1. + Mayukha Bairy Disk Intersection graphs and CDS as a backbone in wireless ad hoc networks

2. + Outline Wireless Ad hoc networks Disk Intersection Graphs Graph Construction Real World Problem Solution by CDS (as virtual backbone) References

3. + Wireless Ad hoc networks Wireless Ad hoc network: A wireless ad hoc network (WANET) is a decentralized type of wireless network. The network is ad hoc because it does not rely on a pre existing infrastructure, such as routers in wired networks. Instead, each node participates in routing by forwarding data for other nodes. Every node has a particular transmission range

4. + Disk Intersection Graphs In general, we define disk graph (DG) as the intersection graph of a set of disks. There are a number of variants for DG. One among them is Unit disk graph.

5. + Graph Representation An ad-hoc network can be intuitively casted into the format of a graph which is a set of vertex and a set of edges that might connect pairs of the nodes. The ad-hoc network consists of devices (vertex or nodes) and the communication links (edges)between them. Consider a set S of closed disks in the plane The intersection graph of S: has a vertex v for every disk D(v), has an edge between u and v if and only if the disks D(v) and D(u) intersect. (touching disks also intersect)

6. + Real World problem As mentioned earlier, ad hoc networks have no fixed network infrastructure or administrative support. The topology of the network changes dynamically as mobile nodes join or depart the network or radio links between nodes become unusable. Ensuring effective routing is one of the great challenges for ad hoc networking.

7. + Solution: Connected Dominating Set (CDS) In order to overcome the problems of effective routing in an ad hoc network,there is a need of backbone to the network through which the nodes communicate with each other. A virtual backbone called as Connected Dominating Set (CDS) is constructed to ensure effective routing in the ad hoc networks. With the help of the CDS, routing is easier and can adapt quickly to topology changes of a network. The virtual backbone can be maintained efficiently such that its good quality can be preserved all the time. The updating of the virtual backbone occurs only at a topology change.

8. + CDS Construction A connected dominating set (CDS) for a graph G(V,E) is a subset V' of V, such that each node in V - V' is adjacent to some node in V', and V' induces a connected subgraph. We take advantage of the maximal independent set (MIS) properties to construct a CDS for wireless ad hoc networks. To build a CDS, most of current algorithms first find a Maximal Independent Set (MIS) I of G and then connect all nodes in I to have a CDS.

9. + Construction A CDS of a graph G is a set D must be constructed in such a way that : Any node in D can reach any other node in D by a path that stays entirely within D. That is, D induces a connected sub-graph of G. Every vertex in G either belongs to D or is adjacent to a vertex in D. That is, D is a dominating set of G. Consider graph representation of an ad hoc network. Find maximum independent sets in the graph and mark them as in figure 2.

10. + Construction The obtained nodes in the Maximum independent set are now connected and a sub graph is formed. This infrastructure supports routing and topology control that makes routing-related tasks very complicated. A good CDS should first and foremost be small, additionally, it should have other characteristics such as robustness to node failures and low stretch

11. + Problem complexity This problem is known to be NP hard In general graphs and in UDGs as well the problem is NP hard. log approximation algorithm is best for general graphs in UDGs a constant approximation is possible This paper has this information http://ac.els-cdn.com/S0304397505005888/1-s2.0- S0304397505005888-main.pdf?_tid=a1a8a872-6f68-11e4- 8ae0- 00000aab0f01&acdnat=1416345770_cce89d216ee56b2bfa42 b93ce15bca2e http://ac.els-cdn.com/S0304397505005888/1-s2.0- S0304397505005888-main.pdf?_tid=a1a8a872-6f68-11e4- 8ae0- 00000aab0f01&acdnat=1416345770_cce89d216ee56b2bfa42 b93ce15bca2e

12. + Special Properties If all disks have the same radius, their intersection graph is a unit disk graph All planar graphs are disk graphs (varying radii) We take advantage of the maximal independent set (MIS) properties to construct a CDS for wireless ad hoc networks.

13. + References http://link.springer.com/chapter/10.1007%2F978-3-540- 24592-6_23 http://link.springer.com/chapter/10.1007%2F978-3-540- 24592-6_23 http://en.wikipedia.org/wiki/Wireless_ad_hoc_network http://en.wikipedia.org/wiki/Connected_dominating_set http://www.cis.upenn.edu/~sudipto/mypapers/cds_algorith mica.pdf http://www.cis.upenn.edu/~sudipto/mypapers/cds_algorith mica.pdf

14. + Thank you

15. + Any queries ??