Network topology

About: Network topology is a research topic. Over the lifetime, 52259 publications have been published within this topic receiving 1006627 citations.

Onset of traffic congestion in complex networks

Abstract: Free traffic flow on a complex network is key to its normal and efficient functioning. Recent works indicate that many realistic networks possess connecting topologies with a scale-free feature: the probability distribution of the number of links at nodes, or the degree distribution, contains a power-law component. A natural question is then how the topology influences the dynamics of traffic flow on a complex network. Here we present two models to address this question, taking into account the network topology, the information-generating rate, and the information-processing capacity of individual nodes. For each model, we study four kinds of networks: scale-free, random, and regular networks and Cayley trees. In the first model, the capacity of packet delivery of each node is proportional to its number of links, while in the second model, it is proportional to the number of shortest paths passing through the node. We find, in both models, that there is a critical rate of information generation, below which the network traffic is free but above which traffic congestion occurs. Theoretical estimates are given for the critical point. For the first model, scale-free networks and random networks are found to be more tolerant to congestion. For the second model, the congestion condition is independent of network size and topology, suggesting that this model may be practically useful for designing communication protocols.

A topology control approach for utilizing multiple channels in multi-radio wireless mesh networks

Abstract: We consider the channel assignment problem in a multi-radio wireless mesh network that involves assigning channels to radio interfaces for achieving efficient channel utilization. We propose the notion of a traffic-independent base channel assignment to ease coordination and enable dynamic, efficient and flexible channel assignment. We present a novel formulation of the base channel assignment as a topology control problem, and show that the resulting optimization problem is NP-complete. We then develop a new greedy heuristic channel assignment algorithm (termed CLICA) for finding connected, low interference topologies by utilizing multiple channels. Our extensive simulation studies show that the proposed CLICA algorithm can provide large reduction in interference (even with a small number of radios per node), which in turn leads to significant gains in both link layer and multihop performance in 802.11-based multi-radio mesh networks.

Consensus-Based Distributed Support Vector Machines

Abstract: This paper develops algorithms to train support vector machines when training data are distributed across different nodes, and their communication to a centralized processing unit is prohibited due to, for example, communication complexity, scalability, or privacy reasons. To accomplish this goal, the centralized linear SVM problem is cast as a set of decentralized convex optimization sub-problems (one per node) with consensus constraints on the wanted classifier parameters. Using the alternating direction method of multipliers, fully distributed training algorithms are obtained without exchanging training data among nodes. Different from existing incremental approaches, the overhead associated with inter-node communications is fixed and solely dependent on the network topology rather than the size of the training sets available per node. Important generalizations to train nonlinear SVMs in a distributed fashion are also developed along with sequential variants capable of online processing. Simulated tests illustrate the performance of the novel algorithms.

Consensus Computation in Unreliable Networks: A System Theoretic Approach

Abstract: This paper addresses the problem of ensuring trustworthy computation in a linear consensus network. A solution to this problem is relevant for several tasks in multi-agent systems including motion coordination, clock synchronization, and cooperative estimation. In a linear consensus network, we allow for the presence of misbehaving agents, whose behavior deviate from the nominal consensus evolution. We model misbehaviors as unknown and unmeasurable inputs affecting the network, and we cast the misbehavior detection and identification problem into an unknown-input system theoretic framework. We consider two extreme cases of misbehaving agents, namely faulty (non-colluding) and malicious (Byzantine) agents. First, we characterize the set of inputs that allow misbehaving agents to affect the consensus network while remaining undetected and/or unidentified from certain observing agents. Second, we provide worst-case bounds for the number of concurrent faulty or malicious agents that can be detected and identified. Precisely, the consensus network needs to be 2k+1 (resp. k+1) connected for k malicious (resp. faulty) agents to be generically detectable and identifiable by every well behaving agent. Third, we quantify the effect of undetectable inputs on the final consensus value. Fourth, we design three algorithms to detect and identify misbehaving agents. The first and the second algorithm apply fault detection techniques, and affords complete detection and identification if global knowledge of the network is available to each agent, at a high computational cost. The third algorithm is designed to exploit the presence in the network of weakly interconnected subparts, and provides local detection and identification of misbehaving agents whose behavior deviates more than a threshold, which is quantified in terms of the interconnection structure.