K-clustering in Wireless Ad Hoc Networks
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Transcript of K-clustering in Wireless Ad Hoc Networks
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K-clustering in Wireless Ad Hoc Networks
Fernandess and MalkhiHebrew University of Jerusalem
Presented by: Ashish Deopura
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Outline of the presentation
• Motivation for clustering in Mobile Ad hoc networks
• Problem Statement• Algorithm Description• Conclusions / Summary
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Wireless Ad-hoc networks
• Dynamic topology• Power and bandwidth limitations• Broadcast network• Routing
– How to determine path from source to destination
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Cluster-based Routing Protocol
The network is divided to non overlapping sub-networks (clusters) with bounded diameter.
• Intra-cluster routing: pro-actively maintain state information for links within the cluster.
• Inter-cluster routing: use a route discovery
protocol for determining routes.
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Cluster-based Routing Protocol (Cntd.)
• Limit the amount of routing information stored and maintained at individual hosts.
• Clusters are manageable. Node mobility events are handled locally within the clusters. Hence, far-reaching effects of topological changes are minimized.
• Overcome mobility by adjusting cluster size (diameter) according to network stability.
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Cluster-heads
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CH Denote Cluster-heads
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Problem Statement
• Minimum k-clustering: given a graph G = (V,E) and a positive integer k, find the smallest value of ƒ such that there is a partition of V into ƒ disjoint subsets V1,…,Vƒ and diam(G[Vi]) <= k for i = 1…ƒ.
• The algorithmic complexity of k-clustering is known to be NP-complete for simple undirected graphs.
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Example K-clustering (for K = 3)
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Algorithm Description
• A two phase distributed algorithm for k-clustering where k > 1 that has a competitive worst case ratio of O(k)– First phase: construct a MCDS tree of the
network– Second phase: partition the spanning tree into
sub-trees with bounded diameter.
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System Model
Two general assumptions regarding the state of the network’s communication links and topology:
1. The network may be modeled as an unit disk graph (represents effective broadcast range).
2. The network topology remains unchanged throughout the execution of the algorithm.
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Unit Disk Graph
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The distance between adjacent nodes = 1
The distance between non adjacent nodes is >= 2
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Preliminaries IGiven an undirected graph G = (V,E) consider
the following general definitions regarding k-clustering:
• Diameter:• Dominating Set (DS):
• Connected Dominating Set (CDS): The induced sub graph G[D] is connected.
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DinnodesometoadjacentisDVinnodeeachtsVDSubset
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Preliminaries II
• Independent Set (IS):
• Maximal Independent Set (MIS): An independent set S where no proper superset of S is also an IS.
• A MIS is also DS.
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SinnodesofpairanybetweenedgenoistheretsVSSubset
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Maximal Independent Set (MIS)
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CH Denote MIS & DS nodes
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First Phase: MCDS Tree Construction
Given an unit disk graph G = (V,E) the algorithm executes as follows:
• Step 1: Construct a spanning tree T.• partitions the nodes into disjoints sets Si
• Si is a set of nodes at level equal to i• Every node knows its neighbors• A rank associated with every node
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Spanning tree (Cntd.)
• Maximal Independent Set Construction
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Spanning tree (Cntd.)
• Connected Dominating Set, parent child pointers
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INV INV
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Connected Dominating Set
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Denote MIS nodes
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DenoteNS nodes
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Second Phase: K-sub tree
• Partition the spanning tree into sub-trees– Bounded Diameter
• Each node maintains – Height– Highest child
• Detach child if– H+ Height + 1 > k– Where H is the height received from a child
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K-sub-tree Converge-cast (K=4)
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Denote MCDS spanning tree edge.
leaf
The tree rooted at this node exceeds k detach the highest child
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K-sub-tree Converge-cast (K=4)
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leaf
The tree rooted at this node exceeds k detach the highest child.
Denote MCDS spanning tree edge.
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K-sub-tree Converge-cast (K=4)
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Denote MCDS spanning tree edge.
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Summary• A distributed k-clustering algorithm• Competitive worst case ratio of O(k)• Building-block – essential for cluster-
based routing protocols.• Flexible - cluster diameter is a part
of the algorithm parameter.
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Thanks