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
1
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
2
Wireless communication model
u
r
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.
3
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, …
4
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
5
Relevant work – Topology control
MST
LMST
Minimum Spanning Tree (MST) and
Localized Minimum Spanning Tree
(LMST): Calculated with Dijkstra’s
algorithm and Li, Hou & Sha, respectively.
sample graph
w
u
u
v
Relative Neighborhood Graph (RNG): An
edge uv is included in RNG iff it is not the
longest edge in any triangle uvw.
v
uv not included
uv included
w
w
v
u
uv included
u
v
Grabriel Graph (GG): An edge uv is
included in GG iff the disk with diameter uv
contains no other node inside it.
uv not included
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
8
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
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Well-known CDS algorithm
Wu and Li’s algorithm (Pruning Rules 1 & 2)
Open neighbor set N(v) = {u | u is a neighbor of v}
Closed neighbor set N[v] = N(v)∪{v}
v
u
v
u
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
u
v
w
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
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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 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
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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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