A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems

AN ENERGY EFFICIENT DEACTIVATION TECHNIQUE FOR REACTIVE JAMMERS IN WIRELESS SENSOR NETWORKS

In recent days, reactive jamming attack has emerged as a great security threat to wireless sensor network [WSN]. Several strategies are developed to identify the trigger nodes, whose legitimate transmission activates any reactive jammer. After identifying the trigger node, the node will be shut down to deactivate the jammer and its routing information is deleted from the routing table, then the node can’t be used again in the network. Since the node can’t be used again in the network it is one of the major drawbacks. Hence to overcome the problem, In this paper we propose a novel approach, where the identified trigger nodes are put in to the scanning mode, so that we can reuse the trigger nodes, after deactivating the jammer node in the network

Structures from Distances in Two and Three Dimensions using Stochastic Proximity Embedding

The point placement problem is to determine the locations of a set of distinct points uniquely (up to translation and reflection) by making the fewest possible pairwise distance queries of an adversary. Deterministic and randomized algorithms are available if distances are known exactly. In this thesis, we discuss a 1-round algorithm for approximate point placement in the plane in an adversarial model. The distance query graph presented to the adversary is chordal. The remaining distances are uniquely determined using the Stochastic Proximity Embedding (SPE) method due to Agrafiotis, and the layout of the points is also generated from SPE. We have also computed the distances uniquely using a distance matrix completion algorithm for chordal graphs, based on a result by Bakonyi and Johnson. The layout of the points is determined using the traditional Young- Householder approach. We compared the layout of both the method and discussed briefly inside. The modified version of SPE is proposed to overcome the highest translation embedding that the method faces when dealing with higher learning rates. We also discuss the computation of molecular structures in three-dimensional space, with only a subset of the pairwise atomic distances available. The subset of distances is obtained using the Philips model for creating artificial backbone chain of molecular structures. We have proposed the Degree of Freedom Approach to solve this problem and carried out our implementation using SPE and the Distance matrix completion Approac

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

Semantic Similarity of Spatial Scenes

The formalization of similarity in spatial information systems can unleash their functionality and contribute technology not only useful, but also desirable by broad groups of users. As a paradigm for information retrieval, similarity supersedes tedious querying techniques and unveils novel ways for user-system interaction by naturally supporting modalities such as speech and sketching. As a tool within the scope of a broader objective, it can facilitate such diverse tasks as data integration, landmark determination, and prediction making. This potential motivated the development of several similarity models within the geospatial and computer science communities. Despite the merit of these studies, their cognitive plausibility can be limited due to neglect of well-established psychological principles about properties and behaviors of similarity. Moreover, such approaches are typically guided by experience, intuition, and observation, thereby often relying on more narrow perspectives or restrictive assumptions that produce inflexible and incompatible measures. This thesis consolidates such fragmentary efforts and integrates them along with novel formalisms into a scalable, comprehensive, and cognitively-sensitive framework for similarity queries in spatial information systems. Three conceptually different similarity queries at the levels of attributes, objects, and scenes are distinguished. An analysis of the relationship between similarity and change provides a unifying basis for the approach and a theoretical foundation for measures satisfying important similarity properties such as asymmetry and context dependence. The classification of attributes into categories with common structural and cognitive characteristics drives the implementation of a small core of generic functions, able to perform any type of attribute value assessment. Appropriate techniques combine such atomic assessments to compute similarities at the object level and to handle more complex inquiries with multiple constraints. These techniques, along with a solid graph-theoretical methodology adapted to the particularities of the geospatial domain, provide the foundation for reasoning about scene similarity queries. Provisions are made so that all methods comply with major psychological findings about people’s perceptions of similarity. An experimental evaluation supplies the main result of this thesis, which separates psychological findings with a major impact on the results from those that can be safely incorporated into the framework through computationally simpler alternatives

Kernel Functions for Graph Classification

Graphs are information-rich structures, but their complexity makes them difficult to analyze. Given their broad and powerful representation capacity, the classification of graphs has become an intense area of research. Many established classifiers represent objects with vectors of explicit features. When the number of features grows, however, these vector representations suffer from typical problems of high dimensionality such as overfitting and high computation time. This work instead focuses on using kernel functions to map graphs into implicity defined spaces that avoid the difficulties of vector representations. The introduction of kernel classifiers has kindled great interest in kernel functions for graph data. By using kernels the problem of graph classification changes from finding a good classifier to finding a good kernel function. This work explores several novel uses of kernel functions for graph classification. The first technique is the use of structure based features to add structural information to the kernel function. A strength of this approach is the ability to identify specific structure features that contribute significantly to the classification process. Discriminative structures can then be passed off to domain-specific researchers for additional analysis. The next approach is the use of wavelet functions to represent graph topology as simple real-valued features. This approach achieves order-of-magnitude decreases in kernel computation time by eliminating costly topological comparisons, while retaining competitive classification accuracy. Finally, this work examines the use of even simpler graph representations and their utility for classification. The models produced from the kernel functions presented here yield excellent performance with respect to both efficiency and accuracy, as demonstrated in a variety of experimental studies

Algorithms to Explore the Structure and Evolution of Biological Networks

High-throughput experimental protocols have revealed thousands of relationships amongst genes and proteins under various conditions. These putative associations are being aggressively mined to decipher the structural and functional architecture of the cell. One useful tool for exploring this data has been computational network analysis. In this thesis, we propose a collection of novel algorithms to explore the structure and evolution of large, noisy, and sparsely annotated biological networks. We first introduce two information-theoretic algorithms to extract interesting patterns and modules embedded in large graphs. The first, graph summarization, uses the minimum description length principle to find compressible parts of the graph. The second, VI-Cut, uses the variation of information to non-parametrically find groups of topologically cohesive and similarly annotated nodes in the network. We show that both algorithms find structure in biological data that is consistent with known biological processes, protein complexes, genetic diseases, and operational taxonomic units. We also propose several algorithms to systematically generate an ensemble of near-optimal network clusterings and show how these multiple views can be used together to identify clustering dynamics that any single solution approach would miss. To facilitate the study of ancient networks, we introduce a framework called ``network archaeology'') for reconstructing the node-by-node and edge-by-edge arrival history of a network. Starting with a present-day network, we apply a probabilistic growth model backwards in time to find high-likelihood previous states of the graph. This allows us to explore how interactions and modules may have evolved over time. In experiments with real-world social and biological networks, we find that our algorithms can recover significant features of ancestral networks that have long since disappeared. Our work is motivated by the need to understand large and complex biological systems that are being revealed to us by imperfect data. As data continues to pour in, we believe that computational network analysis will continue to be an essential tool towards this end