Analysis of very large resistive networks using low distortion embedding

GPU-resident sparse direct linear solvers for alternating current optimal power flow analysis

The vision of Large Scale Network Analysis (LSNA) states on large amounts of network data, which are produced by social media applications like Facebook, Twitter, and the competitive domain of biological networks as well as their needs for network data extraction and analysis. That raises data management challenges which are addressed by biological, data mining and linked (web) data management communities. So far, mainly these domains were considered when identifying research topics and measuring approaches and progress. We argue that an important domain, the Business Network Management (BNM), representing business and (technical) integration data, implicitely linked and available in enterprises, has been neglected. Not only do enterprises need visibilities into their business networks, they need ad-hoc analysis capabilities on them. In this paper, we introduce BNM as domain, which comes with large scale network data. We discuss how linked business data can be made explicit by what we called Network Mining (NM) from dynamic, heterogeneous enterprise environments to combine it to a (cross-) enterprise linked business data network and state on its different facets w.r.t large network analysis and highlight challenges and opportunities.

In this paper we present a novel strategy to discover the community structure\nof (possibly, large) networks. This approach is based on the well-know concept\nof network modularity optimization. To do so, our algorithm exploits a novel\nmeasure of edge centrality, based on the k-paths. This technique allows to\nefficiently compute a edge ranking in large networks in near linear time. Once\nthe centrality ranking is calculated, the algorithm computes the pairwise\nproximity between nodes of the network. Finally, it discovers the community\nstructure adopting a strategy inspired by the well-known state-of-the-art\nLouvain method (henceforth, LM), efficiently maximizing the network modularity.\nThe experiments we carried out show that our algorithm outperforms other\ntechniques and slightly improves results of the original LM, providing reliable\nresults. Another advantage is that its adoption is naturally extended even to\nunweighted networks, differently with respect to the LM.\n

The problem of dynamic traffic grooming in optical mesh networks is usually solved by applying the Dijsktra's algorithm on an auxiliary graph. Although such algorithms can give very good performance since they have a global view of the whole network, they are very time-consuming and thus cannot be applied in large networks. Therefore, maybe for the first time, we propose a heuristic algorithm to reduce the required computations by minimizing the size of the graph. The simulations in a typical mesh network conclusively demonstrate that our algorithm is very time-efficient while performing better than existing algorithms

Bounded link prediction in very large networks

Mathematical modeling is seen as a key step to understand, predict, and control the temporal dynamics of interacting systems in such diverse areas like physics, biology, medicine, and economics. However, for large and complex systems we usually have only partial knowledge about the network, the coupling functions, and the interactions with the environment governing the dynamic behavior. This incomplete knowledge induces structural model errors which can in turn be the cause of erroneous model predictions or misguided interpretations. Uncovering the location of such structural model errors in large networks can be a daunting task for a modeler. Here, we present a data driven method to search for structural model errors and to confine their position in large and complex dynamic networks. We introduce a coherence measure for pairs of network nodes, which indicates, how difficult it is to distinguish these nodes as sources of an error. By clustering network nodes into coherence groups and inferring the cluster inputs we can decide, which cluster is affected by an error. We demonstrate the utility of our method for the C. elegans neural network, for a signal transduction model for UV-B light induced morphogenesis and for synthetic examples.

Research is on-going that examines parallel direct block-diagonal-bordered sparse linear solvers for irregular sparse matrix problems derived from electrical power system applications. Parallel block-diagonal-bordered sparse linear solvers exhibit distinct advantages when compared to current general parallel direct sparse matrix solvers. Our research shows that actual power system matrices can be readily ordered into block-diagonal-bordered form, although load imbalance becomes excessive beyond 16 processors, limiting scalability for a single parallel linear solver within an application. Nevertheless, other dimensions exist in electrical power system applications that can be exploited to efficiently make use of large-scale multi-processors. >

Approach of automatic selection of parallel sparse linear solver and tuning its parameters is discussed. Performance of linear solver is considered as function of sparse matrix features, selected sparse solver and its settings, hardware platform. Supervised learning is used to create this function and is based on gathering of empirical performance data and the following use of the support vector regression. After creating complexity function, a genetic algorithm is used to find its minimum across the solver types and settings to find locally optimal solver. Results of experiments with PETSc linear solvers are presented for several classes of sparse problems from different applications.

This paper proposes fast map building algorithm for multiple modal exteroceptive(external) sensors based on trajectory optimization. To realize localization using multiple modal exteroceptive sensors needs consistent environment maps (landmark maps). Multiple sensor SLAM (simultaneous localization and mapping) is one of solutions to build maps consistently. In implementation of SLAM, approximations of sensor model contribute to get speeded up the algorithm. However in several case, these approximations deteriorate quality of the map. This paper proposes fast and accurate map building algorithm using multiple modal sensors based on sparse linear equations solver. This algorithm needs less approximations-but computation speed is fast. In addition, application of measured data from multiple sensors to this algorithm is described.

The throughput of large wireless networks with regular topologies is analyzed under two medium-access control schemes: synchronous array method (SAM) and slotted ALOHA. The regular topologies considered are square, hexagon, and triangle. Both nonfading channels and Rayleigh fading channels are examined. Furthermore, both omnidirectional antennas and directional antennas are considered. Our analysis shows that the SAM leads to a much higher network throughput than the slotted ALOHA. The network throughput in this paper is measured in either bits-hops per second per Hertz per node or bits-meters per second per Hertz per node. The exact connection between the two measures is shown for each topology. With these two fundamental units, the network throughput shown in this paper can serve as a reliable benchmark for future works on network throughput of large networks.

In this paper, we develop a Linearizer-type approximation technique for the analysis of large multiple-chain queueing networks that contain multi-server first-come, first-served queues with service times that are chain dependent. Use is made of a waiting time approximation based on Mean Value Analysis that has recently been developed by Souza e Silva and Muntz. The storage requirements of the iterative scheme are of the order of NR2, and the computational requirements are of the order of NR3, where N is the number of nodes and R is the number of closed routing chains. In comparing the results obtained with published empirical stress test results, the accuracy of the Linearizer-type approximation is found to be acceptable. An application in which the proposed iterative technique is found to be particularly useful is in the analysis of large queueing networks with nested passive resources and many closed routing chains, of the type arising in the modeling of computer systems with multi-programming constraints and of computer-communication networks with window flow controls.

Low cost ad hoc networks like Wireless Sensor Networks (WSNs) are best suited to gather sensory information. Sensitivity of these classified information leads to the necessity of implementing security protocols during their exchange. Such implementations use cryptosystems that may suit resourceful Internet of Things (IoT) devices; but overburdens tiny sensors. Moreover most protocols assume that an adversary is well versed with all system information, barring the cryptographic keys. As such the (fixed) operational frequency bands between a given pair of nodes is assumed to be known at all times. Such a strong assumption may not be always necessary in real life deployment zones. In fact tracking an operational frequency between sensors from a range of bands may be difficult in a large network [15]; though not hard. This leads to a hard problem, i.e., to keep track of recursive switch of operational frequencies between a given pair of sensors for consecutive timestamps. We exploit hardness of this problem to achieve confidentiality of message exchange between pairs of nodes. Message to be transmitted is split using secret sharing technique [18]. Each piece is then transmitted via different bands obtained by recursive use of cryptographic hash function on initial preallocated bands. Our approach does not consume extra energy during message transmission or receipt in comparison to existing wireless systems. Storage requirement is minimized to storage of hash functions; no cryptographic key stored. Security achieved is comparable to any existing cryptosystem.

Using random graphs to model networks has a rich history. In this paper, we analyze and improve the multifractal network generators (MFNG) introduced by Palla et al. We provide a new result on the probability of subgraphs existing in graphs generated with MFNG. This allows us to quickly compute moments of an important set of graph properties, such as the expected number of edges, stars, and cliques for graphs generated using MFNG. Specifically, we show how to compute these moments in time complexity independent of the size of the graph and the number of recursive levels in the generative model. We leverage this theory to propose a new method of moments algorithm for fitting MFNG to large networks. Empirically, this new approach effectively simulates properties of several social and information networks. In terms of matching subgraph counts, our method outperforms similar algorithms used with the Stochastic Kronecker Graph model. Furthermore, we present a fast approximation algorithm to generate graph instances following the multifractal structure. The approximation scheme is an improvement over previous methods, which ran in time complexity quadratic in the number of vertices. Combined, our method of moments and fast sampling scheme provide the first scalable framework for effectively modeling large networks with MFNG.

Users of large scale network testbeds often execute experiments that require a set of nodes that behave and communicate among themselves in a reasonably stable pattern. In this work we call such a set of nodes a stable clique, and introduce a monitoring strategy that allows their detection in PlanetLab, a non-trivial task for such a large scale dynamic network. Nodes monitor each other by sampling the RTT (Round-Trip-Time) and computing its variation. Based on this data and a threshold, pairs of nodes are classified as stable or unstable. A set of graphs is generated, on which maximum sized cliques are computed. Three experiments were conducted in which hundreds of nodes were monitored for several days. Results show the unexpected behavior of some nodes, and the size of the maximum stable clique for different time windows and different thresholds.

The Sybil attack is a particularly harmful threat to sensor networks where a single sensor node illegitimately claims multiple identities. A malicious node may generate an arbitrary number of additional node identities using only one physical device. The Sybil attack can disrupt normal functioning of the sensor network, such as the multipath routing, used to explore the multiple disjoint paths between source-destination pairs. But the Sybil attack can disrupt it when a single adversary presents multiple identities, which appear on the multiple paths. Digital certificates are a way to prove identities, but they are not suitable for the sensor network because of the large computational overheads. Researchers have proposed a light-weight identity certificate method to defeat Sybil attacks, but it is not suitable for a large scale sensor network because of the huge memory usage required at each node. In this paper, we propose a light-weight Sybil attack detection method based on a hierarchical architecture in sensor networks. The proposed method can be used in a large scale sensor network, and it only uses the symmetric cryptography avoiding the use of the public key cryptography. Simulation results show that the proposed method only needs a small memory (below 140 KB) for each node (even in a large scale sensor network). In addition, the energy consumption by new identity generations within each group is low (below 60 mJ), which is much lower than the available energy at each sensor node.