Results 1 
5 of
5
ModularityDriven Clustering of Dynamic Graphs
, 2010
"... Maximizing the quality index modularity has become one of the primary methods for identifying the clustering structure within a graph. As contemporary networks are not static but evolve over time, traditional static approaches can be inappropriate for specific tasks. In this work we pioneer the NP ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
(Show Context)
Maximizing the quality index modularity has become one of the primary methods for identifying the clustering structure within a graph. As contemporary networks are not static but evolve over time, traditional static approaches can be inappropriate for specific tasks. In this work we pioneer the NPhard problem of online dynamic modularity maximization. We develop scalable dynamizations of the currently fastest and the most widespread static heuristics and engineer a heuristic dynamization of an optimal static algorithm. Our algorithms efficiently maintain a modularitybased clustering of a graph for which dynamic changes arrive as a stream. For our quickest heuristic we prove a tight bound on its number of operations. In an experimental evaluation on both a realworld dynamic network and on dynamic clustered random graphs, we show that the dynamic maintenance of a clustering of a changing graph yields higher modularity than recomputation, guarantees much smoother clustering dynamics and requires much lower runtimes. We conclude with giving sound recommendations for the choice of an algorithm.
Temporal Multivariate Networks
"... Abstract. Networks that evolve over time, or dynamic graphs, have been of interest to the areas of information visualization and graph drawing for many years. Typically, its the structure of the dynamic graph that evolves as vertices and edges are added or removed from the graph. In a multivariate ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Abstract. Networks that evolve over time, or dynamic graphs, have been of interest to the areas of information visualization and graph drawing for many years. Typically, its the structure of the dynamic graph that evolves as vertices and edges are added or removed from the graph. In a multivariate scenario, however, attributes play an important role and can also evolve over time. In this chapter, we characterize and survey methods for visualizing temporal multivariate networks. We also explore future applications and directions for this emerging area in the fields of information visualization and graph drawing. 1
On Dynamic Graph Partitioning and Graph Clustering using Diffusion
"... Abstract. Load balancing is an important requirement for the efficient execution of parallel numerical simulations. In particular when the simulation domain changes over time, the mapping of computational tasks to processors needs to be modified accordingly. Stateoftheart libraries for this prob ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. Load balancing is an important requirement for the efficient execution of parallel numerical simulations. In particular when the simulation domain changes over time, the mapping of computational tasks to processors needs to be modified accordingly. Stateoftheart libraries for this problem are based on graph repartitioning. They have a number of drawbacks, including the optimized metric and the difficulty of parallelizing the popular repartitioning heuristic KernighanLin (KL). Here we further explore the very promising diffusionbased graph partitioning algorithm DIBAP (Meyerhenke et al., JPDC 69(9):750–761, 2009) by adapting DIBAP to the related problem of load balancing. Experiments with graph sequences that imitate adaptive numerical simulations demonstrate the applicability and high quality of DIBAP for load balancing by repartitioning. Compared to the faster stateoftheart repartitioners PARMETIS and parallel JOSTLE, DIBAP’s solutions have partitions with significantly fewer external edges and boundary nodes and the resulting average migration volume in the important maximum norm is also the best in most cases. We also prove that one of DIBAP’s key components optimizes a relaxed version of the minimum edge cut problem. Moreover, we hint at a distributed algorithm based on ideas used in DIBAP for clustering a virtual P2P supercomputer.
1A Distributed Diffusive Heuristic for Clustering a Virtual P2P Supercomputer
"... Abstract—For the management of a virtual P2P supercomputer one is interested in subgroups of processors that can communicate with each other efficiently. The task of finding these subgroups can be formulated as a graph clustering problem, where clusters are vertex subsets that are densely connected ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract—For the management of a virtual P2P supercomputer one is interested in subgroups of processors that can communicate with each other efficiently. The task of finding these subgroups can be formulated as a graph clustering problem, where clusters are vertex subsets that are densely connected within themselves, but sparsely connected to each other. Due to resource constraints, clustering using global knowledge (i. e., knowing (nearly) the whole input graph) might not be permissible in a P2P scenario, e. g., because collecting the data is not possible or would consume a high amount of resources. That is why we present a distributed heuristic using only limited local knowledge for clustering static and dynamic graphs. Based on disturbed diffusion, our algorithm DIDIC implicitly optimizes cutrelated quality measures such as modularity. It thus settles between distributed clustering algorithms for other quality measures (e. g., energy efficiency in the field of adhocnetworking) and graph clustering algorithms optimizing cutrelated measures with global knowledge. Our experiments show the promising potential of our new approach: Although each node starts with a random cluster number, may communicate only with its direct neighbors within the graph, and requires only a small amount of additional memory space, the solutions computed by DIDIC converge to clusterings that are comparable in quality to those computed by the established nondistributed graph clustering library mcl, whose main algorithm uses global knowledge.