Medical, Pharma, Engineering, Science, Technology and Business

Department of Information Management, National Changhua University of Education, #1, Jin-De Road, Changhua City 50007, Taiwan

- *Corresponding Author:
- Wan-Shiou Yang
**Email:**[email protected]

**Received date:** 27 March 2012; **Accepted date**: 28 May 2012

**Visit for more related articles at** International Journal of Swarm Intelligence and Evolutionary Computation

influence maximization; social network; ant colony optimization algorithm; e-commerce

Consumers often form complex social networks based on a multitude of different relations and interactions. A piece of information can quickly spread between individuals within the social network in the form of “word-of-mouth” communication. A company can exploit such effects of social networks when marketing a new product. For example, if a company can identify and target a relatively small number of influential consumers, this could trigger a cascade of influence by which these people will recommend the new product to their friends.

The above influence-maximization problem has been
formally defined by Domingos and Richardson [8] and
Kempe et al. [11] as follows: given a social network
and a prescribed number k, pick the* k* most “influential”
individuals that will function as the initial adopters of
a new product, so as to maximize the final number
of infected individuals, subject to a specified model of
influence diffusion. This influence-maximization problem
has been extended as follows to the problem of introducing
a new product into a market where competing products
exist [5]: given the competitor’s choice of initial adopters of technology B, maximize the spread of technology A by
choosing a set of initial adopters so as to maximize the
expected spread of technology A.

Several studies have addressed this influence-maximization problem. Kempe et al. [11] approached the problem from the perspective of two models of the diffusion of information: the threshold model and the cascade model. They showed that the underlying objective function of the problem is NP-hard and has monotonicity and submodularity properties. This led Kempe et al. [11,12] to apply a wellknown greedy approximation to solve the original problem and competitive extensions thereof. Many of the existing approaches for solving the influence-maximization problem are based on approximation algorithms and assume that the objective function is monotonic and submodular [1,4,5,6, 13,14].

However, as identified by Borodin et al. [3], there is a complex and broad family of diffusion models, and the properties of monotonicity and submodularity may not hold—in which case the greedy approach cannot be used. Therefore, in this study we borrowed from swarm intelligence— specifically the ant colony optimization (ACO) algorithm— to address the influence-maximization problem. The proposed approaches were evaluated using a coauthorship data set from the arXiv e-print (www.arxiv.org), and the obtained experimental results demonstrated that our approaches outperform two well-known benchmark heuristics.

This paper is organized as follows. Section 2 reviews related studies, and Section 3 describes the proposed approaches applying the ACO algorithm to the influencemaximization problem. The results of evaluating the proposed approaches are reported in Section 4, and Section 5 concludes with a summary of this study and a discussion of future research directions.

A social network is a set of individuals connected through socially meaningful relationships, such as friendship, coworking, or information exchange [20]. Social networks are formed when people interact with each other, and thus manifest in many aspects of everyday life. Social network theory traditionally views social relationships in terms of nodes and links [20], where the nodes are the individual actors within the networks and the links are the relationships between them. A social network plays a fundamental role as a medium for spreading information, ideas, or influence among its members [11,20]. These interactions influence decisions made by the individuals, and may allow any idea or innovation to make significant inroads into the population. Many diffusion models have been proposed for investigating how an idea or innovation spreads through a social network [3,17, 19].

Motivated by applications to marketing, Domingos
and Richardson [8] defined the influence-maximization
problem as finding a* k*-node set that maximizes the
expected number of influenced nodes at the end of the
diffusion process. The authors modeled this problem using
an arbitrary Markov random field, and provided heuristics
for identifying individuals who exert a large overall effect
on the network. Richardson and Domingos [16] extended
their models to the continuous case so that businesses
can allocate marketing funds more effectively.* K*empe et
al. [11] introduced various diffusion models such as the
threshold model and the cascade model. They showed that
determining an optimal seeding set is NP-hard, and that
a natural greedy strategy yields provable approximation
guarantees if the diffusion model has the properties of
monotonicity and submodularity. This line of research was
extended by introducing other competitors so as to produce
the most far-ranging influence [1,4,5,6,12,13,14].

As noted by Borodin et al. [3], certain diffusion models—particularly those for investigating competitive influence in social networks—may not be monotonic or submodular, and hence the original greedy approach cannot be used. In the present study we therefore exploited the search capacity of the ACO algorithm to find an (approximate) solution for the influence-maximization problem. ACO, initially proposed by Dorigo [9], is a metaheuristic developed for composing approximate solutions. ACO is inspired by observations of the collective foraging behavior in real ant colonies and represents problems as graphs, with solutions being constructed within a stochastic iterative process by adding solution components to partial solutions. Each individual ant constructs part of the solution using an artificial pheromone and heuristic information dependent on the problem. ACO has been receiving extensive attention due to its successful applications to many NP-hard combinatorial optimization problems [2, 7,10,18].

The advent of recent information techniques, especially in communication systems (e.g., email, bulletin boards, and messaging) and contacting systems [e.g., ICQ (www.icq.com), Friendster (www.friendster.com), and Facebook (www.facebook.com)], has led to a rapid growth in computer-mediated social networks. Data on the connectedness of humans can be obtained by links either explicitly stated by consumers (e.g., friendships stated on contacting systems) or implicitly inferred from previous interaction data (e.g., email logs). In this research we transform the connectedness data into a consumer’s social network and represent the network as a directed graph, where each node represents a consumer and each edge represents the connectedness between two consumers. Our view is formally described in Definition 1.

Definition 1. A social network *SN* is a directed graph
SN =* (V,E),* where *V* is the set of nodes and E is the
set of edges. Each node *V _{i} ∈ V* represents a consumer,
and each edge

We assume that a company has a fixed budget for targeting
k consumers who will trigger a cascade of influence. If *S*
is the initial set of adopters, then its influence is expressed as
the expected number of adopters at the end of the diffusion
process (see Definition 2).

**Definition 2.** Given a set S of initial adopters, the influence
of *S*, denoted as Inf(S), is the expected number of
the adopters at the end of the diffusion process, subject to
a specified diffusion model ς.

In the case that there is no competing product, our goal
is to identify a set of initial adopters *S* of size k that will
maximize the expected number of the adopters influenced
by* S* (see Definition 3).

**Definition 3** (without a competing product). Given a social
network *SN = (V,E)*, a prescribed number *k*, and a diffusion
model ς, our goal is to find a set of nodes* S, S ⊆ V* and
*|S| = k*, that maximizes Inf(*S*).

In the case that there is a competing product, we
consider the influence-maximization problem from the
follower’s perspective. Therefore, suppose the competitor’s
choice of initial adopters is *C*, our goal is to choose a set of
initial adopters that will maximize the expected spread of
our new product (see Definition 4).

Definition 4 (with a competing product). Given a social networkSN
=(V,E), a set C of initial adopters of a competing
product, a prescribed number k, and a diffusion model ς, our
goal is to find a set of nodes *S, S ⊆ V −C* and *|S| = k*, that
maximizes Inf(S).

The inspiration for ACO is the foraging behavior of real ants [10].When searching for food, ants initially explore the area surrounding their nest in a random manner. As soon as an ant finds a food source, it evaluates the quantity and quality of the food and carries some of it back to the nest. During the return trip, the ant deposits a chemical pheromone trail on the ground. The quantity of pheromone deposited depends on the quantity and quality of the food, and this will guide other ants to the food source. Indirect communication between the ants via pheromone trails enables them to find the shortest paths between their nest and food sources. This characteristic of real ant colonies is exploited in artificial ant colonies, and the ACO algorithm utilizes a graph representation to find (approximate) solutions for the target problem. We construct a complete digraph to represent the original social network (see Definition 5).

Definition 5. A complete digraph SN^{} = (V,E^{}) is
constructed to represent the original social network,
SN = (V,E). Each node in SN^{ }represents a node in SN,
and for each pair of nodes (V_{i},V_{j}) in SN, a bidirectional
edge (V_{i},V_{j}) is constructed in SN^{}.

**Figure 1(a) **shows an example of a social network of
size 7, and **Figure 1(b) **shows the corresponding complete
digraph.

Also, we transform the defined influence-maximization problem into a problem of finding a circle of prescribed length so as to maximize the expected spread from the set of nodes in the circle (see Definitions 6 and 7).

**Definition 6 **(without a competing product). Given a social
network SN = (V,E), a corresponding complete digraph
SN^{} = (V,E^{}), a prescribed number k, and a diffusion
model ς, our goal is to find a circle *S, S ⊆ V* and |*S| = k,*
on SN^{} that maximizes Inf(S) on SN.

**Definition 7 **(with a competing product). Given a social
network SN = (V,E), a corresponding complete digraph
SN^{} = (V,E^{}), a set C of initial adopters of a competing
product, a prescribed number k, and a diffusion model ς, our goal is to find a circle* S, S ⊆ V −C* and* |S| = k,* on
SN that maximizes Inf(S) on SN.

The central component of an ACO algorithm is a parameterized
probabilistic model, which is called the pheromone
model. This model is used to probabilistically generate
solutions to the problem under consideration by assembling
them using a finite set of solution components. At run-time,
ACO algorithms update the pheromone values using previously
generated solutions. The update aims to concentrate
the search within regions of the search space containing
high-quality solutions. We therefore design a basic ACO
algorithm as shown in **Figure 2**, which works as follows.
The algorithm first initializes all of the pheromone values
according to the InitializePheromoneValue() function. An
iterative process then starts, with the GenerateSolutions() function being used by all ants to probabilistically construct
solutions to the problem based on a given pheromone model
in each iteration. The EvaluateSolutions() function is used to
evaluate the quality of the constructed solutions, and some
of the solutions are used by the UpdatePheromoneValue()
function to update the pheromone before the next iteration
starts.

The InitializePheromoneValue() function is used to
initialize the pheromone values of all nodes of the
constructed complete digraph. Initially, each node has a
very small pheromone value of ε ≠ 0. A possible solution is
then created for each node by assembling the solution components
as follows. Starting node i is added first, and each
of its first-level neighbors are independently selected with
probability p; then its second-level neighbors are selected,
and so on, until k nodes are assembled in the solution.
The influence of the solution—which corresponds to the
expected number of the adopters at the end of the diffusion
process—is then evaluated. The influences of the top-m
solutions are then used as the pheromone and lay down on
all component nodes of the solution. Different solutions
may lay down pheromone values on the same nodes, in
which case all pheromone values of the same node are
summarized. The detailed algorithm is shown in **Figure 3**.

Consider the example shown in **Figure 1(b). **Suppose
each solution has three nodes and that each node has an initial
pheromone value of 1. The InitializePheromoneValue()
function creates 7 solutions since there are 7 nodes in the
complete digraph. Suppose each solution is created and the
influence of each solution is evaluated as listed in **Table 1**.
Then nodes 3, 4, and 5 will have a pheromone value of 7 and
the other nodes all have a pheromone value of 1 if only the
best solution (i.e., solution 4) lay down its pheromone.

In the iterative process, all ants probabilistically construct
solutions to the problem. In the GenerateSolutions()
function, each artificial ant generates a complete target set
by choosing the nodes according to a probabilistic statetransition
rule: an ant positioned on node *r *chooses node
*s *to move to by applying the rule given by

where q is a random number uniformly distributed in [0,1], q0 is a parameter (0 ≤ q0 ≤ 1), τ is the pheromone value, η is the heuristic value, and S is a random variable selected according to the probability distribution given by

The above state-transition rule clearly favors transitions
toward nodes with large pheromone and heuristic values.
Parameter q0 determines the relative importance of exploitation
versus exploration: every time an ant in node* r* has to
choose a node s to move to, it samples a random number
0 ≤ q ≤ 1. If q ≤ q0, the best node (according to (1)) is
chosen (exploitation); otherwise a node is chosen according
to (2) (biased exploration).

We also propose using three methods for determining the heuristic values of nodes:

(1) Degree centrality approach: degree centrality is defined
as the number of links incident upon a node [15]. Since
outdegree is often interpreted as a form of gregariousness
in a social network [15], we define the number of links that connects the node to other nodes as its degree
heuristic value. For the example shown in **Figure 1(a), **the degree heuristic value of node 4 is 4.

(2) Distance centrality approach: distance centrality is
another commonly used influence measure [15]. The
distance centrality of a node is defined as the average
distance from this node to all of the other nodes in
the graph. Again considering node 4 in **Figure 1(a), **its
distance centrality is 1.33 since its distances from nodes
1, 2, 3, 5, 6, and 7 are 2, 1, 1, 1, 1, and 2, respectively.
We define the distance heuristic value of a node as the
number of nodes minus its distance centrality.

(3) Simulated influence approach: for each node *i,* we also
use its influence* Inf(i)* as its heuristic value. However,
as described by Kempe et al. [11], it is an open question
to compute this quantity exactly. We therefore simulate
the random process to obtain a feasible estimate. Specifically,
given a particular diffusion model, we simulate
the process* N* times, and compute the average number
of influenced nodes for each node as its heuristic value.

The detailed algorithm of the GenerateSolutions() function
is shown in **Figure 4**.

First suppose the pheromone and heuristic values of all
nodes in **Figure 1 **are updated as listed in **Table 2**. Then
suppose that an artificial ant is going to choose a 3-node
solution, and that three random numbers are generated: 0.6,
0.9, and 0.5. Let *α = 1, β = 1, *and q_{0} = 0.8. For the first
node, the ant will select node 4 since this has the largest value according to (1); for the second node, since *q _{0} *< 0.9
the ant will select one node according to the probability
distribution given in (2); suppose that node 6 is selected in
this step. Finally, the ant will select node 3 since this node
has the largest value among the leaving nodes. A set of nodes
{4,6,3} is then generated as the solution.

The EvaluateSolutions() function is then used to evaluate
the performance of each solution. The performance of a
target set *S *is evaluated by computing the value of Inf(S).
Again, we obtain estimates by simulating the diffusion models
in a random process. Specifically, given a particular diffusion
model, we simulate the process *N* times, and compute
the average number of influenced nodes for each target
set. A detailed algorithm is shown in **Figure 5**.

Once all ants have found their target sets, the pheromone is updated on all nodes. In our system the global updating rule is implemented according to

Similar to the InitializePheromoneValue() function,
the influences of the top-*m* solutions are used as the
pheromone and lay down on all component nodes of the
solution, and all pheromone values of the same node are
summarized. The *ρ *parameter is the evaporation rate and is
implemented to avoid the algorithm converging too rapidly
toward a suboptimal region. The detailed algorithm of the
UpdatePheromoneValue() function is shown in **Figure 6**.

Consider the example in **Table 2**. Let *ρ* be 0.9. Suppose
there is an artificial ant who finds a 3-node solution
{3,4,6}, whose expected influence Inf() is 5, and the current
pheromone values of nodes 3, 4, and 6 are 7, 7, and
1, respectively. After updating the pheromone, these values
will be set as 11.3, 11.3, and 5.9, respectively.

The iterative process of the ACO InfluenceMaximization() function ends when some termination condition is met, such as exceeding the execution time limit or a certain ratio of the nodes being influenced. The result, which is the best target set, is then returned.

We evaluated the efficacy of the proposed approaches by
conducting experiments on a real world coauthorship data
set. The coauthorship network was compiled from the
complete list of papers on the arXiv e-print dated between
January 1, 2006 and December 31, 2010. We constructed
a coauthorship network as a directed graph in which each
node represents an author and each directed edge represents
a coauthor relationship from the author to another author
(i.e., if they have coauthored at least one paper). Each
edge (s_{i},s_{j}) in the constructed coauthorship network is
associated with a weight defined as
, where A_{i}
and A_{j} denote the sets of papers authored by si and sj ,
respectively. The coauthorship network contained 8,436
nodes representing all of the authors of the included papers, and 168,712 edges representing the coauthor relationships
between these authors.

We first evaluated the proposed approaches in the noncompetitive
case. In this case we used the original linear
threshold model [3] as the diffusion model. In this model,
each node v initially chooses a threshold* θ _{v} *∈ [0,1] that represents
the minimum fraction of active neighbors necessary
for the activation of v. Also, each directed edge (u,v) is
assigned a weight i

The first set of experiments aimed at finding the best
combinations of the *α, β*, and ρ ACO parameters of the proposed
approaches in the noncompetitive case. These experiments
used α values of 0, 1, 2, 3, and 4; *β* values of 0, 1,
2, 3, and 4; and ρ values of 1, 0.9, 0.8, 0.7, and 0.6. Each
combination of different *α, β*, and ρ values corresponded
to a single experiment. Also, the size of a target set and
random number *q _{0} *were set as 30 and 0.8, respectively. We
simulate the diffusion process N times for each targeted set
and compute the averaged influence. Previous runs indicate
that the quality of approximation after 1000 iterations is
comparable to that after 10000 or more iterations. In this and
subsequent experiments, we therefore simulate the diffusion
process 1000 times.

The results in **Table 3 **indicate that the performance of
the proposed approaches was best with *α = 1, β = 1,* and
*ρ = 0.8 *for the degree centrality heuristic; *α = 1, β = 1,* and
*ρ = 0.8* for the distance centrality heuristic; and* α = 1, β =
2*, and *ρ = 0.9* for the simulated influence heuristic. These
settings were therefore used in the subsequent experiment.
Also, it is worth noting that *α* and* β* are not equal to 0 in
these best settings, which indicates that both the pheromone
and heuristic values contribute to the performance of the
proposed approaches.

We then compared the performances of the proposed
approaches in the noncompetitive case. This experiment
used two benchmarks—the maximum degree approach
and the minimum distance approach—as baselines for our
comparisons. In the maximum degree approach, we simply
pick *k* nodes in the coauthorship network having the* k* highest degree centrality values. In the minimum distance
centrality approach, we pick *k* nodes in the coauthorship
network having the *k* lowest distance centrality values.
For our approach the three different heuristics described in
Section 3 were used. These values were averaged over 1000
runs. **Figure 7 **shows the average spread of the approximate
solutions generated by our approaches and two benchmarks
when solution size k was 10, 20, 30, 40, 50, 60, 70, 80, and
90.

It can be seen that the performance was best for our approach with the simulated influence heuristic, followed by our approach with the distance heuristic, our approach with the degree heuristic, the minimum distance approach, and the maximum degree approach (in that order). The performances of all of our three proposed approaches were better than those of the two benchmarks. The experimental results demonstrate the effectiveness of the search capacity of the ACO algorithm. Also, for the three proposed approaches, the approach using the simulated influence heuristic had the highest diffusion values. This indicates that the simulated influence heuristic was superior to the degree and distance heuristics.

We also compared the performances of the proposed
approaches in the competitive environment. In this case we
used the weight-proportional competitive linear threshold
model [3] as the diffusion model. In this model, each node
v initially chooses a threshold θ_{v} ∈ [0,1], and each directed
edge (u,v) is assigned a weight w_{u,v} ∈ [0,1]. Given sets
IA and IB of initial adopters, the diffusion process unfolds
as follows. In each step t, every inactive node v checks the
set of edges incoming from its active neighbors. If their
collective weight exceeds the threshold value, the node
becomes active. In that case the node will adopt technology
A with a probability equal to the ratio between the collective
weight of edges outgoing from A active neighbors and the
total collective weight of edges outgoing from all active
neighbors. It has been proven that the weight-proportional competitive linear threshold model does not have the
properties of monotonicity and submodularity [3].

We again attempted to find the best combinations of
parameters *α, β,* and *ρ* of the proposed approaches in the
competitive case. These experiments investigated the same
values of *α, β*, and* ρ* as used in the noncompetitive case.
At the beginning of each experiment, a set of 30 nodes was
randomly selected as the initial adopter of a competitive
product. Also, the size of a target set and random number q_{0}
were again set as 30 and 0.8, respectively. **Table 4 **lists the
best combinations of parameters *α, β,* and *ρ* of the proposed
approaches with different heuristics.

The results in **Table 4 **indicate that the performance of
the proposed approaches was best with *α = 1, β = 2,* and
*ρ = 0.9* for the degree heuristic;* α = 1, β = 2,* and* ρ = 0.8*
for the distance heuristic; and* α = 1, β = 3*, and *ρ = 0.9*
for the simulated influence heuristic. These settings were
used in the subsequent experiment. Also, comparison with
the experimental results in **Table 3 **reveals that* β* was larger
in the competitive case. It is inferred that using heuristics to
select influential nodes plays a more important role in the
competitive case.

We finally compared the performances of the proposed
approaches in the competitive case. This experiment also
used the maximum degree approach and minimum distance
approach as baselines for our comparisons. Moreover, the
size of a target set and random number q_{0} were again set as
30 and 0.8, respectively. At the beginning of the experiment,
a set of 30 nodes was randomly selected as the initial adopter
of a competitive product. **Figure 8 **shows the average spread
of the approximate solution generated by our approaches
and two benchmarks when solution size k was 10, 20, 30,
40, 50, 60, 70, 80, and 90.

**Figure 8 **shows there were only small increases in
the influenced nodes in the initial stage (i.e.,* k* = 10 and
k = 20), which is expected since the number of initial
adopters of a competitive product (i.e., 30) is larger than *k*
and hence more nodes may be influenced by the adopters
of the competitive product. The diffusion values for the
three proposed approaches were highest for the simulated
influence heuristic. The performances of all of our three
proposed approaches were again better than those of the
two benchmarks. The experimental results show that the
proposed approaches can be used even when the diffusion
model does not have the properties of monotonicity and
submodularity, and provides superior performance.

This research used the search capacity of the ACO algorithm to solve the influence-maximization problem in both noncompetitive and competitive cases. The proposed approaches use the degree centrality, distance centrality, and simulated influence methods for determining the heuristic values. Experiments revealed that the proposed approach with the simulated influence heuristic provides the best performance.

Our work could be extended in several directions, such as testing the proposed methods in different social networks and using different diffusion models. It would also be interesting to investigate other heuristic methods that could further improve the proposed approaches.

- S. Bharathi, D. Kempe, and M. Salek, Competitive influence maximization in social networks, in Proc. of the 3rd International Conference on Internet and Network Economics (WINE’07), San Diego, CA, 2007, 306–311.
- C. Blum, Ant colony optimization: introduction and recent trends, Physics of Life Reviews, 2 (2005), 353–373.
- A. Borodin, Y. Filmus, and J. Oren, Threshold models for competitive influence in social networks, in Proc. of the 6th International Conference on Internet and Network Economics (WINE’10), Stanford, CA, 2010, 539–550.
- T. Cao, X.Wu, S.Wang, and X. Hu, Maximizing influence spread in modular social networks by optimal resource allocation, Expert Systems with Applications, 38 (2011), 13128–13135.
- T. Carnes, C. Nagarajan, S. M. Wild, and A. van Zuylen, Maximizing influence in a competitive social network: a follower’s perspective, in Proc. of the 9th International Conference on Electronic Commerce (ICEC ’07), New York, 2007, 351–360.
- W. Chen, Y.Wang, and S. Yang, Efficient influence maximization in social networks, in Proc. of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD ’09), Paris, France, 2009, 199–208.
- O. Cordon, F. Herrera, and T. St¨utzle, A review on the ant colony optimization metaheuristic: basis, models and new trends, Mathware & Soft Computing, 9 (2002), 141–175.
- P. Domingos and M. Richardson, Mining the network value of customers, in Proc. of the 7th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD ’01), San Francisco, CA, 2001, 57–66.
- M. Dorigo, Optimization, learning and natural algorithms, PhD thesis, Politecnico di Milano, Milan, Italy, 1992.
- M. Dorigo and C. Blum, Ant colony optimization theory: a survey, Theoretical Computer Science, 344 (2005), 243–278.
- D. Kempe, J. Kleinberg, and E. Tardos, Maximizing the spread of influence through a social network, in Proc. of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD ’03), Washington, DC, 2003, 137–146.
- D. Kempe, J. Kleinberg, and E. Tardos, Influential nodes in a diffusion model for social networks, in Proc. of the 32nd International Conference on Automata, Languages and Programming (ICALP’05), Lisboa, Portugal, 2005, 1127–1138.
- J. Kostka, Y. A. Oswald, and R. Wattenhofer, Word of mouth: rumor dissemination in social networks, in Structural Information and Communication Complexity, vol. 5058 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, 2008, 185–196.
- E. Mossel and S. Roch, Submodularity of influence in social networks: from local to global, SIAM Journal on Computing, 39 (2010), 2176–2188.
- T. Opsahl, F. Agneessens, and J. Skvoretz, Node centrality in weighted networks: generalizing degree and shortest paths, Social Networks, 32 (2010), 245–251.
- M. Richardson and P. Domingos, Mining knowledge-sharing sites for viral marketing, in Proc. of the 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD ’02), Edmonton, Canada, 2002, 61–70.
- E. M. Roger, Diffusion of Innovations, Free Press, New York, 5th ed., 2003.
- K. Thangavel, M. Karnan, P. Jeganathan, A. P. Lakshmi, R. Sivakumar, and G. Geetharamani, Ant colony algorithms in diverse combinational optimization problems – a survey, ACSE Journal, 6 (2006), 7–26.
- T. Valente, Network Models of the Diffusion of Innovations, Hampton Press, New York, 1995.
- S. Wasserman, K. Faust, D. Iacobucci, and M. Granovetter, Social Network Analysis: Methods and Applications, Cambridge University Press, Cambridge, UK, 1994.

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- Sensor Technology
- Sensors and Actuators
- Simulation
- Social Robots
- Soft Computing
- Software Architecture
- Software Component
- Software Quality
- Studies on Computational Biology
- Swarm Robotics
- Swarm intelligence
- Systems Biology
- Telerobotics
- Web Service
- Wireless Sensor Networks
- Wireless Technology
- ZIPBEE Protocol
- swarm intelligence and robotics

- 4th Global Summit and Expo on Multimedia &
**Artificial Intelligence**

July 19-21, 2018 Rome, Italy - International Conference on
**Artificial Intelligence**,**Robotics**& IoT

August 21-22, 2018 Paris, France - 6th World Convention on
**Robots**and Deep Learning

September 10-11, 2018 Singapore City, Singapore - International Conference on Mechatronics &
**Robotics**

October 15-16, 2018 Helsinki, Finland

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