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A Distributed Algorithm to Find kdominating Sets
, 1999
"... We consider a connected undirected graph G(n; m) with n nodes and m edges. A kdominating set D in G is a set of nodes having the property that every node in G is at most k edges away from at least one node in D. ..."
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Cited by 16 (0 self)
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We consider a connected undirected graph G(n; m) with n nodes and m edges. A kdominating set D in G is a set of nodes having the property that every node in G is at most k edges away from at least one node in D.
Small kDominating Sets in Planar Graphs with Applications
 IN GRAPHTHEORETIC CONCEPTS IN COMPUTER SCIENCE (BOLTENHAGEN
, 2001
"... A subset of nodes S in a graph G is called kdominating if, for every node u of the graph, the distance from u to S is at most k. We consider the parameter k (G) de ned as the cardinality of the smallest kdominating set of G. For planar graphs, we show that for every > 0 and for every k & ..."
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Cited by 9 (0 self)
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A subset of nodes S in a graph G is called kdominating if, for every node u of the graph, the distance from u to S is at most k. We consider the parameter k (G) de ned as the cardinality of the smallest kdominating set of G. For planar graphs, we show that for every > 0 and for every k
SelfStabilizing Small kDominating Sets
, 2012
"... A selfstabilizing algorithm, after transient faults hit the system and place it in some arbitrary global state, recovers in finite time without external (e.g., human) intervention. In this paper, we propose a distributed asynchronous silent selfstabilizing algorithm for finding a minimal kdominat ..."
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Cited by 7 (1 self)
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A selfstabilizing algorithm, after transient faults hit the system and place it in some arbitrary global state, recovers in finite time without external (e.g., human) intervention. In this paper, we propose a distributed asynchronous silent selfstabilizing algorithm for finding a minimal kdominating
SelfStabilizing Small kDominating Sets
"... A selfstabilizing algorithm, after transient faults hit the system and place it in some arbitrary global state, recovers in finite time without external (e.g., human) intervention. In this paper, we propose a distributed asynchronous silent selfstabilizing algorithm for finding a minimal kdomina ..."
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A selfstabilizing algorithm, after transient faults hit the system and place it in some arbitrary global state, recovers in finite time without external (e.g., human) intervention. In this paper, we propose a distributed asynchronous silent selfstabilizing algorithm for finding a minimal kdominating
Fast Distributed Construction of Small kDominating Sets and Applications
, 2000
"... This paper presents a fast distributed algorithm to compute a small kdominating set D (for any xed k) and its induced graph partition (breaking the graph into radius k clusters centered around the vertices of D). The time complexity of the algorithm is O(k log n). ..."
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Cited by 65 (8 self)
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This paper presents a fast distributed algorithm to compute a small kdominating set D (for any xed k) and its induced graph partition (breaking the graph into radius k clusters centered around the vertices of D). The time complexity of the algorithm is O(k log n).
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 ..."
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Cited by 7 (0 self)
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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
The expected size of the rule k dominating set
 Algorithmica
, 2006
"... Dai, Li, and Wu proposed Rule k, a localized approximation algorithm that attempts to find a small connected dominating set in a graph. Here we consider the “average case”performance of Rule k for the model of random unit disk graphs constructed from n random points in an ℓn × ℓn square. If k ≥ 3 an ..."
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Cited by 7 (0 self)
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Dai, Li, and Wu proposed Rule k, a localized approximation algorithm that attempts to find a small connected dominating set in a graph. Here we consider the “average case”performance of Rule k for the model of random unit disk graphs constructed from n random points in an ℓn × ℓn square. If k ≥ 3
On Constructing kConnected kDominating Set in Wireless Networks
 In Proceedings of the 19 th International Parallel & Distributed Processing Symposium (IPDPS
, 2005
"... An important problem in wireless ad hoc and sensor networks is to select a few nodes to form a virtual backbone that supports routing and other tasks such as area monitoring. Previous work in this area has focused on selecting a small virtual backbone for high efficiency. In this paper, we propose ..."
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Cited by 53 (1 self)
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the construction of a kconnected kdominating set (kCDS) as a backbone to balance efficiency and fault tolerance. Four localized kCDS construction protocols are proposed. The first protocol randomly selects virtual backbone nodes with a given probability pk, where pk depends on the value of k and network
On Constructing kConnected kDominating Set in Wireless Networks ∗
"... An important problem in wireless networks, such as wireless ad hoc and sensor networks, is to select a few nodes to form a virtual backbone that supports routing and other tasks such as area monitoring. Previous work in this area has focused on selecting a small virtual backbone for high efficiency. ..."
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. We propose to construct a kconnected kdominating set (kCDS) as a backbone to balance efficiency and fault tolerance. Three localized kCDS construction protocols are proposed. The first protocol randomly selects virtual backbone nodes with a given probability pk, where pk depends on network
Hierarchical routing in sensor networks using kdominating sets
"... For a connected graph, representing a sensor network, distributed algorithms for the Set Covering Problem can be employed to construct reasonably small subsets of the nodes, called kSPR sets. Such a set can serve as a virtual backbone to facilitate shortest path routing, as introduced in [40], [12] ..."
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been used to construct virtual backbones in ad hoc and sensor networks, this is the first attempt to use khop connected kdominating sets for hierarchical routing that is also minimal path routing. I.
Results 1  10
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