Book ChapterDOI
Practical Discrete Unit Disk Cover Using an Exact Line-Separable Algorithm
Francisco Claude,Reza Dorrigiv,Stephane Durocher,Robert Fraser,Alejandro López-Ortiz,Alejandro Salinger +5 more
- pp 45-54
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TLDR
This work considers the line-separable discrete unit disk cover problem (the set of disk centres can be separated from the set of points by a line) and presents an O(m 2 n)-time algorithm that finds an exact solution.Abstract:
Given m unit disks and n points in the plane, the discrete unit disk cover problem is to select a minimum subset of the disks to cover the points. This problem is NP-hard [11] and the best previous practical solution is a 38-approximation algorithm by Carmi et al. [4]. We first consider the line-separable discrete unit disk cover problem (the set of disk centres can be separated from the set of points by a line) for which we present an O(m 2 n)-time algorithm that finds an exact solution. Combining our line-separable algorithm with techniques from the algorithm of Carmi et al. [4] results in an O(m 2 n 4) time 22-approximate solution to the discrete unit disk cover problem.read more
Citations
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Journal ArticleDOI
Two-Tiered Constrained Relay Node Placement in Wireless Sensor Networks: Computational Complexity and Efficient Approximations
TL;DR: This paper studies two-tiered constrained relay node placement problems, where the relay nodes can be placed only at some prespecified candidate locations, and proposes novel polynomial time approximation algorithms for these problems.
Journal ArticleDOI
Optimized relay node placement for connecting disjoint wireless sensor networks
Sookyoung Lee,Mohamed Younis +1 more
TL;DR: An effective strategy for establishing connectivity among the partitioned segments by deploying the least count of relay nodes (RNs) by using an Optimized Relay node placement algorithm using a minimum Steiner tree on the Convex hull (ORC).
Proceedings ArticleDOI
Two-Tiered Constrained Relay Node Placement in Wireless Sensor Networks: Efficient Approximations
TL;DR: This paper studies two-tiered constrained relay node placement problems, where the relay nodes can only be placed at some pre-specified candidate locations, and proposes novel polynomial time approximation algorithms for these problems.
Journal ArticleDOI
An improved line-separable algorithm for discrete unit disk cover
Francisco Claude,Gautam K. Das,Reza Dorrigiv,Stephane Durocher,Robert Fraser,Alejandro López-Ortiz,Bradford G. Nickerson,Alejandro Salinger +7 more
TL;DR: This work considers the line-separable discrete unit disk cover problem (the set of disk centers can be separated from the set of points by a line) and presents an O(n(log n + m) time algorithm that finds an exact solution.
Journal ArticleDOI
One-Step Approach for Two-Tiered Constrained Relay Node Placement in Wireless Sensor Networks
TL;DR: This letter proposes a one-step constrained RN placement (OSRP) algorithm which yields a network tree and shows that OSRP outperforms the only algorithm in the literature for two-tiered constrained RNs placement.
References
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Journal ArticleDOI
The NP-completeness column: An ongoing guide
TL;DR: This is the fourteenth edition of a quarterly column that provides continuing coverage of new developments in the theory of NP-completeness, and readers who have results they would like mentioned (NP-hardness, PSPACE- hardness, polynomialtime-solvability, etc.), or open problems they wouldlike publicized, should send them to David S. Johnson.
Journal ArticleDOI
Approximation schemes for covering and packing problems in image processing and VLSI
Dorit S. Hochbaum,Wolfgang Maass +1 more
TL;DR: The unified technique that is introduced here, referred to as the shifting strategy, is applicable to numerous geometric covering and packing problems and how it varies with problem parameters is illustrated.
Journal ArticleDOI
Optimal packing and covering in the plane are NP-complete☆
TL;DR: This paper proves that even severely restricted instances of packing and covering problems remain NP-hard in two or more dimensions, and helps to fill the gap by showing that some very constrained intersection graph problems in two dimensions are not very constrained.
Journal ArticleDOI
Almost optimal set covers in finite VC-dimension
TL;DR: A deterministic polynomial-time method for finding a set cover in a set system (X, ℛ) of dual VC-dimensiond such that the size of the authors' cover is at most a factor ofO(d log(dc)) from the optimal size,c.
Journal ArticleDOI
Fast algorithms for shortest paths in planar graphs, with applications
TL;DR: In this article, graph decomposition and data structures techniques are presented that exploit the structure of planar graphs to yield faster algorithms for a number of shortest path problems and related problems.