Open Access
A Simple Improved Distributed Algorithm for Minimum CDS in Unit Disk Graphs
Stefan Funke,Alexander Kesselmann,Ulrich Meyer,Michael Segal +3 more
- pp 220-223
TLDR
This paper presents a very simple distributed algorithm for computing a small CDS, improving upon the previous best known approximation factor of 8 and implying improved approximation factors for many existing algorithm.Abstract:
Several routing schemes in ad hoc networks first establish a virtual backbone and then route messages via back-bone nodes. One common way of constructing such a backbone is based on the construction of a minimum connected dominating set (CDS). In this paper we present a very simple distributed algorithm for computing a small CDS. Our algorithm has an approximation factor of at most 6.91, improving upon the previous best known approximation factor of 8 due to Wan et al. [INFOCOM'02], The improvement relies on a refined analysis of the relationship between the size of a maximal independent set and a minimum CDS in a unit disk graph. This subresult also implies improved approximation factors for many existing algorithm.read more
Citations
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Book
Design and Analysis of Approximation Algorithms
Ding-Zhu Du,Ker-I Ko,Xiaodong Hu +2 more
TL;DR: This book organizes approximation algorithms into different chapters, based on the design techniques for the algorithms, so that the reader and teacher can study approximation algorithms of the same nature together.
Journal ArticleDOI
Constructing Minimum Connected Dominating Sets with Bounded Diameters in Wireless Networks
TL;DR: This paper presents two centralized algorithms having constant performance ratios for its size and diameter of the constructed CDS and gives its distributed version, which not only can be implemented in real situation easily but also considers energy to extend network lifetime.
Journal ArticleDOI
Review: Connected dominating sets in wireless ad hoc and sensor networks - A comprehensive survey
TL;DR: A comprehensive survey for CDSs and related problems with various network models and specific applications is given and some open problems and interesting issues in this field are proposed.
Journal ArticleDOI
Minimum Connected Dominating Set Using a Collaborative Cover Heuristic for Ad Hoc Sensor Networks
Rajiv Misra,Chittaranjan Mandal +1 more
TL;DR: This work proposes a new heuristic called collaborative cover using two principles: domatic number of a connected graph is at least two and optimal substructure defined as subset of independent dominator preferably with a common connector.
Journal ArticleDOI
CDS-Based Virtual Backbone Construction with Guaranteed Routing Cost in Wireless Sensor Networks
TL;DR: This work proposes an innovative polynomial-time constant-approximation algorithm, GOC-MCDS-C, that produces a CDS D whose size I D is within a constant factor from that of the minimum CDS.
References
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Journal ArticleDOI
Unit disk graphs
Brent N. Clark,Brent N. Clark,Charles J. Colbourn,Charles J. Colbourn,David S. Johnson,David S. Johnson +5 more
TL;DR: It is shown that many standard graph theoretic problems remain NP-complete on unit disks, including coloring, independent set, domination, independent domination, and connected domination; NP-completeness for the domination problem is shown to hold even for grid graphs, a subclass of unit disk graphs.
Proceedings ArticleDOI
A simple parallel algorithm for the maximal independent set problem
TL;DR: Powerful and general techniques for converting Monte Carlo algorithms into deterministic algorithms are used to convert the Monte Carlo algorithm for the MIS problem into a simple deterministic algorithm with the same parallel running time.
Proceedings ArticleDOI
Distributed construction of connected dominating set in wireless ad hoc networks
TL;DR: This work presents their own distributed algorithm that outperforms the existing algorithms for minimum CDS and establishes the /spl Omega/(n log n) lower bound on the message complexity of any distributed algorithm for nontrivial CDS, which is thus message-optimal.
Journal ArticleDOI
A Polynomial-Time Approximation Scheme for the Minimum-Connected Dominating Set in Ad Hoc Wireless Networks
TL;DR: This paper designs a (1 + 1/s)‐approximation for the minimum‐connected dominating set in unit‐disk graphs, running in time nO((s log s)2).
Book
Design and Analysis of Approximation Algorithms
Ding-Zhu Du,Ker-I Ko,Xiaodong Hu +2 more
TL;DR: This book organizes approximation algorithms into different chapters, based on the design techniques for the algorithms, so that the reader and teacher can study approximation algorithms of the same nature together.