  
Finite Length ◽  
Optimal Solution ◽  
Mobile Sensors ◽  
Continuous Curve ◽  
Mobile Sensor ◽  
Coverage Problem ◽  
Line Segments ◽  
Approximation Factor

Time-varying coverage, namely sweep coverage is a recent development in the area of wireless sensor networks, where a few mobile sensors sweep or monitor a comparatively large number of locations periodically. In this article, we study barrier sweep coverage with mobile sensors where the barrier is considered as a finite length continuous curve on a plane. The coverage at every point on the curve is time-variant. We propose an optimal solution for sweep coverage of a finite length continuous curve. Usually, energy source of a mobile sensor is a battery with limited power, so energy restricted sweep coverage is a challenging problem for long running applications. We propose an energy-restricted sweep coverage problem where every mobile sensor must visit an energy source frequently to recharge or replace its battery. We propose a [Formula: see text]-approximation algorithm for this problem. The proposed algorithm for multiple curves achieves the best possible approximation factor 2 for a special case. We propose a 5-approximation algorithm for the general problem. As an application of the barrier sweep coverage problem for a set of line segments, we formulate a data gathering problem. In this problem a set of mobile sensors is arbitrarily monitoring the line segments one for each. A set of data mules periodically collects the monitoring data from the set of mobile sensors. We prove that finding the minimum number of data mules to collect data periodically from every mobile sensor is NP-hard and propose a 3-approximation algorithm to solve it.

Constrained k-Center Problem on a Convex Polygon

2020 ◽  
Vol 31 (02) ◽  
pp. 275-291 ◽  
Author(s):  
Manjanna Basappa ◽  
Ramesh K. Jallu ◽  
Gautam K. Das
Keyword(s):  
Approximation Algorithm ◽  
Convex Polygon ◽  
Covering Problem ◽  
Center Problem ◽  
Entire Region ◽  
Approximation Factor ◽  
Minimum Radius

In this paper, we consider a restricted covering problem, in which a convex polygon [Formula: see text] with [Formula: see text] vertices and an integer [Formula: see text] are given, the objective is to cover the entire region of [Formula: see text] using [Formula: see text] congruent disks of minimum radius [Formula: see text], centered on the boundary of [Formula: see text]. For [Formula: see text] and any [Formula: see text], we propose an [Formula: see text]-factor approximation algorithm for this problem, which runs in [Formula: see text] time. The best known approximation factor of the algorithm for the problem in the literature is 1.8841 [H. Du and Y. Xu: An approximation algorithm for [Formula: see text]-center problem on a convex polygon, J. Comb. Optim. 27(3) (2014) 504–518].

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