The Geodesic Broadcast Scheme for Wireless Ad Hoc Networks

1. The Geodesic Broadcast Scheme for Wireless Ad Hoc Networks Dimitrios Katsaros, Ph.D. Yannis Manolopoulos, prof. @ Dept. Informatics Aristotle University, Thessaloniki, Greece Presentation by: Panickos Neophytou @ Dept. of Computer Science University of Pittsburgh, USA IEEE Mobile Distributed Computing Workshop: 26/06/2006

2. Mobile Ad Hoc Networks • No wired infrastructure • Self-organized • All nodes act as routers • Broadcasted signal • Powered by battery (majority) • Mobile (maybe) • Potential Multi-hop routes

3. u r Wireless communication model Every node that falls inside the communication range r of a node u, is considered reachable (one-to-all broadcast). In practice, it is more complicated than this! We adopt this model due to its simplicity.

4. Broadcasting – Applications • Alarm signal • Route discovery in non-GPS routing • Paging • Destination search in GPS routing: • Source S broadcasts short message that will search for destination D • Destination D will route back to S with a short message location report • S will route full message to D • Location updates for routing, geocasting, …

5. Relevant work - Broadcasting • A straightforward method for implementing broadcasting is by use of flooding (reliable, but broadcast-storm problem) • probability-based methods (non-reliable) • area-based methods (reliable) • neighbour-knowledge-basedmethods • Are based on the concept of identifying a small forward node set, which has the property that the nodes of this set form aconnected dominating set (CDS) for thead hoc network graph

6. u w u v v uv not included uv included w w v v u u uv not included uv included Relevant work – Topology control Minimum Spanning Tree (MST) and Localized Minimum Spanning Tree (LMST): Calculated with Dijkstra’s algorithm and Li, Hou & Sha, respectively. MST LMST sample graph Relative Neighborhood Graph (RNG): An edge uv is included in RNG iff it is not the longest edge in any triangle uvw. Grabriel Graph (GG): An edge uv is included in GG iff the disk with diameter uv contains no other node inside it. Delaunay Triangulation (DT), Partial Delaunay Triangulation (PDT),Yao graph (YG), etc: A lot of other (variants of) geometric structures • Topology Control: Choosing a set of links from the possible ones. Not exactly our problem. So graph-theoretic concepts, than geometric ones.

7. Minimal Dominating Set • A vertex set is DS (Dominating Set) • Any other vertex connected to one DS vertex • It is CDS, if it is connected • It is MCDS if its size is minimum among CDS • Discovery of the MCDS of a graph is in NP-complete DS CDS • A lot of methods perform broadcasting with the aid of CDS …

8. Motivation for new broadcasting protocol • The protocol should: • be localized, and thus distributed • incur moderate number of message exchange among the nodes • be computationally efficient, and thus able to cope with frequent changes inthe network topology due to high/moderate mobility • not make use of “variants”, e.g., node IDs, because a (locally) bestdecision might not be reached (even if it does exist) • fully exploit the locally available information in making the best decisions

9. Well-known CDS algorithm Wu and Li’s algorithm • Each node exchanges its neighborhood information with all of its one-hop neighbors • Any node with two unconnected neighbors becomes a dominator (red) • The set of all the red nodes form a CDS

10. v u v u u v w Well-known CDS algorithm Wu and Li’s algorithm (Pruning Rules 1 & 2) A node v can be taken out from the CDS if there exists a node u such that N[v] is a subset of N[u] and the ID of v is smaller than the ID of u Open neighbor set N(v) = {u | u is a neighbor of v} Closed neighbor set N[v] = N(v)∪{v} A node u can be taken out from the CDS if u has two neighbors v and w such that N(u) is covered by N(v)∪N(w) and its ID is the smallest of the other two nodes’ IDs

11. Weaknesses of current approaches • Some approaches can not detect all possible eliminationsbecause ordering based on node ID prevents this. As a consequence they incursignificantlyexcessive retransmissions • Others rely on a lot of “local” information, forinstance knowledge of k-hop neighborhood (k > 2), e.g., [WD04,WL04] • Other methodsare computationally expensive, incurring a cost of O(f2) or O(f3), where f is themaximum degree of a node of the ad hoc network, e.g., the methodsreported in [WL01, WD03, DW04] and [SSZ02] • some methods(e.g., [QVLl00,SSZ02]) do not fully exploit the compiled information; forinstance, the use of the degree of a node as its priority when deciding itspossibleinclusion in the dominating set might not result in the best local decision

12. Terminology • A MANET is abstracted as a graph G(V,E) • An edge e=(u,v), exists if and onlyif u is in the transmission range ofv and vice versa. All links in the graph arebidirectional • The network is assumed to be in a connected state • The set of neighborsof a node v is represented by N1(v), i.e., N1(v)={u: (v,u)  E} • The set oftwo-hop nodes of node v, i.e., the nodes which are the neighbors of node v's neighborsexcept for the nodes that are the neighbors of node v, is represented by N2(v) • The combined set of one-hop and two-hop neighbors of v is denoted as N12(v).

13. A new measure of node importance • Let σuw=σwu denote the number of shortest paths from u  V tow  V (by definition, σuu=0). • Let σuw(v) denote the number ofshortest paths from u to w that some vertex v  V lies on. • We define thenode importance index NI(v) of a vertex v as: • Large values for the NI index of a node v indicate that this node v can reach otherson relatively short paths, or that the node v lies on considerable fractions of shortestpaths connecting others. In the former case, it captures the fact of a possibly large degreeof node v, and in the latter case, it captures the fact that v might have one (some) “isolated” neighbors

14. The NI index in sample graphs In parenthesis, the NI index of the respective node; i.e., 7(156): node with ID 7 has NI equal to 156. • Nodes with large NI: • Articulation nodes (in bridges), e.g., 3, 4, 7, 16, 18 • With large fanout, e.g., 14, 8, U • Therefore: geodesic nodes

15. The NI index in a localized algorithm • For any nodev, the NI indexes of the nodes in N12(v) calculatedonly for the subgraph of the 2-hop (in general, k-hop) neighborhood reveal the relative importance of the nodes in coveringN12 • For a node u (of the 2-hop neighbourhood of anode v), the NI index of u will bedenoted as NIv(u)

16. How to compute the NI index? • At a first glance, NI computation seems expensive, i.e., O(m*n2)operations in total for a 2-hop neighbourhood, which consists of n nodes and m links: • calculating the shortest path between a particular pair of vertices (assume for the momentthat there exists only one) can be done using breadth-first search in O(m) time, andthere exist O(n2) vertex pairs • Fortunately, we can do better than this by making somesmart observations. The improved algorithm (CalculateNodeImportanceIndex) is quite complicated and beyond the scope of this presentation • THEOREM. The complexity of the algorithm CalculateNodeImportanceIndex is O(n*m) for agraph with n vertices and m edges

17. Exploitation of NI in broadcasting • Design of a traditional source-dependent neighbor-designating method for broadcasting • Each node selects (designates) its neighbors, which will rebroadcast the message • The NIBB or Geodesic broadcasting algorithm • THEOREM. TheNIBB algorithm is reliable, in the sense that the broadcasting packet can bedisseminated to every node in the network (if it is connected)

18. Evaluation setting • Evaluation against: • WL, the basic scheme of [WL01] without thetwo rules (Rule 1 and Rule 2) • WL1+2, improved scheme incorporating theserules indicated • MPR, the MultiPoint Relaying method denoted as [QVL00] • SSZ, reported in [SSZ02], which was selected as a Fast Breaking Paper for October 2003 • Evaluation w.r.t.: • Number of nodes of the MANET • Average node degree (i.e., density of the MANET) • Number of clusters (implementation of a suitable network topology generator) • Strength of the clusters, called graph assortativity, (i.e., are there many bridges and nodes with large fanout)

19. Performance: vs. #nodes

20. Performance: vs. avg node degree

21. Performance: vs. #clusters

22. Performance: vs. cluster “strength”

23. Conclusions on NIBB • The proposed protocol is based on a novel localizedmetric for measuring the value of a node in “covering” the neighbourhood with its rebroadcast • The calculation of this metric is very efficient, linear in the number of nodesand linear in the number of links • The protocol is able to reap significant performance gains, reducing the number of rebroadcasting nodes

24. Conclusions on NIBB • This metric itself is of independent importance, since it can beused: • in performing wireless (ad hoc or sensor) network clustering • for detection of critical nodes and links for connectivity in MANETs • Wedescribed the protocol as a neighbour designating method, although a self-pruningversion of it is also possible with the exploitation of a backoff procedure

25. References • J. Wu, and H. Li, H. A dominating-set-based routing scheme in ad hoc wireless networks, Telecommunication Systems, 18(1–3), 13–36, 2001. • I. Stojmenovic, M. Seddigh and J.D. Zunic. Dominating sets and neighbor elimination-based broadcasting algorithms in wireless networks, IEEE Transactions on Parallel and Distributed Systems, 13(1), 14–25, 2002. • A. Qayyum, L. Viennot and A. Laouiti. Multipoint Relaying: An efficient technique for flooding in mobile wireless networks,Technical Report, Institut National de Recherche en Informatique et Automatique (INRIA), No. 3898,March,2000. • J. Wu and F. Dai. Broadcasting in ad hoc networks based on self-pruning,International Journal of Foundations of Computer Science,14(2),201–221, 2003. • J. Wu and F. Dai. A generic distributed broadcast scheme in ad hoc wireless networks,IEEE Transactions on Computers,53(10), 1343–1354, 2004.

26. References • F. Dai and J. Wu. An extended localized algorithm for connected dominating set formation in ad hoc wireless networks,IEEE Transactions on Parallel and Distributed Systems,15(10), 908–920, 2004. • F. Dai and J. Wu. Performance analysis of broadcast protocols in ad hoc networks based on self-pruning,IEEE Transactions on Parallel and Distributed Systems,15(11),1027–1040, 2004. • J. Wu and W. Lou. Extended multipoint relays to determine connected dominating sets in MANETs, IEEE Transactions on Computers,55(3), 334–347, 2006. • W. Lou and J. Wu. On reducing broadcast redundancy in ad hoc wireless networks,IEEE Transactions on Mobile Computing,1(2),111–122,2002. • N. Li, J. C. Hou, L. Sha. Design and Analysis of an MST-Based Topology Control Algorithm, IEEE INFOCOM, 2003