Hirsch M.J., Pardalos P.M., Murphey R. Dynamics of Information Systems: Theory and Applications
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96 T.N. Dinh et al.
number of nodes is no more than twice the number of modules in the original net-
work that is relative small to the number of nodes in the original network. Updating
the compact representation can introduce at most O(vol(V
C
)) new nodes and links
into the compact representation. Hence, we only need to run the algorithm A on a
compact network that size is proportional to the amount of changes |V
t
|+|E
t
|
instead of running A on the complete network G
t
(V
t
,E
t
).
For very large networks such as World Wide Web, the changing part is much
smaller than the scale of whole network. Hence, our online algorithm works much
faster than running algorithm A on individual snapshots. For dynamic biological
networks that the structures evolve rapidly, our algorithm can be applied to recom-
pute the structures whenever changes happen.
In the worst case, when all nodes are excluded from their modules i.e., V
C
=V
t
the compact representation will be exactly the original network and the running
time is equal to the running time without using the compact representation plus
the overhead O(|V
t
|+|E
t
|) for updating the compact representation. Hence, if the
network changes too much since the last time point, our online algorithm will show
no advantages compared to using algorithm A directly. In this case, what we can
do is to divide the long evolving duration into smaller ones. Note that we should
not divide the duration into too small intervals due to the overhead of updating the
compact representation and running algorithm A . Or we can simply reconstruct the
compact representation at that time point and continue the updating process.
4.5 Experimental Evaluation
We test the performance of our approach with CNM algorithm [12] that is capable
of identifying modules in networks of millions nodes. We show that our approach
is faster in significant magnitude in the case of identifying modules in evolving
networks.
We perform extensive experiments on different types of networks. We present
here results for the Terrorist network, ENRON email network [23], and the citation
network of arXiv e-print provided in the KDD Cup 2003 [24]. Time information are
extracted in different ways for each network. In the terrorist network, the network
topology after and before September 11 are directly given. In the email network, a
link between the sender and the receiver is timed to the point the email sent. Based
on timing information, we construct two snapshots of the email network at two time
points; the later is one week after the former. Two snapshots have approximately
10K links. Two snapshots of the citation networks are also constructed in a same
way. Each snapshot includes around 30K nodes and 300K links.
For each data set, modules in the first snapshot of the network are identified using
CNM algorithm [12]. Then we run our approach on the second snapshot using the
information about the modules identified by CNM. To demonstrate the effectiveness
of our approach, we compare it with the results obtained by running CNM directly
on the second snapshot.
4 A General Approach for Modules Identification in Evolving Networks 97
Fig. 4.5 The growth of the terrorist network. Nodes with same color belong to the same module.
The modular structure returned by the MIEN algorithm is only different with the result using CNM
algorithm at place of one node (Nawaf Alhazmi)
We observe that the modules identified by our approach in the second snapshots
show high similarity in the structure with the results of running CNM directly, mean-
while the computation cost is significantly reduced as the size of compact repre-
sentation is much smaller than that of the original network. Figure 4.5 shows the
modules in terrorist networks. CNM detects 4 modules in the terrorist network be-
fore September 11 and 5 modules after September 11. Our approach also returns 5
modules for the network after September 11, different from the CNM in place of
only one node. Note that our partition has a slightly higher modularity, 0.408 com-
paring to 0.407 of CNM’s. We present the modularity and running time achieved by
CNM in comparison to our approach in Table 4.1. The difference in modularity is
small suggesting our approach results are consistent with the results of the selected
algorithm A , CNM in our experiments. However, our approach shows considerable
advantage in term of running time. For example, our approach is more than 1000
times faster in the citation network. We further perform an intensive experiment on
98 T.N. Dinh et al.
Table 4.1 Performance of
our approach comparing to
CNM
CNM MIEN
QTimeQTime
Terrorist network 0.407 <1 ms 0.408 <1ms
ENRON email 0.568 50 ms 0.555 2 ms
ArXiv citation 0.617 105 s 0.615 5 ms
Fig. 4.6 Modules Identification of the Citation Network Through Time. Module structure of the
network is identified everymonth between Jan. 1997 and Jan. 2003 using CNM and MIEN al-
gorithms. The quantitative measurement modularity, running time, and size of the network are
measured at every time point
the Arxiv citation network. We identify modules in the citation network every month
in the duration between Jan. 1997 and Jan. 2003. The number of nodes and links in
the network are shown in the Figs. 4.6(a) and 4.6(b). The size of network increase
linearly and the number of links steps up slightly faster. The compact representation
shows its advantages with substantial reduction in size. The modularity and running
time at each time point is presented in Figs. 4.6(c) and 4.6(d). The running time
of the CNM algorithm increase almost linearly in term of the size of the network
4 A General Approach for Modules Identification in Evolving Networks 99
that conforms to the known average O(nlog
2
n) complexity of CNM. Because of
running on the small size compact representation, the MIEN algorithm is dramati-
cally faster as shown in Fig. 4.6(d). The graph for the modularity (Fig. 4.6(c)) is a
rough line that shows the significant changes in memberships at each time point. The
CNM produces inconsistent partition between consecutive time points. Only small
changes in the network can result in large changes in assigning nodes to modules.
On the other hand, the MIEN algorithm results in a smoother graph showing the
stability of module detection algorithm. Moreover, predicting the trend of module
structure in the network is also easier with MIEN algorithm than with the unstable
CNM.
4.6 Conclusions
In this chapter, we have analyzed the evolving of modules in networks and proposed
a general approach for adaptively updating modules in evolving networks. We show
that using modules information of the network at a given time can help ‘predicting’
effectively the modules of network later. Our algorithm is especially designed for
very large networks such as the World Wide Web in that the proportion of changes
is relatively small to the scale of the network. The approach shows enormous im-
provement in terms of running time compared to one of the fastest module identifi-
cation method, CNM, and promises tremendous applications as it can be integrated
to many different modules identification algorithms. Still the approach needs to be
further explored as it is limited to nonoverlapping modules. Our future work is to
find a more flexible and efficient representation of networks based on their modular
structures.
References
1. Macqueen, J.B.: Some methods of classification and analysis of multivariate observations.
In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability,
pp. 281–297 (1967)
2. Donetti, L., Munoz, M.A.: Detecting network communities: a new systematic and efficient
algorithm (October 2004)
3. Newman, M.E.J.: Modularity and partition in networks. In: Proceedings of the National
Academy of Sciences, pp. 8577–8582 (2005)
4. White, S., Smyth, P.: A spectral partition approach to finding communities in graph. In: SIAM
Data Mining Conference (2005)
5. Wu, F.: The Potts model. Rev. Mod. Phys. 54(1), 235 (1982)
6. Reichardt, J., Bornholdt, S.: Detecting fuzzy partition in complex networks. Phys. Rev. Lett.
93(21) (2005)
7. Reichardt, J., Bornholdt, S.: Statistical mechanics of community detection (Mar 2006)
8. Palla, G., Derenyi, I., Farkas, I., Vicsek, T.: Uncovering the overlapping partition of complex
networks in nature and society. Nature 435, 814–818 (2005)
9. Duch, J., Arenas, A.: Weighted network communities. New J. Phys. 9, 180 (2007)
100 T.N. Dinh et al.
10. Palla, G., Farkas, I., Pollner, P., Derenyi, I., Vicsek, T.: Directed network communities. New
J. Phys. 9, 186 (2007)
11. Newman, M.E.J.: Fast algorithm for detecting community structure in networks (September
2003)
12. Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks
(August 2004)
13. Duch, J., Arenas, A.: Community detection in complex networks using extremal optimization.
Phys.Rev.E72 (2005)
14. Guimera, R., Sales-Pardo, M., Amaral, L.A.N.: Modularity from fluctuations in random
graphs and complex networks (Aug 2004)
15. Hopcroft, J., Khan, O., Kulis, B., Selman, B.: Tracking evolving communities in large linked
networks. Proc. Natl. Acad. Sci. USA 101(1), 5249–5253 (2004)
16. Palla, G., Barabasi, A.: T. Vicsek. Quantifying social group evolution. Nature 446(7136),
664–667 (2007)
17. Pollner, P., Palla, G., Vicsek, T.: Preferential attachment of communities: the same principle,
but a higher level. Europhys. Lett. 73, 478 (2006)
18. Newman, M.E.J.: Analysis of weighted networks. Phys. Rev. E 70(5), 056131 (2004)
19. Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys.
Rev. E Stat. Nonlinear Soft Matter Phys. 69(2) (2004)
20. Arenas, A., Duch, J., Fernandes, A., Gomez, S.: Size reduction of complex networks preserv-
ing modularity. New J. Phys. 9, 176–180 (2007)
21. Blondel, V.D., Guillaume, J., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in
large networks. J. Stat. Mech. P10008 (2008)
22. Arenas, A., Danon, L., Diaz-Guilera, A., Gleiser, P.M., Guimera, R.: Community analysis in
social networks (2003)
23. Sun, J., Papadimitriou, S., Yu, P.S., Faloutsos, C.: Graphscope: Parameter-free mining of large
time-evolving graphs. In: KDD (August 2007)
24. Arxiv citation datasets. KDD Cup 2003, in Conjunction with the Ninth Annual ACM
SIGKDD. http://www.cs.cornell.edu/projects/kddcup/datasets.html (2003)
Chapter 5
Topology Information Control in Feedback
Based Reconfiguration Processes
Alexandru Murgu, Ian Postlethwaite, Dawei Gu,
and Chris Edwards
Summary In this paper, we describe an information control and coding framework
devoted to reconfiguration processes based on a modified perspective on the Shan-
non information where the information flows are regarded as network commodities.
This interpretation is suitable for independent multipoint-to-multipoint channels in
group communication, such as the multiple-access or broadcast channels, and al-
lows the flow control class of techniques to implement the information coding by
invoking the multi-layered protocol stack. Iterative parametric dynamic program-
ming is a good modeling candidate for describing the reconfiguration process as
multi-objective relational optimization in a multilevel fashion. At the lower process-
ing level, an auxiliary weighted power Lagrangian problem is solved using dynamic
programming associated to the topology control. The upper processing level adjusts
the value of the weighting vector in a weighted power Lagrangian formulation which
is responsible for the information control monitoring. The low level solution process
is repeated until the optimal solution of the nonseparable optimization problem is
attained by the optimal solution of an auxiliary weighted power Lagrangian prob-
lem. The application of this information control framework is to the management
traffic in self-healing networks of UAV surveillance missions.
5.1 Introduction and Motivation
One of the features of the new information organizational forms that is of great inter-
est to the military establishment is to increase the ability to adapt to a dynamic envi-
ronment through networked and/or distributed information processing technologies.
Command and control of autonomous unmanned aerial vehicles (UAVs) by remote
supervision over ad-hoc networks is a demonstrated technology, including the two-
way communication of commands to the aircraft fleets and telemetry data to the
A. Murgu (
) · I. Postlethwaite · D. Gu · C. Edwards
Department of Engineering, Control and Instrumentation Group, University of Leicester,
Leicester LE1 7RH, UK
e-mail: murgu@btinternet.com
M.J. Hirsch et al. (eds.), Dynamics of Information Systems,
Springer Optimization and Its Applications 40, DOI 10.1007/978-1-4419-5689-7_5,
© Springer Science+Business Media, LLC 2010
101
102 A. Murgu et al.
headquartered supervisors [1]. The important aspect is that the network is not con-
figured in advance, but the ad-hoc networking protocols self-organize in response
to the dynamic environment, aircraft motion, and changing network demands. The
traffic transport allows the mobile nodes to store and carry delay-tolerant data be-
tween nodes in the network. This concept enables communication in stressed or
highly dynamic networks that otherwise would not be possible and, in some cases,
can improve the network performance over relaying or direct communication. De-
centralized adaptive model free control strategies can mitigate the interference and
uncertainty effects that cannot be predicted in advance. Multivariable extremum
seeking control is applied to the problem of UAV motion control in a communica-
tion field, and such an approach can lead to improvements of communication ability
over position-based policies [2]. Networked communication demands of UAVs are
large compared to manned aircraft since telemetry, command and control, health and
safety, and payload/mission management data must be sent from multiple UAVs to
other UAVs in the vicinity. Other communication needs are related to detecting,
sensing, and obstacle avoidance requirements. This may require onboard radar (ac-
tive sensing), backhauling of image data (passive sensing), transponders, or cooper-
ative sharing of information between UAVs. Amongst the networking technologies,
meshing is a networking architecture where each node (e.g., a radio on a UAV or
coordination center) can act as a relay to forward data. Communication between a
UAV and a supervisor can take place over several hops through intermediate nodes.
The shorter range simplifies the link requirements, and the bandwidth can be reused
more frequently and thus more efficiently. UAV-to-UAV communication can be di-
rect and also benefit from the mesh routing protocols that employ additional relays
as needed to maintain communication. However, such meshing requires intermedi-
ate nodes to be present for such relaying to take place. Nodes may be required to
move specifically in order to support communication.
Reconfiguration of the UAVs working in networked environments is primarily
seen as an operational planning framework concerning the optimal functional or-
ganization and deployment of the UAVs in the battlefield during ongoing missions
in the presence of subsystem failures, battle-damage or changes of asset function-
ality as a result of multi-standard cooperative tasks [3]. The defining attribute of
the networked operational framework is concerned with the control of dynamics of
the leaving/joining entities in the network and the information processing related
to failure localization and isolation in the network. Related features such as quality
of service (QoS), resilience, control of distributed interactions, resource allocation
and location based control are the basic artifacts that characterize the operational
means by which the mission success can be guaranteed. Increasing demand for the
overall system safety and reliability calls for integrating the fault detection and iso-
lation (FDI) and fault-tolerant control (FTC) methods at the very early stages of
control design. Typically, FDI involves checking the consistency of interactions and
measurements from the real-time system operation. With FTC, the problem is con-
trolling to the maximum extent possible, the interactions and operation of the system
in the presence of faults.
The paper is organized as follows. In Sect. 5.2, we discuss the group communica-
tion paradigm for realizing the FDI/FTC system functionality based on a modified
5 Topology Information Control in Feedback Based Reconfiguration Processes 103
perspective on the Shannon information where the information flows are regarded as
network commodities. Section 5.3 is devoted to the formal statement of the recon-
figuration process as a optimization problem. A feedback information control loop
is formulated via dynamic programming as multi-objective relational optimization.
In Sect. 5.4, the topology information control solution is presented and qualitative
results are discussed. Finally, in Sect. 5.5, we draw conclusions of this research work
and discuss some perspectives on the potential future work.
5.2 Group Communication Networking
With the growth of complexity and functional extent, the network management op-
erations are steadily becoming autonomous, scalable, interoperable and adaptable
to increasingly dynamic and distributed network demands. The emergence of dis-
tributed computing environments is a major shift in designing the Operations Sup-
port System (OSS) for current services. Packet switched networks use the spanning
tree protocol (IEEE 802.1d) for routing data packets in the network. Spanning Tree
Protocol (STP) is standardized in IEEE 802.1d and it is a Layer 2 protocol that can
be implemented in switches and bridges. STP essentially uses a shortest-path ap-
proach in forming a tree that is overlaid on top of the mesh engineered networks.
Spanning trees are used primarily to avoid the formation of cycles or loops in the
network. For example, unlike IP packets, the Ethernet frames do not have a time-to-
live field and the STP prevents the formation of loops in the network by blocking
the redundant links. Correspondingly, the load is concentrated on a single link which
leaves it at risk of failures and with no load balancing mechanism [4]. The root of the
information distribution tree is chosen based on the bridge priority, and the path cost
to the root is propagated throughout so that each switch can determine the state of its
ports. Only the ports that are in the forwarding state can forward incoming frames.
This ensures a shortest single path to the root. Whenever there is a change in the
connectivity topology, switches rerun the protocol that can take 30 to 60 seconds.
At any one time, only one spanning tree dictates the network [5]. These shortcom-
ings are listed as follows: (1) Spanning trees restrict the number of ports being used
(in high-capacity networks, this restriction translates to a very low utilization of the
network); (2) STP has reduced resiliency and a very high self-healing time (30 to 60
seconds) after a link failure; (3) STP does not have any mechanisms to balance the
traffic load across the network; (4) STP does not support directly the quality of ser-
vice (QoS) mechanisms. An improvement of STP is the Rapid Spanning Tree Proto-
col (RSTP) specified in IEEE 802.1w [6, 7]. RSTP is designed to reduce the number
of port states from five in STP to three: discarding, learning, and forwarding are the
fundamental options for connectivity enhancement. Through faster aging time and
rapid transition to forwarding state, RSTP is able to reduce the convergence time
depending on the network topology. Additionally, the topology change notification
is propagated throughout the network simultaneously, unlike STP, in which a node
first notifies the root and then the root broadcasts the changes. Similar to STP, there
is only one spanning tree over the whole network. RSTP still blocks the redundant
104 A. Murgu et al.
links to ensure loop free paths leaving the network underutilized, vulnerable to fail-
ures, and with no load balancing facility. Multiple Spanning Tree Protocol (MSTP)
is defined in IEEE 802.1 [7]. MSTP uses a common spanning tree that connects all
of the regions in the topology. The regions in MSTP are multiple instances of the
spanning tree. Each instance is an instance of the RSTP. An instance of RSTP gov-
erns a region, where each region has its own regional root. The regional roots are in
turn connected to the common root that belongs to the common spanning tree. Since
MSTP runs a pure RSTP as the underlying protocol, it inherits some drawbacks of
RSTP as well. However, a failure in MSTP can be isolated into a separate region
leaving the traffic flows in other regions untouched. In addition, the administrators
can perform light load balancing manually by assigning certain flows to a specific
spanning tree. The primary motivation of this study is to allow the information al-
location flexibility of using more than one spanning tree while a flow is on its way
to the destination and describe a mathematical framework for modeling the con-
nectivity reconfiguration information to be broadcast around the faulty region of the
network. In order to avoid the formation of cycles in the network, certain restrictions
are imposed. The basic idea is to identify multiple spanning trees for management
information distribution and to index these trees sequentially in an ordered list. Typ-
ically, the Virtual Local Area Network (VLAN) identification numbers can be used
as sequences for the spanning trees. Frames of a flow start using one spanning tree
and can be switched over to the next spanning trees. None of the other variants of
spanning tree allow this flexibility in the information sequencing. This procedure
can be repeated until the cooperation information reaches the spanning tree which
has the highest identifier in the sequence, as seen in Fig. 5.1. At no point in time is
an information frame allowed to change from a spanning tree with a higher identifier
to a spanning tree with a lower identifier. A flow is switched, or crossed-over, from
one spanning tree to another spanning tree whenever one of the following events
occurs: (1) link failure; (2) load imbalance.
The main issue with the Spanning Tree Protocol for topology information distri-
bution used in a Local Area Network (LAN) is the potential conflict with the infor-
mation SPT. As shown in Fig. 5.2, suppose that the information flow dashed circuit
has two physical connections to provide redundancy in the event of a connection
or network failure. This creates the possibility of two physical loops due to the two
physical connections. The IEEE 802.1d Spanning Tree Protocols solution to heal the
problem of loops is to allow only one path by blocking and separating the redun-
dant paths [8]. Consequently, we are concerned with the modeling of a distributed
topology information control management system and the corresponding control
Fig. 5.1 UAV formation
involving three cooperating
layers
5 Topology Information Control in Feedback Based Reconfiguration Processes 105
Fig. 5.2 Physical loops of
information management
Fig. 5.3 Shannon model of point-to-point communication
processes among the cooperative network elements regarded as agents broadcasting
periodical signals to enable the network connectivity information propagation.
Let us consider a group communication network represented by a directed graph
G = (V , E), where the set of nodes is V ={v
0
,v
1
,...,v
M
} and E ⊆V ×V is the
set of edges. For the edge (v
i
,v
j
) ∈ E, node i can send messages to node j over a
discrete time memoryless channel represented as a triple (
˜
X
ij
,p
ij
(y|x),
˜
Y
ij
) having
the capacity C
ij
= max
p
ij
(x)
I(X
ij
;Y
ij
). In the channel notation,
˜
X
ij
denotes the
transmitted control symbol,
˜
Y
ij
represents the received control symbol, and p
ij
(y|x)
is the transmission error conditional probability. Also, I(X
ij
;Y
ij
) is the information
function of the transmission channel (Fig. 5.3)[9]. At the node v
i
∈ V , a random
variable U
i
, i =0, 1,...,M, is observed and drawn from a known joint probability
distribution p(U
0
,U
1
,...,U
M
). Node v
0
represents the decoder and its goal is to
process the received information such that [U
1
,...,U
M
] can be reliably reproduced
at the node v
0
. The time is discrete and every N time steps, the node v
i
collects
a block U
N
i
of control symbols. The set of all blocks [U
N
0
(k), U
N
1
(k), . . . , U
N
M
(k)]
collected at time kN, k ≥ 1, is called the control snapshot. Then, node v
i
sends a
control signal X
N
ij
to node v
j
related to a connectivity request. This control signal
depends on a window of K previous blocks of control sequences U
N
i
observed at
node v
i
and of T previously received blocks of channel outputs, corresponding to
noisy versions of the control signals sent by all nodes to the node v
i
in the previous
T signaling steps (corresponding to NT time steps).