Defective Coloring on Classes of Perfect Graphs

In Defective Coloring we are given a graph $G$ and two integers $\chi_d$, $\Delta^*$ and are asked if we can $\chi_d$-color $G$ so that the maximum degree induced by any color class is at most $\Delta^*$. We show that this natural generalization of Coloring is much harder on several basic graph classes. In particular, we show that it is NP-hard on split graphs, even when one of the two parameters $\chi_d$, $\Delta^*$ is set to the smallest possible fixed value that does not trivialize the problem ($\chi_d = 2$ or $\Delta^* = 1$). Together with a simple treewidth-based DP algorithm this completely determines the complexity of the problem also on chordal graphs. We then consider the case of cographs and show that, somewhat surprisingly, Defective Coloring turns out to be one of the few natural problems which are NP-hard on this class. We complement this negative result by showing that Defective Coloring is in P for cographs if either $\chi_d$ or $\Delta^*$ is fixed; that it is in P for trivially perfect graphs; and that it admits a sub-exponential time algorithm for cographs when both $\chi_d$ and $\Delta^*$ are unbounded

Defective and Clustered Graph Colouring

Consider the following two ways to colour the vertices of a graph where the requirement that adjacent vertices get distinct colours is relaxed. A colouring has "defect" $d$ if each monochromatic component has maximum degree at most $d$. A colouring has "clustering" $c$ if each monochromatic component has at most $c$ vertices. This paper surveys research on these types of colourings, where the first priority is to minimise the number of colours, with small defect or small clustering as a secondary goal. List colouring variants are also considered. The following graph classes are studied: outerplanar graphs, planar graphs, graphs embeddable in surfaces, graphs with given maximum degree, graphs with given maximum average degree, graphs excluding a given subgraph, graphs with linear crossing number, linklessly or knotlessly embeddable graphs, graphs with given Colin de Verdi\`ere parameter, graphs with given circumference, graphs excluding a fixed graph as an immersion, graphs with given thickness, graphs with given stack- or queue-number, graphs excluding $K_t$ as a minor, graphs excluding $K_{s,t}$ as a minor, and graphs excluding an arbitrary graph $H$ as a minor. Several open problems are discussed.Comment: This is a preliminary version of a dynamic survey to be published in the Electronic Journal of Combinatoric

Improper colouring of weighted grid and hexagonal graphs

International audienceWe study a weighted improper colouring problem motivated by a frequency allocation problem. It consists of associating to each vertex a set of p(v) (weight) distinct colours (frequencies), such that the set of vertices having a given colour induces a graph of degree at most k (the case k = 0 corresponds to a proper coloring). The objective is to minimize the number of colors. We propose approximation algorithms to compute such colouring for general graphs. We apply these to obtain good approximation ratio for grid and hexagonal graphs. Furthermore we give exact results for the 2-dimensional grid and the triangular lattice when the weights are all the same

Improper colouring of weighted grid and hexagonal graphs

We study a weighted improper colouring problem on graph, and in particular of triangular and hexagonal grid graphs. This problem is motivated by a frequency allocation problem. We propose approximation algorithms to compute such colouring

On the optimization problems in multiaccess communication systems

In a communication system, the bandwidth is often a primary resource. In order to support concurrent access by numerous users in a network, this finite and expensive resource must be shared among many independent contending users. Multi-access protocols control this access of the resource among users to achieve its efficient utilization, satisfy connectivity requirements and resolve any conflict among the contending users. Many optimization problems arise in designing a multi-access protocol. Among these, there is a class of optimization problems known as NP-complete, and no polynomial algorithm can possibly solve them. Conventional methods may not be efficient arid often produce poor solutions. In this dissertation, we propose a neural network-based algorithm for solving NP-complete problems encountered in multi-access communication systems. Three combinatorial optimization problems have been solved by the proposed algorithms; namely, frame pattern design in integrated TDMA communication networks, optimal broadcast scheduling in multihop packet radio networks, and optimal channel assignment in FDM A mobile communication networks. Numerical studies have shown encouraging results in searching for the global optimal solutions by using this algorithm. The determination of the related parameters regarding convergence and solution quality is investigated in this dissertation. Performance evaluations and comparisons with other algorithms have been performed

Theory and design of portable parallel programs for heterogeneous computing systems and networks

A recurring problem with high-performance computing is that advanced architectures generally achieve only a small fraction of their peak performance on many portions of real applications sets. The Amdahl\u27s law corollary of this is that such architectures often spend most of their time on tasks (codes/algorithms and the data sets upon which they operate) for which they are unsuited. Heterogeneous Computing (HC) is needed in the mid 90\u27s and beyond due to ever increasing super-speed requirements and the number of projects with these requirements. HC is defined as a special form of parallel and distributed computing that performs computations using a single autonomous computer operating in both SIMD and MIMD modes, or using a number of connected autonomous computers. Physical implementation of a heterogeneous network or system is currently possible due to the existing technological advances in networking and supercomputing. Unfortunately, software solutions for heterogeneous computing are still in their infancy. Theoretical models, software tools, and intelligent resource-management schemes need to be developed to support heterogeneous computing efficiently. In this thesis, we present a heterogeneous model of computation which encapsulates all the essential parameters for designing efficient software and hardware for HC. We also study a portable parallel programming tool, called Cluster-M, which implements this model. Furthermore, we study and analyze the hardware and software requirements of HC and show that, Cluster-M satisfies the requirements of HC environments

Ordonnancement de l'activité des noeuds dans les réseaux ad hoc et les réseaux de capteurs sans fil

National audienceL'efficacité énergétique est une exigence majeure pour les réseaux sans fil où certains noeuds opèrent sur batterie. L'ordonnancement de l'activité des noeuds permet de distinguer périodes actives où la communication radio est possible et périodes inactives où la radio est arrêtée. Cet ordonnancement contribue largement à améliorer l'efficacité énergétique : d'une part en évitant les collisions entre transmissions conflictuelles et donc les retransmissions associées et d'autre part en permettant aux noeuds non concernés par la transmission de dormir pour économiser leur énergie. Parmi les solutions possibles, nous étudierons plus particulièrement le coloriage des noeuds. Après avoir défini le problème et ses différentes déclinaisons, nous donnerons sa complexité et proposerons SERENA, un algorithme de coloriage distribué qui s'adapte à la collecte de données. Nous présenterons OSERENA, l'optimisation de SERENA pour les réseaux denses et son utilisation dans le réseau de capteurs sans fil OCARI. Lorsque les noeuds ont des charges de trafic fortement hétérogènes, il devient plus intéressant d'effectuer une assignation de slots. Disposer d'un accès au médium multicanal et d'un puits multi-interfaces permet de gagner en nombre de slots nécessaires à la collecte de données, de réduire les interférences et d'améliorer la résistance aux perturbations. Nous présenterons une formalisation en ILP (Integer Linear Programming) du problème d'assignation de slots visant à minimiser le nombre de slots en profitant d'un environnement mono ou multicanal et d'un puits mono ou multi-interfaces. Nous donnerons des bornes théoriques sur le nombre optimal de slots dans diverses configurations et divers environnements (mono ou multicanal, puits mono ou multi-interfaces). Nous présenterons MODESA un algorithme centralisé d'allocatoion conjointe de canaux et slots temporels. Nous terminerons par quelques questions ouvertes

Interference cancellation and Resource Allocation approaches for Device-to-Device Communications

Network assisted Device-to-Device (D2D) communication as an underlay to cellular spectrum has attracted much attention in mobile network standards for local area connectivity as a means to improve the cellular spectrum utilization and to reduce the energy consumption of User Equipments (UEs). The D2D communication uses resources of the underlying mobile network which results in different interference scenarios. These include interference from cellular to D2D link, D2D to cellular link and interference among D2D links when multiple D2D links share common resources. In this thesis, an orthogonal precoding interference cancellation method is initially presented to reduce the cellular to D2D and D2D to cellular interferences when the cellular channel resources are being shared by a single D2D link. Three different scenarios have been considered when establishing a D2D communication along with a Base Station-to-UE communication. The proposed method is analytically evaluated in comparison with the conventional precoding matrix allocation method in terms of ergodic capacity. This method is then extended for a cluster based multi-link D2D scenario where interference between D2D pairs also exists in addition to the other two interference scenarios. In this work, cluster denotes a group of devices locally communicating through multi-link D2D communications sharing the same radio resources of the Cluster Head. Performance of the proposed method is evaluated and compared for different resource sharing modes. The analyses illustrate the importance of cluster head in each cluster to save the battery life of devices in that cluster. The outage probability is considered as a performance evaluation matrix for guaranteeing QoS constrain of communication links. Hence, the mathematical expressions for outage probability of the proposed method for single-link and multi-link D2D communications are presented and compared with an existing interference cancellation technique. To execute the cluster based interference cancellation approach, a three-step resource allocation scheme is then proposed. It first performs a mode selection procedure to choose the transmission mode of each UEs. Then a clustering scheme is developed to group the links that can share a common resource to improve the spectral efficiency. For the selection of suitable cellular UEs for each cluster whose resource can be shared, a cluster head selection algorithm is also developed. Maximal residual energy and minimal transmit power have been considered as parameters for the cluster head selection scheme. Finally, the expression for maximum number of links that the radio resource of shared UE can support is analytically derived. The performance of the proposed scheme is evaluated using a WINNER II A1 indoor office model. The performance of D2D communication practically gets limited due to large distance and/or poor channel conditions between the D2D transmitter and receiver. To overcome these issues, a relay-assisted D2D communication is introduced in this thesis where a device relaying is an additional transmission mode along with the existing cellular and D2D transmission modes. A transmission mode assignment algorithm based on the Hungarian algorithm is then proposed to improve the overall system throughput. The proposed algorithm tries to solve two problems: a suitable transmission mode selection for each scheduled transmissions and a device selection for relaying communication between user equipments in the relay transmission mode. Simulation results showed that our proposed algorithm improves the system performance in terms of the overall system throughput and D2D data rate in comparison with traditional D2D communication schemes

Channel assembling and resource allocation in multichannel spectrum sharing wireless networks

Submitted in fulfilment of the academic requirements for the degree of Doctor of Philosophy (Ph.D.) in Engineering, in the School of Electrical and Information Engineering, Faculty of Engineering and the Built Environment, at the University of the Witwatersrand, Johannesburg, South Africa, 2017The continuous evolution of wireless communications technologies has increasingly imposed a burden on the use of radio spectrum. Due to the proliferation of new wireless networks applications and services, the radio spectrum is getting saturated and becoming a limited resource. To a large extent, spectrum scarcity may be a result of deficient spectrum allocation and management policies, rather than of the physical shortage of radio frequencies. The conventional static spectrum allocation has been found to be ineffective, leading to overcrowding and inefficient use. Cognitive radio (CR) has therefore emerged as an enabling technology that facilitates dynamic spectrum access (DSA), with a great potential to address the issue of spectrum scarcity and inefficient use. However, provisioning of reliable and robust communication with seamless operation in cognitive radio networks (CRNs) is a challenging task. The underlying challenges include development of non-intrusive dynamic resource allocation (DRA) and optimization techniques. The main focus of this thesis is development of adaptive channel assembling (ChA) and DRA schemes, with the aim to maximize performance of secondary user (SU) nodes in CRNs, without degrading performance of primary user (PU) nodes in a primary network (PN). The key objectives are therefore four-fold. Firstly, to optimize ChA and DRA schemes in overlay CRNs. Secondly, to develop analytical models for quantifying performance of ChA schemes over fading channels in overlay CRNs. Thirdly, to extend the overlay ChA schemes into hybrid overlay and underlay architectures, subject to power control and interference mitigation; and finally, to extend the adaptive ChA and DRA schemes for multiuser multichannel access CRNs. Performance analysis and evaluation of the developed ChA and DRA is presented, mainly through extensive simulations and analytical models. Further, the cross validation has been performed between simulations and analytical results to confirm the accuracy and preciseness of the novel analytical models developed in this thesis. In general, the presented results demonstrate improved performance of SU nodes in terms of capacity, collision probability, outage probability and forced termination probability when employing the adaptive ChA and DRA in CRNs.CK201