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The Geodesic Broadcast Scheme for Wireless Ad Hoc Networks Dimitrios Katsaros, Ph.D.

Yannis Manolopoulos, prof.

@ Dept. InformaticsAristotle University, Thessaloniki, Greece

IEEE Mobile Distributed Computing Workshop: 26/06/2006

Presentation by: Panickos Neophytou@ Dept. of Computer ScienceUniversity of Pittsburgh, USA

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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

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Wireless communication model

r

u

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.

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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, …

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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-based methods

• Are based on the concept of identifying a small forward node set, which has the property that the nodes of this set form a connected dominating set (CDS) for the ad hoc network graph

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Relevant work – Topology control

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.

Minimum Spanning Tree (MST) and Localized Minimum Spanning Tree (LMST): Calculated with Dijkstra’s algorithm and Li, Hou & Sha, respectively.

u v

uv included

u v

uv not included

w

w

u v

uv included uv not included

vuw

sample graph

MST

LMST

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.

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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 …

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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 in the network topology due to high/moderate mobility

• not make use of “variants”, e.g., node IDs, because a (locally) best decision might not be reached (even if it does exist)

• fully exploit the locally available information in making the best decisions

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Well-known CDS 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

Wu and Li’s algorithm

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Well-known CDS algorithm

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

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

Open neighbor set N(v) = {u | u is a neighbor of v}Closed neighbor set N[v] = N(v)∪{v}

Wu and Li’s algorithm (Pruning Rules 1 & 2)

v u v u u v w

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Weaknesses of current approaches

• Some approaches can not detect all possible eliminations because ordering based on node ID prevents this. As a consequence they incur significantly excessive retransmissions

• Others rely on a lot of “local” information, for instance knowledge of k-hop neighborhood (k > 2), e.g., [WD04,WL04]

• Other methods are computationally expensive, incurring a cost of O(f2) or O(f3), where f is the maximum degree of a node of the ad hoc network, e.g., the methods reported in [WL01, WD03, DW04] and [SSZ02]

• some methods (e.g., [QVLl00,SSZ02]) do not fully exploit the compiled information; for instance, the use of the degree of a node as its priority when deciding its possible inclusion in the dominating set might not result in the best local decision

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Terminology

• A MANET is abstracted as a graph G(V,E) • An edge e=(u,v), exists if and only if u is in the

transmission range of v and vice versa. All links in the graph are bidirectional

• The network is assumed to be in a connected state• The set of neighbors of a node v is represented by

N1(v), i.e., N1(v)={u: (v,u) E}• The set of two-hop nodes of node v, i.e., the nodes

which are the neighbors of node v's neighbors except 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).

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A new measure of node importance• Let σuw=σwu denote the number of shortest paths

from u V to w V (by definition, σuu=0). • Let σuw(v) denote the number of shortest paths from

u to w that some vertex v V lies on. • We define the node 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 others on relatively short paths, or that the node v lies on considerable fractions of shortest paths connecting others. In the former case, it captures the fact of a possibly large degree of node v, and in the latter case, it captures the fact that v might have one (some) “isolated” neighbors

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The NI index in sample graphsIn 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

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The NI index in a localized algorithm• For any node v, the NI indexes of the nodes in N12(v)

calculated only for the subgraph of the 2-hop (in general, k-hop) neighborhood reveal the relative importance of the nodes in covering N12

• For a node u (of the 2-hop neighbourhood of a node v), the NI index of u will be denoted as NIv(u)

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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 moment that there exists only one) can be done using breadth-first search in O(m) time, and there exist O(n2) vertex pairs

• Fortunately, we can do better than this by making some smart 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 a graph with n vertices and m edges

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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. The NIBB algorithm is reliable, in the sense that the broadcasting packet can be disseminated to every node in the network (if it is connected)

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Evaluation setting

• Evaluation against:• WL, the basic scheme of [WL01] without the two rules

(Rule 1 and Rule 2)• WL 1+2, improved scheme incorporating these rules

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)

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Performance: vs. #nodes

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Performance: vs. avg node degree

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Performance: vs. #clusters

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Performance: vs. cluster “strength”

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Conclusions on NIBB

• The proposed protocol is based on a novel localized metric 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 nodes and linear in the number of links

• The protocol is able to reap significant performance gains, reducing the number of rebroadcasting nodes

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Conclusions on NIBB

• This metric itself is of independent importance, since it can be used: • in performing wireless (ad hoc or sensor)

network clustering• for detection of critical nodes and links for

connectivity in MANETs

• We described the protocol as a neighbour designating method, although a self-pruning version of it is also possible with the exploitation of a backoff procedure

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References

1. 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.

2. 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.

3. 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.

4. 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.

5. J. Wu and F. Dai. A generic distributed broadcast scheme in ad hoc wireless networks, IEEE Transactions on Computers, 53(10), 1343–1354, 2004.

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References

6. 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.

7. 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.

8. J. Wu and W. Lou. Extended multipoint relays to determine connected dominating sets in MANETs, IEEE Transactions on Computers, 55(3), 334–347, 2006.

9. W. Lou and J. Wu. On reducing broadcast redundancy in ad hoc wireless networks, IEEE Transactions on Mobile Computing, 1(2), 111–122, 2002.

10. N. Li, J. C. Hou, L. Sha. Design and Analysis of an MST-Based Topology Control Algorithm, IEEE INFOCOM, 2003