Results 1 
7 of
7
Incremental Construction of kDominating Sets in Wireless Sensor Networks
, 2006
"... Given a graph G, a kdominating set of G is a subset S of its vertices with the property that every vertex of G is either in S or has at least k neighbors in S. We present a new incremental local algorithm to construct a kdominating set. The algorithm constructs a monotone family of dominating sets ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
(Show Context)
Given a graph G, a kdominating set of G is a subset S of its vertices with the property that every vertex of G is either in S or has at least k neighbors in S. We present a new incremental local algorithm to construct a kdominating set. The algorithm constructs a monotone family of dominating sets D1 ⊆ D2... ⊆ Di... ⊆ Dk such that each Di is an idominating set. For unit disk graphs, the size of each of the resulting idominating sets is at most six times the optimal. 1
Connected Dominating Sets
"... Wireless sensor networks (WSNs), consist of small nodes with sensing, computation, and wireless communications capabilities, are now widely used in many applications, including environment and habitat monitoring, traffic control, and etc. Routing in WSNs is very challenging due to the inherent chara ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Wireless sensor networks (WSNs), consist of small nodes with sensing, computation, and wireless communications capabilities, are now widely used in many applications, including environment and habitat monitoring, traffic control, and etc. Routing in WSNs is very challenging due to the inherent characteristics that distinguish these networks from other wireless networks like mobile ad hoc networks or cellular networks. Hierarchical or clusterbased methods, originally proposed in wireline networks, are wellknown techniques with special advantages related to scalability and efficient communication. As such, the concept of hierarchical routing is also utilized to perform energyefficient routing in WSNs. Using a virtual backbone infrastructure which is one kind of hierarchical methods has received more attention. Thus, a Connected Dominating Set (CDS) has been recommended to serve as a virtual backbone for a WSN to reduce routing overhead. Having such a CDS simplifies routing by restricting the main routing tasks to the dominators only. Fault tolerance and routing flexibility are necessary for routing since nodes in WSNs are prone to failures and nodes may have mobility and turn on and off frequently. Thus, it is important to maintain a certain degree of redundancy in a CDS. Unfortunately, a CDS only preserves 1connectivity and it is therefore very vulnerable. Therefore, the concept of kconnected mdominating sets (kmCDS) are used to provide these redundancy. In this chapter, we first survey some existing clusterbased algorithms. After that, we focus on connected dominating set algorithms, including both centralized and distributed, for how to construct CDS. Theoretical analysis are also presented. Furthermore, some algorithms for kmCDS are described in detail.
Analysis on a Localized Pruning Method for Connected Dominating Sets
"... While restricted rulek has been succeeded in generating a connected dominating set (CDS) of small size, not much theoretical analysis on the size has been done. In this paper, an analysis on the expected size of a CDS generated by such algorithm and its relation to different node density is present ..."
Abstract
 Add to MetaCart
(Show Context)
While restricted rulek has been succeeded in generating a connected dominating set (CDS) of small size, not much theoretical analysis on the size has been done. In this paper, an analysis on the expected size of a CDS generated by such algorithm and its relation to different node density is presented. Assume N nodes are deployed uniformly and randomly in a square of size LN × LN (where N and LN → ∞); three results are obtained. (1) It is proved that the node degree distribution of such a network follows a Poisson distribution. (2) The expected size of a CDS that is derived by the restricted pruning rulek is a decreasing function with respect to the node density n ˆ. For ˆn ≥ 30. it is found that the expected size is close to N / n ˆ. (3) It is proved that the lower bound on the expected size of a CDS for a Poissonian network of node density ˆn is given by 1 nˆ { − exp ( − ( nˆ − 1))} N. The second result is of paramount importance for practinˆ − 1 nˆ − 1 tioners. It provides the information about the expected size of a CDS when the node density ˆn is between 6 and 30. The data (expected CDS size) for this range can hardly be provided by simulations.
Some Analytical Results on a Localized Pruning Method for Connected Dominating Sets in MANETs
"... Generating a small size connected dominating set (CDS) for message routing in wireless ad hoc networks is always a challenging problem. In a recent paper, a local pruning algorithm called restricted rulek has been proposed, and succeeds in generating a small size CDS. In this paper, a statistical a ..."
Abstract
 Add to MetaCart
Generating a small size connected dominating set (CDS) for message routing in wireless ad hoc networks is always a challenging problem. In a recent paper, a local pruning algorithm called restricted rulek has been proposed, and succeeds in generating a small size CDS. In this paper, a statistical analysis on the size of the CDS generated is presented. For a network of N nodes (where N → ∞) that are uniformly randomly generated in a square of size LN × LN (where LN → ∞), three results are obtained. (1) It is proved that the node degree distribution of such a network follows a Poisson distribution. (2) The expected size of a CDS that is derived by the restricted pruning rulek is a decreasing function with respect to the node density ˆn. For ˆn ≥ 30, it is found that the expected size is N/ˆn. (3) A tighter lower bound on the expected size of a CDS, for Poissonian node degree distribution, is deduced. For a � network of node denisty (λ + 1), the lower bound is 1 λ+1 λ − λ exp(−λ) � N which is larger than the lower bound recently deduced by Hansen et al..
n̂−1 − n̂n̂−1 exp(−(n̂ − 1))
"... While restricted rulek has been succeeded in generating a connected dominating set (CDS) of small size, not much theoretical analysis on the size has been done. In this paper, an analysis on the expected size of a CDS generated by such algorithm and its relation to different node density is present ..."
Abstract
 Add to MetaCart
(Show Context)
While restricted rulek has been succeeded in generating a connected dominating set (CDS) of small size, not much theoretical analysis on the size has been done. In this paper, an analysis on the expected size of a CDS generated by such algorithm and its relation to different node density is presented. Assume N nodes are deployed uniformly randomly in a square of size LN × LN (where N and LN → ∞), three results are obtained. (1) It is proved that the node degree distribution of such a network follows a Poisson distribution. (2) The expected size of a CDS that is derived by the restricted pruning rulek is a decreasing function with respect to the node density n̂. For n ̂ ≥ 30, it is found that the expected size is close to N/n̂. (3) It is proved that the lower bound on the expected size of a CDS for a Poissonian network of node density n ̂ is given by 1
Analysis on a Localized Pruning Method for Connected Dominating Sets
"... While restricted rulek has been succeeded in generating a connected dominating set (CDS) of small size, not much theoretical analysis on the size has been done. In this paper, an analysis on the expected size of a CDS generated by such algorithm and its relation to different node density is present ..."
Abstract
 Add to MetaCart
(Show Context)
While restricted rulek has been succeeded in generating a connected dominating set (CDS) of small size, not much theoretical analysis on the size has been done. In this paper, an analysis on the expected size of a CDS generated by such algorithm and its relation to different node density is presented. Assume N nodes are deployed uniformly and randomly in a square of size LN × LN (where N and LN → ∞); three results are obtained. (1) It is proved that the node degree distribution of such a network follows a Poisson distribution. (2) The expected size of a CDS that is derived by the restricted pruning rulek is a decreasing function with respect to the node density ˆn. For ˆn ≥ 30, it is found that the expected size is close to N/ˆn. (3) It is proved that the lower bound � on the expected size of a �CDS 1 ˆn for a Poissonian network of node density ˆn is given by ˆn−1 − ˆn−1 exp(−(ˆn − 1)) N. The second result is of paramount importance for practitioners. It provides the information about the expected size of a CDS when the node density ˆn is between 6 and 30. The data (expected CDS size) for this range can hardly be provided by simulations.
Analysis on a Localized Pruning Method for Connected Dominating Sets
"... While restricted rulek has been succeeded in generating a connected dominating set (CDS) of small size, not much theoretical analysis on the size has been done. In this paper, an analysis on the expected size of a CDS generated by such algorithm and its relation to different node density is present ..."
Abstract
 Add to MetaCart
(Show Context)
While restricted rulek has been succeeded in generating a connected dominating set (CDS) of small size, not much theoretical analysis on the size has been done. In this paper, an analysis on the expected size of a CDS generated by such algorithm and its relation to different node density is presented. Assume N nodes are deployed uniformly and randomly in a square of size LN × LN (where N and LN → ∞); three results are obtained. (1) It is proved that the node degree distribution of such a network follows a Poisson distribution. (2) The expected size of a CDS that is derived by the restricted pruning rulek is a decreasing function with respect to the node density n ˆ. For ˆn ≥ 30. it is found that the expected size is close to N / n ˆ. (3) It is proved that the lower bound on the expected size of a CDS for a Poissonian network of node density ˆn is given by 1 nˆ { − exp ( − ( nˆ − 1))} N. The second result is of paramount importance for practinˆ − 1 n ˆ − 1 tioners. It provides the information about the expected size of a CDS when the node density ˆn is between 6 and 30. The data (expected CDS size) for this range can hardly be provided by simulations.