scholarly journals Efficient Algorithms for Max-Weighted Point Sweep Coverage on Lines

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1457
Author(s):  
Dieyan Liang ◽  
Hong Shen
Keyword(s):  
Optimal Algorithm ◽  
Approximate Solutions ◽  
Approximation Ratio ◽  
Mobile Sensors ◽  
Np Hard ◽  
Coverage Problem ◽  
Polynomial Time Approximation Algorithm ◽  
Weighted Point ◽  
Eulerian Graph ◽  
Set Of Points

As an important application of wireless sensor networks (WSNs), deployment of mobile sensors to periodically monitor (sweep cover) a set of points of interest (PoIs) arises in various applications, such as environmental monitoring and data collection. For a set of PoIs in an Eulerian graph, the point sweep coverage problem of deploying the fewest sensors to periodically cover a set of PoIs is known to be Non-deterministic Polynomial Hard (NP-hard), even if all sensors have the same velocity. In this paper, we consider the problem of finding the set of PoIs on a line periodically covered by a given set of mobile sensors that has the maximum sum of weight. The problem is first proven NP-hard when sensors are with different velocities in this paper. Optimal and approximate solutions are also presented for sensors with the same and different velocities, respectively. For M sensors and N PoIs, the optimal algorithm for the case when sensors are with the same velocity runs in O(MN) time; our polynomial-time approximation algorithm for the case when sensors have a constant number of velocities achieves approximation ratio 12; for the general case of arbitrary velocities, 12α and 12(1−1/e) approximation algorithms are presented, respectively, where integer α≥2 is the tradeoff factor between time complexity and approximation ratio.

Coverage Control for Mobile Sensor Networks on a Circle

2014 ◽  
Vol 02 (03) ◽  
pp. 243-248 ◽  
Author(s):  
Cheng Song ◽  
Gang Feng
Keyword(s):  
Sensor Networks ◽  
Mobile Agents ◽  
Mobile Sensor Networks ◽  
Mobile Sensors ◽  
Mobile Sensor ◽  
Coverage Problem ◽  
Control Laws ◽  
Coverage Control ◽  
Order Preservation ◽  
Multi Agent

This paper investigates the coverage problem for mobile sensor networks on a circle. The goal is to minimize the largest distance from any point on the circle to its nearest sensor while preserving the mobile sensors' order. The coverage problem is translated into a multi-agent consensus problem by showing that the largest distance from any point to its nearest sensor is minimized if the counterclockwise distance between each sensor and its right neighbor reaches a consensus. Distributed control laws are also developed to drive the mobile agents to the optimal configuration with order preservation. Simulation results illustrate the effectiveness of the proposed control laws.

COMPLEXITY AND APPROXIMABILITY OF DOUBLE DIGEST

2005 ◽  
Vol 03 (02) ◽  
pp. 207-223
Author(s):  
MARK CIELIEBAK ◽  
STEPHAN EIDENBENZ ◽  
GERHARD J. WOEGINGER
Keyword(s):  
Real Life ◽  
Approximation Ratio ◽  
Additional Restriction ◽  
Np Hard ◽  
Model Errors ◽  
Np Completeness ◽  
The Third ◽  
Np Complete ◽  
Feasible Solutions

We revisit the DOUBLE DIGEST problem, which occurs in sequencing of large DNA strings and consists of reconstructing the relative positions of cut sites from two different enzymes. We first show that DOUBLE DIGEST is strongly NP-complete, improving upon previous results that only showed weak NP-completeness. Even the (experimentally more meaningful) variation in which we disallow coincident cut sites turns out to be strongly NP-complete. In the second part, we model errors in data as they occur in real-life experiments: we propose several optimization variations of DOUBLE DIGEST that model partial cleavage errors. We then show that most of these variations are hard to approximate. In the third part, we investigate variations with the additional restriction that coincident cut sites are disallowed, and we show that it is NP-hard to even find feasible solutions in this case, thus making it impossible to guarantee any approximation ratio at all.

scholarly journals THE POINT-SET EMBEDDABILITY PROBLEM FOR PLANE GRAPHS

2013 ◽  
Vol 23 (04n05) ◽  
pp. 357-395 ◽  
Author(s):  
THERESE BIEDL ◽  
MARTIN VATSHELLE
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Line Drawing ◽  
Np Hard ◽  
Bounded Treewidth ◽  
Straight Line ◽  
Triangulated Graphs ◽  
Point Set ◽  
Fixed Embedding ◽  
Set Of Points

In this paper, we study the point-set embeddability problem, i.e., given a planar graph and a set of points, is there a mapping of the vertices to the points such that the resulting straight-line drawing is planar? It was known that this problem is NP-hard if the embedding can be chosen, but becomes polynomial for triangulated graphs of treewidth 3. We show here that in fact it can be answered for all planar graphs with a fixed combinatorial embedding that have constant treewidth and constant face-degree. We prove that as soon as one of the conditions is dropped (i.e., either the treewidth is unbounded or some faces have large degrees), point-set embeddability with a fixed embedding becomes NP-hard. The NP-hardness holds even for a 3-connected planar graph with constant treewidth, triangulated planar graphs, or 2-connected outer-planar graphs. These results also show that the convex point-set embeddability problem (where faces must be convex) is NP-hard, but we prove that it becomes polynomial if the graph has bounded treewidth and bounded maximum degree.

scholarly journals Channel Density Minimization by Pin Permutation

VLSI Design ◽  
1994 ◽  
Vol 2 (2) ◽  
pp. 171-183
Author(s):  
Yang Cai ◽  
D. F. Wong ◽  
Jason Cong
Keyword(s):  
Optimal Algorithm ◽  
Linear Time ◽  
Layout Design ◽  
Strong Sense ◽  
Np Hard ◽  
Wire Length ◽  
Channel Density ◽  
Time Optimal ◽  
Two Sides ◽  
Intergrated Circuits

We present in this paper a linear time optimal algorithm for minimizing the density of a channel (with exits) by permuting the terminals on the two sides of the channel. This compares favorably with the previously known near-optimal algorithm presented in [6] that runs in superlinear time. Our algorithm has important applications in hierarchical layout design of intergrated circuits. We also show that the problem of minimizing wire length by permuting terminals is NP-hard in the strong sense.

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.

scholarly journals ACO-Based Sweep Coverage Scheme in Wireless Sensor Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Peng Huang ◽  
Feng Lin ◽  
Chang Liu ◽  
Jian Gao ◽  
Ji-liu Zhou
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Mobile Sensors ◽  
Wireless Sensor ◽  
Data Delivery ◽  
Network Coverage ◽  
Coverage Problem ◽  
Points Of Interest ◽  
Novel Algorithm

Coverage problem is one of the major issues in wireless sensor networks (WSN). In order to optimize the network coverage, different coverage formulations have been proposed. Recently, a newly emerging coverage scheme in wireless sensor networks, sweep coverage, which uses mobile sensors to monitor certain points of interest (POIs), is proposed. However, the data delivery to sink, an important problem in WSN, is not considered in original sweep coverage and many of the existing works did not consider it yet. In this work, a novel algorithm named ACOSC (ACO-based sweep coverage) to solve the sweep coverage problem considering periodical coverage of POIs and delivery of data simultaneously is proposed. The evaluation results show that our algorithm has better performance than existing schemes.

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