Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications Nam P . Nguyen, Thang N. Dinh, Sindhura Tokala, My T. Thai Department of Computer and Information Science and Engineering, University of Florida, USA Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 1 / 38
Motivation Better uderstanding of mobile networks in practice underlying structures organization of mobile devices Better solutions for mobile networking problems forwarding and routing methods in MANETs worm containment methods in OSNs (on mobile devices) Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 2 / 38
Motivation Better uderstanding of mobile networks in practice underlying structures organization of mobile devices Better solutions for mobile networking problems forwarding and routing methods in MANETs worm containment methods in OSNs (on mobile devices) Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 2 / 38
Communities in mobile networks forwarding and routing on MANETs sensor reprogramming in WSNs worm containment in cellular networks Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 3 / 38
Communities in mobile networks forwarding and routing on MANETs sensor reprogramming in WSNs worm containment in cellular networks Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 3 / 38
Communities in mobile networks forwarding and routing on MANETs sensor reprogramming in WSNs worm containment in cellular networks Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 3 / 38
Community structure concept(-s) are not well-defined yet high density of connetions inside each community small amount of links crossing communities Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 4 / 38
Community structure concept(-s) are not well-defined yet high density of connetions inside each community small amount of links crossing communities Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 4 / 38
Community structure concept(-s) are not well-defined yet high density of connetions inside each community small amount of links crossing communities Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 4 / 38
How do communities help in mobile networks? forwarding and routing on MANETs strategy with a constant knowledge of the network structure can actively forward messages to devices having more common ’friends’ with the destination sensor reprogramming in WSNs Sensors that are close to each other gather similar data, we want to create groups that can compute average of they results and send it further. worm containment in cellular networks send patches to critical users ( which are? ) and let them redistribute to the others Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 5 / 38
How do communities help in mobile networks? forwarding and routing on MANETs strategy with a constant knowledge of the network structure can actively forward messages to devices having more common ’friends’ with the destination sensor reprogramming in WSNs Sensors that are close to each other gather similar data, we want to create groups that can compute average of they results and send it further. worm containment in cellular networks send patches to critical users ( which are? ) and let them redistribute to the others Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 5 / 38
How do communities help in mobile networks? forwarding and routing on MANETs strategy with a constant knowledge of the network structure can actively forward messages to devices having more common ’friends’ with the destination sensor reprogramming in WSNs Sensors that are close to each other gather similar data, we want to create groups that can compute average of they results and send it further. worm containment in cellular networks send patches to critical users ( which are? ) and let them redistribute to the others Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 5 / 38
Community detection Problems: mobile networks are large and dynamic communities tend to overlap with each other What we need is a quick and efficient communities detection algorithm Idea is to create an adaptive communities detection algorithm Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 6 / 38
Community detection Problems: mobile networks are large and dynamic communities tend to overlap with each other What we need is a quick and efficient communities detection algorithm Idea is to create an adaptive communities detection algorithm Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 6 / 38
Community detection Problems: mobile networks are large and dynamic communities tend to overlap with each other What we need is a quick and efficient communities detection algorithm Idea is to create an adaptive communities detection algorithm Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 6 / 38
An adaptive algorithm input network Phase1: Basic X CS detection (B) basic communities network changes Phase2: Adap- X tive CS update udpated communities Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 7 / 38
Solution - AFOCS AFOCS a 2-phase and limited input dependent framework FOCS and AFOCS require β , the overlapping threshold , as the only input for their entire operations Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 8 / 38
Problem formulation (1) G = ( V , E ) ; | V | = N ; | E | = M - unweighted, undirected graph C = { C 1 , C 2 , . . . , C k } - network community structure ∀ 1 � i � k C ∋ C i ⊆ V , C i with its induced subgraph form a community of G for u ∈ V d u - degree of u N ( u ) - neighbours of u Com ( u ) - set of community labels for C ⊆ V , let C in , C out set of links having both endpoints, and exactly one endpoint in C, respectively Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 9 / 38
Problem formulation (1) G = ( V , E ) ; | V | = N ; | E | = M - unweighted, undirected graph C = { C 1 , C 2 , . . . , C k } - network community structure ∀ 1 � i � k C ∋ C i ⊆ V , C i with its induced subgraph form a community of G for u ∈ V d u - degree of u N ( u ) - neighbours of u Com ( u ) - set of community labels for C ⊆ V , let C in , C out set of links having both endpoints, and exactly one endpoint in C, respectively Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 9 / 38
Problem formulation (1) G = ( V , E ) ; | V | = N ; | E | = M - unweighted, undirected graph C = { C 1 , C 2 , . . . , C k } - network community structure ∀ 1 � i � k C ∋ C i ⊆ V , C i with its induced subgraph form a community of G for u ∈ V d u - degree of u N ( u ) - neighbours of u Com ( u ) - set of community labels for C ⊆ V , let C in , C out set of links having both endpoints, and exactly one endpoint in C, respectively Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 9 / 38
Problem formulation (1) G = ( V , E ) ; | V | = N ; | E | = M - unweighted, undirected graph C = { C 1 , C 2 , . . . , C k } - network community structure ∀ 1 � i � k C ∋ C i ⊆ V , C i with its induced subgraph form a community of G for u ∈ V d u - degree of u N ( u ) - neighbours of u Com ( u ) - set of community labels for C ⊆ V , let C in , C out set of links having both endpoints, and exactly one endpoint in C, respectively Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 9 / 38
Problem formulation (1) G = ( V , E ) ; | V | = N ; | E | = M - unweighted, undirected graph C = { C 1 , C 2 , . . . , C k } - network community structure ∀ 1 � i � k C ∋ C i ⊆ V , C i with its induced subgraph form a community of G for u ∈ V d u - degree of u N ( u ) - neighbours of u Com ( u ) - set of community labels for C ⊆ V , let C in , C out set of links having both endpoints, and exactly one endpoint in C, respectively Krzysztof Gogolewski Overlapping Communities in Dynamic Networks: Their Detection and Mobile Applications 5 listopada 2012 9 / 38
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