Abhishek Chakraborty

Delay Optimized Small-World Networks

Many regular networks suffer from significant network delay due to large end-to-end hop distance among source nodes and destination nodes in the network. However, the presence of a few long-ranged links transforms a regular network to a small-world network, and thus, optimizes network delay by minimizing end-to-end hop distance. In this paper, we study various deterministic long-ranged link addition strategies (e.g., based on average path length, average edge length, betweenness centrality, closeness centrality, and closeness centrality disparity) to incorporate small-world characteristics as well as to optimize average network delay of the network. Moreover, we analyze time complexity to assess the efficiency of each strategy in detail. We observe, in an N node network, that deterministic long-ranged link addition by closeness centrality disparity (CCD) strategy is only O(N2 x log N) time complex compared to other optimal long-ranged link addition strategies which take O(N4 x log N) time to achieve similar performance in the context of average network delay.

Graph Fourier transform based on directed Laplacian

In this paper, we redefine the graph Fourier transform (GFT) under the DSPG framework. We consider the Jordan eigenvectors of the directed Laplacian matrix as graph harmonics and the corresponding eigenvalues as the graph frequencies. For this purpose, we propose a shift operator based on the directed Laplacian of a graph. Based on our shift operator, we then define total variation of graph signals, which is used for frequency ordering. We achieve natural frequency ordering as well as interpretation via the proposed definition of GFT. Moreover, we show that our proposed shift operator makes linear shift invariant (LSI) filters under DSPG to become polynomials in the directed Laplacian.

The Reason Behind the Scale-Free World

Most of the real-world networks, existing in nature or observed in the world of technology, follow the power-law degree distribution, and thus, they are called scale-free networks. Barabási first observed that the scale-free network is formed by preferential attachment of new nodes in the existing network. Therefore, a new node is more likely to make a connection with a node having higher neighbor degree in the network. In this paper, we find that greedy decision making is one of the key characteristics for the transformation of a regular network to a scale-free network. Greedy decision making results in long-ranged link affinity, a phenomenon responsible for hub-node creation in the network. Moreover, we show that pure random addition of new links in a regular network does not result in a scale-free network.

Communication overhead of an OpenFlow wireless mesh network

OpenFlow is a new paradigm for running experimental protocols on production networks, and is becoming a standard reference for implementation of the software defined networking. OpenFlow can be deployed on wireless mesh network, a multi-hop relaying wireless network, for efficient network traffic management. Furthermore, various challenges such as load-balancing and control traffic management of wireless mesh networks can be effectively handled with the OpenFlow central controller. In this paper, we develop an OpenFlow wireless mesh network testbed to investigate various performance metrics (e.g., throughput, latency, CPU usage, and control traffic) for full mesh and partial mesh network topologies. Furthermore, we measure empirical controller capacity, a new metric we defined to evaluate the OpenFlow wireless mesh network controller performance. We also address various implementation challenges of real-world OpenFlow wireless mesh networks.

Load-aware routing for non-persistent small-world wireless mesh networks

Wireless mesh network is a distributed multi-hop relaying network. A large scale wireless mesh network typically has high value of network average path length which results in reduced throughput and increased delay in the network. Average path length can be reduced in the network by implementing a few long-links among the network node-pairs, and thus introduces the small-world characteristics in the wireless mesh networks. However, the conventional routing algorithms are not optimized for small-world wireless mesh networks. In this paper, we propose a Load-aware Non-Persistent small-world longlink Routing (LNPR) algorithm for small-world wireless mesh networks to achieve lower average transmission path length for data transfer sessions among a set of source-node and destination-node pairs in the network. LNPR uses load balancing strategy to better distribute the network traffic among the normal-links and the non-persistent long-links in the small-world wireless mesh networks for efficient use of long-links which are precious data transmission paths in the network. LNPR provides 58% to 95% improvement in call blocking probability and 23% to 70% in maximum load reduction with increment ranging from only 0.7% to 9% increase in average transmission path length. Small-world wireless mesh networks find numerous applications in rural and community networks for cost-effective communication.

On spectral analysis of node centralities

In this paper, we study spectral properties of node centralities such as degree, closeness, and betweenness centralities, by utilizing graph Fourier transform. We consider node centralities as signals on various networks, namely, regular, random, small-world, and scale-free networks. The spectral analysis helps us to easily understand centrality patterns over various networks. We observe spectral patterns for different network models and subsequently classify networks from the spectra of node centralities.

Conflict graph based Community Detection

Community is a networks subgraph where vertices share similar properties and reflect interesting characteristics for understanding complex networks more closely. Therefore, community structure analysis is important in understanding and exploring complex networks and helps in describing relationship among nodes in a network. However, efficiently finding communities in a complex network still remains an open problem. Since there exists numerous ways of defining a community, existing strategies have adopted different parameters to reflect varied behavior of a community structure and trying to give a coarser or finer community distribution. In this paper, we propose Conflict graph Transform based Community Detection (CTCD) strategy to improve the quality of community distributions. CTCD focuses on the impact of degree of influence to detect more favorable community partitions. A well known measure, known as Surprise, is used to evaluate and compare the quality of the community distributions obtained using CTCD. Finally, in order to study the performance and usefulness of our strategy, CTCD is applied in real-world networks. Using CTCD, we are able to obtain better community distributions with higher Surprise value in real-world networks. We observe that 1-hop and 2-hop influences improve the Surprise value in higher and lower average clustering coefficient networks, respectively. Moreover, CTCD can efficiently extract the hierarchical nature of communities within networks.

Analytical Identification of Anchor Nodes in a Small-World Network

Addition of new links in a communication network or formation of new social ties in a social network is an important way to improve the performance of the respective networks. In this letter, we consider the optimal link addition for a string network in order to minimize the average path length for the network. In prior work, the optimal addition of links to a string network has been found to lead to a network where all the added links are incident to a single anchor node. Furthermore, the position of the anchor node has been found to be fixed at either approximately 0.2 or 0.8 of the total number of nodes in the string network. In this letter, we provide an analytical justification for this observation and, in the process, identify the fixed fractional positions of the anchor nodes. We also discuss the significance of the anchor nodes for a string network, which is an important network model for several real-world communication and social networks.

An efficient heuristics to realize near-optimal small-world networks

Small-world characteristic brings down average path length of a network by adding a few long-links among network node-pairs. In a real-world deployment scenario, probabilistic long-link addition cannot guarantee optimal value of average path length for a network with limited number of long-links. In this paper, we propose a generalized heuristic, Sequential Deterministic Long-link Addition (SDLA) algorithm to incorporate small-world property for moderate sized string topology networks. Our proposed algorithm has O(k × N) time complexity compared to O(N2(k+2) × log N) for optimal and O(k × N4 × log N) for near-optimal long-link addition strategies for k long links when a string topology network of size N is concerned. Our studies show that SDLA algorithm negligibly deviates in various network properties (e.g., average path length, average clustering coefficient, and graph centralities) from the optimal and near-optimal solutions.