Balanced Overlay Networks (BON): An Overlay Technology for Decentralized Load Balancing

Efficient sampling of complex network with modified random walk strategies

Graphs are commonly used in various applications such as online social networks (OSNs), E-commerce systems and social recommender systems. Random walk sampling is often used to conduct statistical estimation over such graphs. This paper develops an algorithmic framework to reduce the mean square error of such statistical estimation. Our algorithmic framework is inspired by that the mean square error can be decomposed into a sum of the bias and variance of the estimator. More specifically, we apply the bootstrapping technique to design a bias reduction algorithm. A new feature of this bias reduction algorithm is that it allows the variance to increase whenever the bias can be further reduced. The increased variance may lead to a large mean square error of the estimator. We use multiple parallel random walks to reduce this variance such that it can be reduced to arbitrarily small by deploying a sufficient number of random walks. Our algorithmic framework enables one to attain different trade-offs between the sample complexity (i.e., number of parallel random walks) and the mean square error of the statistical estimation. Also, the proposed bias reduction algorithm is generic and can be applied to optimize a large class of random walk sampling algorithms. To demonstrate the versatility of the framework, we apply it to optimize the Metropolis random walk and simple random walk sampling. Extensive experiments confirm the effectiveness and efficiency of our proposed algorithmic framework.

For network graphs, numerous graph features are intimately linked to eigenvalues of the Laplacian matrix, such as connectivity and diameter. Thus, it is very important to solve eigenvalues of the Laplacian matrix for graphs. Similarly, for higher-order networks, eigenvalues of combinatorial Laplacian matrices are also important for invariants of graphs. However, for large-scale networks, it is difficult to calculate eigenvalues of the Laplacian matrix directly because it is either very difficult to obtain the whole network structure or requires a lot of computing resources. Therefore, this article makes the following contributions. Firstly, this paper proposes a random walk approach for estimating the bounds of the greatest eigenvalues of Laplacian matrices for large-scale networks. Considering the relationship between the spectral moments of the adjacency matrix and the closed paths in the network, we utilize the relationship between the adjacency matrix and the Laplacian matrix to establish the relationship between the Laplacian matrix and the closed paths. Then, we employ equiprobable random walks to sample the large graph to obtain the small graph. Through algebraic topology knowledge, we obtain the bounds of the largest eigenvalue of the Laplacian matrix of the large graph by using Laplacian spectral moments of the small graph. Secondly, for high-order networks, this paper proposes a method based on random walks and graph transformations. The graph transformation we propose mainly converts graphs with second-order simplices into ordinary weighted graphs, thereby transforming the problem of solving the spectral moments of the second-order combined Laplacian matrix into solving the spectral moments of the adjacency matrix. Then, we use the aforementioned random walk method to solve bounds of the greatest eigenvalue of the second-order combinatorial Laplacian matrix. Finally, by comparing the proposed method with existing algorithms in synthetic and real networks, its accuracy and superiority are demonstrated.

Resting-state functional magnetic resonance imaging (rs-fMRI) is a non-invasive neuroimaging technique that utilizes spontaneous low-frequency fluctuations of blood-oxygenation-level dependent (BOLD) signals to examine resting-state functional connectivity in the brain. In the past two decades, this technique has been increasingly utilized to investigate properties of large-scale functional neural networks as well as their alterations in various cognitive and disease states. However, much less is known about large-scale functional neural networks of the rodent brain, particularly in the awake state. Therefore, we attempted to unveil local and global functional connectivity in awake rat through a combination of seed-based analysis, independent component analysis and graph-theory analysis. In the current studies, we revealed elementary local networks and their global organization in the awake rat brain. We further systematically compared the functional neural networks in awake and anesthetized states, revealing that the rat brain was locally reorganized while maintaining global topological properties from awake to anesthetized states. Furthermore, specific neural circuitries of the rat brain were examined using resting-state fMRI. First anticorrelated functional connectivity between infralimbic cortex and amygdala were found to be evident with different preprocessing methods (global signal regression, regression of ventricular and white matter signal and no signal regression). Secondly the thalamocortical connectivity was mapped for individual thalamic groups, revealing group-specific functional cortical connections that were generally consistent with known anatomical connections in rat. In conclusion, large-scale neural networks can be robustly and reliably studied using rs-fMRI in awake rat, and with this technique we established a baseline of local and global neural networks in the awake rat brain as well as their alterations in the anesthetized condition.

Performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science, including distributed computing. In this article, we focus on the problem of sampling random walks efficiently in a distributed network and its applications. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain random walk samples. All previous algorithms that compute a random walk sample of length ℓ as a subroutine always do so naively, that is, in O (ℓ) rounds. The main contribution of this article is a fast distributed algorithm for performing random walks. We present a sublinear time distributed algorithm for performing random walks whose time complexity is sublinear in the length of the walk. Our algorithm performs a random walk of length ℓ in Õ (√ℓ D ) rounds ( Õ hides polylog n factors where n is the number of nodes in the network) with high probability on an undirected network, where D is the diameter of the network. For small diameter graphs, this is a significant improvement over the naive O (ℓ) bound. Furthermore, our algorithm is optimal within a poly-logarithmic factor as there exists a matching lower bound [Nanongkai et al. 2011]. We further extend our algorithms to efficiently perform k independent random walks in Õ (√ k ℓ D + k ) rounds. We also show that our algorithm can be applied to speedup the more general Metropolis-Hastings sampling. Our random-walk algorithms can be used to speed up distributed algorithms in applications that use random walks as a subroutine. We present two main applications. First, we give a fast distributed algorithm for computing a random spanning tree (RST) in an arbitrary (undirected unweighted) network which runs in Õ (√ mD ) rounds with high probability ( m is the number of edges). Our second application is a fast decentralized algorithm for estimating mixing time and related parameters of the underlying network. Our algorithm is fully decentralized and can serve as a building block in the design of topologically-aware networks.

It has been a challenge in systems biology to unravel relationships between structural properties and dynamic behaviors of biological networks. A Cytoscape plugin named NetDS was recently proposed to analyze the robustness-related dynamics and feed-forward/feedback loop structures of biological networks. Despite such a useful function, limitations on the network size that can be analyzed exist due to high computational costs. In addition, the plugin cannot verify an intrinsic property which can be induced by an observed result because it has no function to simulate the observation on a large number of random networks. To overcome these limitations, we have developed a novel software tool, PANET. First, the time-consuming parts of NetDS were redesigned to be processed in parallel using the OpenCL library. This approach utilizes the full computing power of multi-core central processing units and graphics processing units. Eventually, this made it possible to investigate a large-scale network such as a human signaling network with 1,609 nodes and 5,063 links. We also developed a new function to perform a batch-mode simulation where it generates a lot of random networks and conducts robustness calculations and feed-forward/feedback loop examinations of them. This helps us to determine if the findings in real biological networks are valid in arbitrary random networks or not. We tested our plugin in two case studies based on two large-scale signaling networks and found interesting results regarding relationships between coherently coupled feed-forward/feedback loops and robustness. In addition, we verified whether or not those findings are consistently conserved in random networks through batch-mode simulations. Taken together, our plugin is expected to effectively investigate various relationships between dynamics and structural properties in large-scale networks. Our software tool, user manual and example datasets are freely available at http://panet-csc.sourceforge.net/.

The short-term behavior of random walks on graphs is studied, in particular, the rate at which a random walk discovers new vertices and edges. A conjecture by Linial that the expected time to find $\cal N$ distinct vertices is $O({\cal N}^{3})$ is proved. In addition, upper bounds of $O({\cal M}^{2})$ on the expected time to traverse $\cal M$ edges and of $O(\cal M \cal N)$ on the expected time to either visit $\cal N$ vertices or traverse $\cal M$ edges (whichever comes first) are proved.

Expander properties and the cover time of random intersection graphs

Despite a large body of literature and methods devoted to the Traffic Matrix (TM) estimation problem, the inference of traffic flows volume from aggregated data still represents a major issue for network operators. Directly and frequently measuring a complete TM in a large-scale network is costly and difficult to perform due to routers limited capacities. In this paper we introduce and evaluate a new method to estimate a TM from easily available link load measurements. The method uses a novel statistical learning technique to unveil the relation between links traffic volume and origin-destination flows volume. By training a system based on Random Neural Networks, we provide a fast and accurate TM estimation tool that attains proper results without assuming any traffic model or particular behavior. Using real data from an operational backbone network, we compare this new method to the most well known and accepted TM estimation techniques, including in the evaluation some more accurate and up-to-date methods developed in recent works. Results show that current TM estimation techniques can still be improved.

From the previous chapter, one can see that software-defined networking (SDN) can be applied to large-scale distributed datacenter networks for network control and management. When this occurs, a logically centralized and physically distributed control plane is usually required. This type of control plane consists of multiple controllers communicating with one another. The collaboration of these controllers facilitates the maintenance of a global consistent view of the entire network. However, there are many new problems that must be addressed when a distributed control plane is deployed in a large-scale network; in particular, controller placement is one key problem. Controller placement refers to selecting the proper positions of the controllers to further improve the scalability and performance of the distributed control plane. In this chapter, we propose a novel placement metric for deploying multiple controllers that measures the cost when controllers with limited capacity handle request messages from switches. Then, we formulate the optimal controller placement problem as an integer linear program (ILP) and use an effective approximation algorithm to find its solution. We conduct intensive experiments based on many real topologies. Our results demonstrate that our strategy can significantly improve performance over existing strategies in terms of both cost and load balance.

Load balancing is performed to achieve the optimal use of the existing computational resources as much as possible whereby none of the resources remains idle while some other resources are being utilized. Balanced load distribution can be achieved by the immigration of the load from the source nodes which have surplus workload to the comparatively lightly loaded destination nodes. Applying load balancing during run time is called dynamic load balancing (DLB). DLB can be realized both in a direct or iterative manner according to the execution node selection. In iterative methods, the final destination node is determined through several iteration steps, while in direct methods it is selected in one step. This paper presents the randomized hydrodynamic load balancing (RHLB) method which is a hybrid method that takes advantage of both direct and iterative methods. Using random load migration as a direct method, RHLB approach intends to solve the problems derived from the exceptional instantaneous load rises, and diffuse the surplus workload to relatively free resources. Besides, using hydrodynamic approach as an iterative method, RHLB aims to consume minimum possible system resources to balance the common workload distributions. The results of the experiments designate that, RHLB outruns other iterative based methods in terms of both balance quality and the total time of the load balancing process.

The aim of this thesis is to design and implement a new Grid Resource Management methodology, where non-massive resources owners would be able to share their resources and integrate human collaboration across multiple domains regardless of network technology, operative platform or administrative domain.<br/>This thesis proposes a distributed and heuristic policy-based resource management architecture for large-scale Grids. The resource management architecture proposed herein is composed of four main building blocs: services management, resource discovery and monitoring, resource scheduling and jobs allocation and activation. The Grid Services Management (GSM) and Jobs Allocation and Activation (JAA) are supported by means of a Policy-based Grid Resource Management Architecture (PbGRMA). This architecture is able to identify service needs arising from diverse sources during the deployment and management of Grid Services, such as requirements demanded by customers, applications and network conditions. Afterwards, the PbGRMA merges these requirements into deployment policies for the corresponding Grid Services. The Grid Resource Discovery and Monitoring (GRDM) is supported by the introduction of the SNMP-based Balanced Load Monitoring Agents for Resource Scheduling (SBLOMARS), in which network and computational resources are monitored by distributed agents. This allows for a flexible, heterogeneous and scalable monitoring system. The Grid Resource Scheduling (GRS) is based on the Balanced Load Multi-Constrained Resource Scheduler (BLOMERS). This heuristic scheduler represents an alternate way of solving the inherent NP-hard problem for resource scheduling in large-scale distributed networks by means of the implementation of a Genetic Algorithm.<br/>Finally, based on the outcome of both the GRDM and GRS, the PbGRMA allocates the corresponding Grid Services by means of its interfaces with Globus ToolKit Middleware and Unix-based CLI commands along of any large-scale Grid Infrastructure. <br/>The synergy obtained by these components allows Grid administrators to exploit the available resources with predetermined levels of Quality of Service (QoS), reducing computational costs and makespan in resource scheduling while ensuring that the resource load is balanced throughout the Grid. The makespan of a schedule is the time required for all jobs to be processed when no one job could be interrupted during its execution and each node can perform at most one operation at any time.<br/>This new approach has been successfully tested in a real large-scale scenario such as Grid5000. The results presented along this Thesis show that our general solution is a reliable, flexible and scalable architecture to deploy and manage Grid Services in large-scale Grid Infrastructures. Moreover, the substitution of the heuristic algorithm approach used into the Grid Resource Scheduling (GRS) phase by other non-heuristics selection algorithms could make our solution useful in smaller Grid Infrastructures.

Using the available but limited resources of sensors more efficiently has been the recent interest in designing the routing protocols for Wireless Sensor Network (WSN). The major concern includes energy, storage and computing resources. Accordingly, we propose an adaptive energy-aware Multi-path routing protocol with load balance (AEMRP-LB). It introduces a concept named direction-angle to overcome the deficiency of broadcast and takes into account the tradeoff between the residual energy and hop count to establish multiple node-disjoint paths. The traffic load is balanced over the selected paths by using a weighted traffic scheduling algorithm considering their transmitting capacity, and then AEMRP-LB uses the advantages of Multi-path Source Routing to report the acquired data as saving the computing and storage resources of the sensors. In the scene with multiple Source-Sink pairs, AEMRP-LB can adaptively adjust the available residual energy of shared nodes so as to make reasonable use of them. The simulation results show that AEMRP-LB outperforms the two comparative schemes, and the sensors consume the energy in a more equitable way which ensures a more graceful degradation of service with time.

Localized connectivity in depression: A meta-analysis of resting state functional imaging studies

In this paper, we investigate the problem of identifying influential users in mobile social networks. Influential users are individuals with high centrality in their social-contact graphs. Traditional approaches find these users through centralized algorithms. However, the computational complexity of these algorithms is known to be very high, making them unsuitable for large-scale networks. We propose a lightweight and distributed protocol, iWander, to identify influential users through fixed-length random-walk sampling. We prove that random-walk sampling with O(logn) steps, where n is the number of nodes in a graph, comes quite close to sampling vertices approximately according to their degrees. To the best of our knowledge, we are the first to design a distributed protocol on mobile devices that leverages random walks for identifying influential users, although this technique has been used in other areas. The most attractive feature of iWander is its extremely low control-message overhead, which lends itself well to mobile applications. We evaluate the performance of iWander for two applications, targeted immunization of infectious diseases and target-set selection for information dissemination. Through extensive simulation studies using a real-world mobility trace, we demonstrate that targeted immunization using iWander achieves a comparable performance with a degree-based immunization policy that vaccinates users with a large number of contacts first, while generating only less than 1% of this policy's control messages. We also show that target-set selection based on iWander outperforms the random and degree-based selections for information dissemination in several scenarios.