Core discovery in hidden networks

Robustness and Optimization of Complex Networks: Reconstructability, Algorithms and Modeling

Interconnection Networks are widely used in many applications such as parallel and massively parallel systems, industrial applications, VLSI circuits, electronic devices and telephone switches etc. The realization of data communication in parallel system is possible all the way through interconnection networks. The whole performance of the system depends on the type of interconnection networks used. Interconnection networks with embed ability by some other interconnection structure, high resilience, simple routing, constant node degree, and scalability are highly desirable. We had introduced Octagon-Cell Networks (OCN), in the past research, which is a new interconnection network. In this research, we introduce and prove the fundamental theorems for finding the optimal path length between any pair of source and destination nodes in Octagon-Cell Network of any depth. The basic objective of these theorems (excluding Horizontal and Vertical Moves) to calculate the optimal path length, is to check whether any intermediate node exists along the optimal path, for which its line number or serial number matches with the line number or the serial number of destination node respectively. We also introduce the theorems to find the total number of horizontal lines, which is the maximum line number of a node, as well the total number of vertical lines, which is the maximum serial number of a node in Octagon-Cell Network of any depth. The theorems are proved mathematically and are tested successfully on all possible cases.

Wireless full-duplex (FD) communication allows a node to send and receive data frames simultaneously within the same frequency channel. Generally, FD transmission is effective when a pair of FD transmission nodes have the same data-transmission duration. The difference in the time duration of the frames transmitted by a pair of the nodes wastes the channel resources where more data could be transmitted. The wasted time duration decreases the system throughput in networks. To adjust the data-frame transmission duration in a pair of FD nodes, previous work has proposed the application of frame aggregation technique to FD communication. However, the work has assumed the network is in saturated condition where each node has enough number of data-frames in its queue. In real networks, each node does not always have enough data frames. For applying the frame aggregation to FD networks, therefore, it is necessary to consider the networks under non-saturated condition. This paper proposes throughput and delay analysis for FD WLANs with frame aggregation. As the contributions, this paper provides the analytical expressions of FD networks under non-saturated condition. From the proposed model, the appropriate aggregation size for both the network throughput and the delay can be derived for each offered load, packet payload size, and the number of nodes in the networks.

Survivability and performance constitute crucial quality of service (QoS) issues in future optical packet switched (OPS) networks. I take an integrated view on survivability and performance in OPS networks by presenting the extended shared packet redundancy scheme (ESPRS). The ESPRS combines shared packet redundancy with 1+1 path protection functionality. I focus on the performance of the ESPRS in different failure situations and show how the packet loss rate is influenced by the number of node- and link-disjoint paths between a node pair, the loss probability on the paths, number of failures, the relative amount of redundancy, and the size of the packet set. An analytical model of the ESPRS is provided.

For a given graph representing a transparent optical network, a given weight associated to each node pair and a given positive integer c, the Critical Node Detection problem variant addressed here is the determination of the set of c nodes that, if removed from the graph, minimizes the total weight of the node pairs that remain connected. In the context of transparent optical networks, a node pair is considered connected only if the surviving network provides it with a shortest path not higher than a given positive value T representing the optical transparent reach of the network. Moreover, the length of a path depends both on the length of its links and on its number of intermediate nodes. A path-based Integer Linear Programming model is presented together with a row generation approach to solve it. We present computational results for a real-world network topology with 50 nodes and 88 links and for \(c=2\) up to 6. The optimal results are compared with node centrality based heuristics showing that such approaches provide solutions which are far from optimal.

Network based attacks on ecommerce websites can have serious economic consequences. Hence, anomaly detection in dynamic network traffic has become an increasingly important research topic in recent years. This paper proposes a novel dynamic Graph and sparse Autoencoder based Anomaly Detection algorithm named GAAD. In GAAD, the network traffic over contiguous time intervals is first modelled as a series of dynamic bipartite graph increments. One mode projection is performed on each bipartite graph increment and the adjacency matrix derived. Columns of the resultant adjacency matrix are then used to train a sparse autoencoder to reconstruct it. The sum of squared errors between the reconstructed approximation and original adjacency matrix is then calculated. An online learning algorithm is then used to estimate a Gaussian distribution that models the error distribution. Outlier error values are deemed to represent anomalous traffic flows corresponding to possible attacks. In the experiment, a network emulator was used to generate representative ecommerce traffic flows over a time period of 225 minutes with five attacks injected, including SYN scans, host emulation and DDoS attacks. ROC curves were generated to investigate the influence of the autoencoder hyper-parameters. It was found that increasing the number of hidden nodes and their activation level, and increasing sparseness resulted in improved performance. Analysis showed that the sparse autoencoder was unable to encode the highly structured adjacency matrix structures associated with attacks, hence they were detected as anomalies. In contrast, SVD and variants, such as the compact matrix decomposition, were found to accurately encode the attack matrices, hence they went undetected.

A wireless sensor network consists of many low-cost, low-power sensor nodes, which can perform sensing, simple computation, and transmission of sensed information. Long distance transmission by sensor nodes is not energy efficient since energy consumption is a superlinear function of the transmission distance. One approach to prolonging network lifetime while preserving network connectivity is to deploy a small number of costly, but more powerful, relay nodes whose main task is communication with other sensor or relay nodes. In this paper, we assume that sensor nodes have communication range r>0, while relay nodes have communication range Rgesr, and we study two versions of relay node placement problems. In the first version, we want to deploy the minimum number of relay nodes so that, between each pair of sensor nodes, there is a connecting path consisting of relay and/or sensor nodes. In the second version, we want to deploy the minimum number of relay nodes so that, between each pair of sensor nodes, there is a connecting path consisting solely of relay nodes. We present a polynomial time 7-approximation algorithm for the first problem and a polynomial time (5+epsi)-approximation algorithm for the second problem, where epsi>0 can be any given constant

Existing work on placing additional relay nodes in wireless sensor networks to improve network connectivity typically assumes homogeneous wireless sensor nodes with an identical transmission radius. In contrast, this paper addresses the problem of deploying relay nodes to provide fault-tolerance with higher network connectivity in heterogeneous wireless sensor networks, where sensor nodes possess different transmission radii. Depending on the level of desired fault-tolerance, such problems can be categorized as: (1) full fault-tolerance relay node placement, which aims to deploy a minimum number of relay nodes to establish k (k ges 1) vertex-disjoint paths between every pair of sensor and/or relay nodes; (2) partial fault-tolerance relay node placement, which aims to deploy a minimum number of relay nodes to establish k (k ges 1) vertex-disjoint paths only between every pair of sensor nodes. Due to the different transmission radii of sensor nodes, these problems are further complicated by the existence of two different kinds of communication paths in heterogeneous wireless sensor networks, namely two-way paths, along which wireless communications exist in both directions; and one-way paths, along which wireless communications exist in only one direction. Assuming that sensor nodes have different transmission radii, while relay nodes use the same transmission radius, this paper comprehensively analyzes the range of problems introduced by the different levels of fault-tolerance (full or partial) coupled with the different types of path (one-way or two-way). Since each of these problems is NP-hard, we develop O(sigmak <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> )-approximation algorithms for both one-way and two-way partial fault-tolerance relay node placement, as well as O(sigmak <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> )-approximation algorithms for both one-way and two-way full fault-tolerance relay node placement (sigma is the best performance ratio of existing approximation algorithms for finding a minimum k-vertex connected spanning graph). To facilitate the applications in higher dimensions, we also extend these algorithms and derive their performance ratios in d-dimensional heterogeneous wireless sensor networks (d ges 3). Finally, heuristic implementations of these algorithms are evaluated via simulations.

For wireless sensor networks, monitoring large inaccessible areas where deterministic node deployment is not possible, self-organized techniques are in demand to cover an area using optimal number of nodes. In this paper, given an initial random deployment of mobile sensor nodes, we propose a simple and novel technique for self-organized node movement to satisfy the coverage of the given region of interest using a least number of nodes, such that the maximum node displacement is minimized. We present a simple centralized algorithm and also a distributed version of it for node placement. Moreover, in case of a node failure, a distributed fault recovery algorithm is proposed to replace it locally utilizing the available free nodes. Analysis, simulation, and comparison studies show that the proposed algorithms with less neighborhood information result in significant improvement in terms of average and maximum displacement of a node, rounds of communication, and number of active nodes.

The k-truss of a graph is the largest edge-induced subgraph such that every edge is contained in at least k triangles within the subgraph, where a triangle is a cycle consisting of three vertices. As a new notion of cohesive subgraphs, truss has recently attracted a lot of research attentions in the database and data mining fields. At the same time, uncertainty is an intrinsic property of massive graph data, and truss decomposition (i.e., finding all k-trusses of a graph) has become a key primitive on uncertain graphs. In this paper, we study the truss decomposition problem on uncertain graphs, that is, finding all highly probable k-trusses of an uncertain graph. We first give an formal statement of the truss decomposition problem on uncertain graphs. Then, we prove that the truss decomposition of an uncertain graph attains two elegant properties, namely uniqueness and hierarchy. We show that the truss decomposition of an uncertain graph can be found in $$O(m^{1.5}Q)$$O(m1.5Q) time by proposing an in-memory algorithm called $$\mathtt {TD_{mem}}$$TDmem, where m is the number of edges of the uncertain graph, and Q is at most the maximum number of common neighbors of the endpoints of an edge. When an uncertain graph is too large to fit into main memory, we propose an external-memory algorithm $$\mathtt {TD_{I/O}}$$TDI/O to find the truss decomposition of the uncertain graph. Extensive experiments have been carried out to evaluate the practical performance of the proposed algorithms. The experimental results verify that both $$\mathtt {TD_{mem}}$$TDmem and $$\mathtt {TD_{I/O}}$$TDI/O are efficient when an uncertain graph is small enough to fit into main memory, and that $$\mathtt {TD_{I/O}}$$TDI/O is much faster than $$\mathtt {TD_{mem}}$$TDmem when the graph is too large to fit into main memory.

We design a wireless sensor network (WSN) in terms of rate and power allocation in order to send without loss the data gathered by the nodes to a common sink. Correlation between the data and channel impairments dictate the constraints of the optimization problem. We further assume that the WSN uses off-the-shelf compression and channel coding algorithms. More precisely source and channel coding are separated and distributed source coding is performed by pairs of nodes. This raises the problem of optimally matching the nodes. We show that under all these constraints the optimal design (including rate/power allocation and matching) has polynomial complexity (in the number of nodes in the network). A closed form solution is given for the rate/power allocation, and the matching solution is readily interpreted. For noiseless channels, the optimization matches close nodes whereas, for noisy channels, there is a tradeoff between matching close nodes and matching nodes with different distances to the sink. This fact is illustrated by simulations based on empirical measures. We also show that the matching technique provides substantial gains in either storage capacity or power consumption for the WSN with regard to the case where the correlation between the nodes is not used.

Wireless Sensor Networks being limited energy source, it must function in energy efficient manner to increase the net lifetime of the network i.e. gathering more information for a longer period from the area sensed [1].Because of limited battery charge, bandwidth and nodes in the transmission range direct communication between sensing nodes to the sink is not a optimal solution for both bandwidth and energy point of view. While the LEACH protocol [2] is used as randomizing cluster heads for equal energy dissemination, the PEGASIS protocol [3] uses a chain of cluster heads participating in different rounds for transmitting data to the base station. As the base station can locate at any distances from the individual nodes, in spite of randomization and chain of cluster heads formation, each node actually dissipates a different amount of energy during its turn of transmission to the base station. DHS takes out this energy difference by data handover in specific cycles through suitable node pairing. But the main limitation of this scheme is its inapplicability to networks with large number of nodes due to the huge amount of computations, in LCMs as proposed in [6], to be carried out for determining the cycle in which a particular pair of nodes should execute a handover. This might time as well as energy consuming. Also, the expanse of self-energy in handover depending on the distance between participating nodes will become considerable if too many handovers take place. In this paper, we propose DHS-with-mean, according to which, all the nodes handover in the same mean cycle, thereby eliminating LCMs, and reducing the complexity of the computations remarkably. Also, we have proposed half DHS with mean, in which not all but only 50% of the nodes execute handovers. Finally, we have proposed 10% DHS-we have experimented with the percentage of nodes participating in handover and have found 10% to be the optimal percentage of nodes to be participating in handover for achieving the maximum network lifetime. Extensive simulations show half DHS gives on the average 3.15%, 5.52%, 3.6% and 6.03% improvement in network lifetime over and above the 10%, 12%, 17%, and 20% improvement achieved by DWeMen alone on PEGASIS, the binary model, LEACH and the direct scheme respectively. Moreover, 10% DHS achieves a further 3.15% and 4.88% improvement over half DHS, in case of PEGASIS and binary model respectively. It thus presents a near optimal solution for equal energy dissipation enhancing network lifetime, for any number of nodes

We consider the shortest paths between all pairs of nodes in a directed or undirected complete graph with edge lengths which are uniformly and independently distributed in [0, 1]. We show that die longest of these paths is bounded by c log n/n almost surely, where c is a constant and n is the number of nodes. Our bound is the best possible up to a constant. We apply this result to some well-known problems and obtain several algorithmic improvements over existing results. Our results hold with obvious modifications to random (as opposed to complete) graphs and to any distribution of weights whose density is positive and bounded from below at a neighborhood of zero. As a corollary of our proof we get a new result concerning the diameter of random graphs.

The Steiner multi-ring network design problem with revenues consists of designing node-disjoint multiple rings connected by a specific node (hub) and passing through all the nodes with high priority of service and some of the nodes with low priority of service. The number of nodes in each ring has an upper bound to assure a certain level of service. Besides the usual arc link costs, we also consider revenues between each pair of nodes in the same ring, even when they are not connected by a direct link. The objective is to minimize the difference between the total connection cost and total revenue. The problem is a generalization of the problem studied in Gouveia and Pires (Eur J Oper Res 133:21–31, 2001a) and it can also be seen as a combination of variants of two NP-Hard problems, the vehicle routing problem and the maximum edge-weighted clique problem. We introduce and discuss two types of integer linear programming formulations and propose some valid inequalities to strengthen the linear programming relaxation. Computational results are presented to evaluate the quality of the linear programming relaxation bounds associated with these formulations as well as efficiency of the models to obtain the optimal integer solutions.

Genetic networks integrate the reported interactions between genes into a global view of the transcription regulation. These networks contain, beyond each specific interaction, the information flow between genes and groups of genes that determine the cellular response to different stimuli. The flow of information in such networks is based on the structure of the directed interactions paths, and is not obviously decipherable from the number of paths between genes in the network, which grows exponentially with the number of nodes. We show here that the directional large scale information flow in genetic networks can be understood by combining the cycle (closed walk in graph theory terms) length and distance distributions. These properties are highly sensitive to the effect of flipping the direction of a small number of random edges. Here we focus on cycles composed of back and forth minimal paths between a pair of nodes that we further denote as loops. Intra-cellular networks contain a surprisingly large number of long directed loops that can carry information through multiple components of the network, and in parallel a surprisingly small number of short loops. The direction of practically every edge affects the network’s loop length distribution and the flow of information in the network. Swapping the direction of even 2.5% of the edges in regulatory genetic networks from their target to their source drastically reduces the number of long directed loops. All other properties tested here, such as the clustering coefficient or the degree distributions, are practically not affected by a swap of even 50% of edges. We propose a model of information flow to explain this hyper-sensitivity of the loop length distribution to the direction of edges.