On minimum weakly connected independent sets for wireless sensor networks: properties and enumeration algorithm

  title={On minimum weakly connected independent sets for wireless sensor networks: properties and enumeration algorithm},
  author={Fatiha Bendali and Jean Mailfert and Djelloul Mameri},
  journal={RAIRO Oper. Res.},
Modeling topologies in Wireless Sensor Networks principally uses domination theory in graphs. Indeed, many dominating structures have been proposed as virtual backbones for wireless networks. In this paper, we study a dominating set that we call Weakly Connected Independent Set (wcis ). Given an undirected connected graph G = (V,E ), we say that an independent set S in G is weakly connected if the spanning subgraph (V, [ S,V \ S ]) is connected, where [ S,V \ S ] is the set of edges having… 
2 Citations
The weakly connected independent set polytope in corona and join of graphs
A theorem about complete description of the wcis polytope has been given for 1-sum operation and a class of graphs is also inductively defined from the connected bipartite graphs, the cycles and the strongly chordal graphs, for which the MWWCISP is polynomially solvable.


Weakly-connected dominating sets and sparse spanners in wireless ad hoc networks
  • K. Alzoubi, P. Wan, O. Frieder
  • Computer Science, Mathematics
    23rd International Conference on Distributed Computing Systems, 2003. Proceedings.
  • 2003
This paper presents two distributed algorithms for finding a WCDS of G, a weakly-connected dominating set of G if S is dominating and G' is connected, and the graph G' generated by the second algorithm forms a sparse spanner with a topological dilation of 3, and a geometricdilation of 6.
Approximation Algorithms for Connected Dominating Sets
This work considers the more general problem of finding a connected dominating set of a specified subset of vertices and provides a polynomial time algorithm with a (c+1) H(Δ) +c-1 approximation factor, where c is the Steiner approximation ratio for graphs.
Approximating minimum size weakly-connected dominating sets for clustering mobile ad hoc networks
The main contribution of this work is a completely distributed algorithm for finding small WCDS's and the performance of this algorithm is shown to be very close to that of the centralized approach.
Minimum connected dominating sets and maximal independent sets in unit disk graphs
Message-optimal connected dominating sets in mobile ad hoc networks
This paper proposes the first distributed approximation algorithm to construct a MCDS for the unit-disk-graph with a emph constant approximation ratio, and emph linear time and emphlinear message complexity.
A Branch-and-Reduce Algorithm for Finding a Minimum Independent Dominating Set
An algorithm computing a minimum independent dominating set of a graph on n vertices in time O(1.3247n) is given, which is a lower bound on the worst-case running time of this algorithm.
Connected Domination in Multihop Ad Hoc Wireless Networks
This study proposes a distributed approximation algorithm with performance ratio at most 8.5, which is the best (time and message efficient) distributed algorithm known so far.
On greedy construction of connected dominating sets in wireless networks
This paper proposes a new greedy algorithm, called S-MIS, with the help of Steiner tree that can construct a CDS within a factor of 4:8 þ ln5 from the optimal solution and introduces the distributed version of this algorithm.
Two-Phased Approximation Algorithms for Minimum CDS in Wireless Ad Hoc Networks
It is proved that the approximation ratio of the two-phased algorithm in [10] is at most 7 1/3, improving upon the previous best-known approximation ratio due to [12], and a new two- phased approximation algorithm is proposed and it is proven that its approximation ratio is at least 6 7/18.
Distributed Construction of Connected Dominating Set in Wireless Ad Hoc Networks
  • P. Wan, K. Alzoubi, O. Frieder
  • Computer Science
    Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies
  • 2002
This paper presents their own distributed algorithm that outperforms the existing algorithms for minimum CDS and establishes the Ω(nlog n) lower bound on the message complexity of any distributed algorithm for nontrivial CDS, thus message-optimal.