A set S of vertices in a graph G = (V, E) is a locating-dominating set if S is a dominating set of G, and every pair of distinct vertices {u, v} in V - S is located with respect to S, that is, if the set of neighbors of u that are in S is not equal to the set of neighbors of v that are in S. We give a construction of trees that have unique minimum locating-dominating sets.

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A mobile ad hoc network (MANET) is a wireless network that uses multi-hop peer-to-peer routing instead of static network infrastructure to provide network connectivity. MANETs have applications in rapidly deployed and dynamic military and civilian systems. The network topology in a MANET usually changes with time. Therefore, there are new challenges for routing protocols in MANETs since traditional routing protocols may not be suitable for MANETs. For example, some assumptions used by these protocols are not valid in MANETs or some protocols cannot efficiently handle topology changes. Researchers are designing new MANET routing protocols and comparing and improving existing MANET routing protocols before any routing protocols are standardized using simulations. However, the simulation results from different research groups are not consistent with each other. This is because of a lack of consistency in MANET routing protocol models and application environments, including networking and user traffic profiles. Therefore, the simulation scenarios are not equitable for all protocols and conclusions cannot be generalized. Furthermore, it is difficult for one to choose a proper routing protocol for a given MANET application. According to the aforementioned issues, my Ph.D. research focuses on MANET routing protocols. Specifically, my contributions include the characterization of differ- ent routing protocols using a novel systematic relay node set (RNS) framework, design of a new routing protocol for MANETs, a study of node mobility, including a quantitative study of link lifetime in a MANET and an adaptive interval scheme based on a novel neighbor stability criterion, improvements of a widely-used network simulator and corresponding protocol implementations, design and development of a novel emulation test bed, evaluation of MANET routing protocols through simulations, verification of our routing protocol using emulation, and development of guidelines for one to choose proper MANET routing protocols for particular MANET applications. Our study shows that reactive protocols do not always have low control overhead, as people tend to think. The control overhead for reactive protocols is more sensitive to the traffic load, in terms of the number of traffic flows, and mobility, in terms of link connectivity change rates, than other protocols. Therefore, reactive protocols may only be suitable for MANETs with small number of traffic loads and small link connectivity change rates. We also demonstrated that it is feasible to maintain full network topology in a MANET with low control overhead. This dissertation summarizes all the aforementioned methodologies and corresponding applications we developed concerning MANET routing protocols. / Ph. D.

Dans le cadre des réseaux ad hoc à grande envergure, le concept de clusterisation peut être mis à profit afin de faire face aux problèmes de passage à l'échelle et d'accroître les performances du système. Tout d’abord, cette thèse présente notre algorithme de clusterisation TBCA ‘Tiered based Clustering algorithm’, ayant pour objectif d’organiser le processus de clusterisation en couches et de réduire au maximum le trafic de contrôle associé à la phase d’établissement et de maintenance de l’infrastructure virtuelle générée. La formation et la maintenance d’une infrastructure virtuelle ne sont pas une fin en soi. Dans cet axe, on a exploité les apports de notre mécanisme de clusterisation conjointement avec le mode veille, à travers la proposition de l’approche de conservation d’énergie baptisée CPPCM ‘Cluster based Prioritized Power Conservation Mechanism’ avec deux variantes. Notre objectif principal est de réduire la consommation d’énergie tout en assurant l’acheminement des paquets de données sans endurer des temps d’attente importants aux niveaux des files d’attente des nœuds impliqués dans le transfert. Nous avons proposé aussi un algorithme de routage LCR ‘Layered Cluster based Routing’ se basant sur l’existence d’une infrastructure virtuelle. L’exploitation des apports de notre mécanisme TBCA et la limitation des tâches de routage additionnelles à un sous ensemble de nœuds sont des atouts pour assurer le passage à l’échelle de notre algorithme. / Relying on a virtual infrastructure seems a promising approach to overcome the scalability problem in large scale ad hoc networks. First, we propose a clustering mechanism, TBCA ‘Tiered based Clustering algorithm’, operating in a layered manner and exploiting the eventual collision to accelerate the clustering process. Our mechanism does not necessitate any type of neighbourhood knowledge, trying to alleviate the network from some control messages exchanged during the clustering and maintenance process. Since the energy consumption is still a critical issue, we combining a clustering technique and the power saving mode in order to conserve energy without affecting network performance. The main contribution of our power saving approach lies on the differentiation among packets based on the amount of network resources they have been so far consumed. Besides, the proposed structure of the beacon interval can be adjusted dynamically and locally by each node according to its own specific requirements. We propose also a routing algorithm, LCR ‘Layered Cluster based Routing’. The basic idea consists on assigning additional tasks to a limited set of dominating nodes, satisfying specific requirements while exploiting the benefits of our clustering algorithm TBCA.

Cette thèse se déroule au sein du projet ToDo (Time versus Optimality in discrete Optimization ANR 09-EMER-010) financé par l'Agence Nationale de la Recherche. Nous nous intéressons à la résolution exacte et approchée de deux problèmes de graphes. Dans un souci de compromis entre la durée d'exécution et la qualité des solutions, nous proposons une nouvelle approche par partition en cliques qui a pour but (1) de résoudre de manière rapide des problèmes exacts et (2) de garantir la qualité des résultats trouvés par des algorithmes d'approximation. Nous avons combiné notre approche avec des techniques de filtrage et une heuristique de liste. Afin de compléter ces travaux théoriques, nous avons implémenté et comparé nos algorithmes avec ceux existant dans la littérature. Dans un premier temps, nous avons traité le problème de l'indépendant dominant de taille minimum. Nous résolvons de manière exacte ce problème et démontrons qu'il existe des graphes particuliers dans lesquels le problème est 2-approximable. Dans un second temps nous résolvons par un algorithme exact et un algorithme d'approximation le problème du vertex cover et du vertex cover connexe. Puis à la fin de cette thèse, nous avons étendu nos travaux aux problèmes proches, dans des graphes comprenant des conflits entre les sommets. / This thesis takes place in the project ToDo 2 funded by the french National Research Agency. We deal with the resolution of two graph problems, by exact and approximation methods. For the sake of compromise between runtime and quality of the solutions, we propose a new approach by partitioning the vertices of the graph into cliques, which aims (1) to solve problems quickly with exact algortihms and (2) to ensure the quality if results with approximation algorithms. We combine our approach with filtering techniques and heuristic list. To complete this theoretical work, we implement our algorithms and compared with those existing in the literature. At the first step, we discuss the problem of independent dominating of minimum size. We solve this problem accurately and prove that there are special graphs where the problem is 2-approximable. In the second step, we solve by an exact algorithm and an approximation algorithm, the vertex cover problem and the connected vertex cover problem. Then at the end of this thesis, we extend our work to the problems in graphs including conflicts between vertices.

The aim of the current research program was to investigate the social context of escalation in response to continued pushy behaviour in the workplace. In doing so, this research program contributes to the development of communication skills by investigating the entire context of skills required for effective communication in managing everyday conflict in the workplace. The response class, Responding to continued pushy or dominating behaviour in the workplace, was selected as a vehicle for examining the context of escalation for two reasons. Firstly, this response class, by the very nature of pushy behaviour, embodies a continued interaction. In the past, assertive communication research has focused on one off responses rather than a continued interaction. Secondly, this response class has been identified in previous research as being of interest to assertiveness trainees (Cooley, 1979, Lefevre & West, 1984, Wilson & Gallios, 1993). The theoretical premise of the current research program resides in the application of Social Rules Theory to the difficult face-to-face communication situation, or response class, of responding to continued pushy behaviour in the workplace. In doing so, this approach also takes into account dialectical theory, conflict resolution theory, and the concept of response components that can be selected and/or combined in order to meet the requirements, or rules, of a specific situation. In adopting the Social Rules approach, the current research program addresses the key criticisms of the traditional approach to assertion and assertion training, namely that people behaving assertively are sometimes negatively evaluated for assertive behaviour (Wilson & Gallois, 1993); and that assertion traditionally focused on the expressiveness of a response at the unintended cost of social or contextual appropriateness (Crawford, 1988); that finding a response is assertive does not delineate which aspects of the response are producing which types of effects (Galassi, 1978; Mullinix & Galassi, 1981). Most importantly, the current research contributes to the field by examining the negative response class in terms of a response sequence of escalation, rather than a one-off response. This is new research and contributes to the field theoretically and to the conceptualisation of assertion and communication. In order to meet the goals of the current research program, the response class Responding to continued pushy behaviour in the workplace, was defined precisely in terms of the situational context. This response class implies a workplace relationship of an ongoing nature. Four other variables were involved in defining and investigating the situation. These were status, gender of message sender, gender of message receiver, and response level (initial response, first escalation or second escalation). The current program of research was carried out in a series of three related studies, and these four variables were examined in each of the three studies. The purpose of the first study was to elicit social rules and goals for interpersonally effective and appropriate escalation strategies in response to pushy dominating communication in the workplace. This study was conducted in two parts, a qualitative questionnaire completed by 20 females and 20 males, and two focus groups, one for females and one for males. Content analysis revealed a set of rules for an escalation sequence for each combination of status and gender. These rules were then operationalized, filmed and analysed in the second study. One hundred and twenty-three participants (64 females and 59 males) with work experience watched the operationalized responses and rated them on a series of seven scales. These scales were effectiveness in stopping the pushy behaviour (task effectiveness), effectiveness in maintaining the relationship (maintenance effectives), social appropriateness, interpersonal skill required, risk involved, personal difficulty in making the response, and likelihood of making the response. Analyses included descriptive statistics, which indicated that the operationalized responses were perceived to be effective and socially appropriate. Multivariate Analysis of Variance (MANOVA) were also conducted and revealed a number of significant interactions for each status level (manager, colleague, subordinate). The third and final study in this research program adopted a qualitative approach to examine continued pushy or dominating communication in the workplace. Eighty-two (45 female and 37 male) participants completed a qualitative questionnaire utilizing an open-ended approach. This questionnaire was designed for the purpose of the third study to elicit the typical behaviours, emotions and cognitions participants have in response to continued pushy behaviour in the workplace. Also, a data analysis process was designed specifically for the third study to provide an analytical procedure that was as systematically rigorous and replicable as possible. This process is explained in detail in Study 3. The results of the third study revealed differences between actual behaviour and rule based behaviour in response to continued pushy behaviour, namely that actual responses are more public and direct in nature, and more likely to promote destructive conflict escalation. This finding implies that typical responses are not as effective as rule based responses, highlighting the benefits of applying social rules to manage difficult face to face communication situations. In summary, the current research project utilized a multi-method approach in a series of three studies to reveal the nature of Social Rules based responses and typical responses. The results of this research program have implications for both the theory and practice of effective communication and effective communication training. Evaluation of both social rules based and typical responses have implications for communication trainees who wish to make informed choice based on a consideration of functionally effective behaviour and personal satisfaction. For example, social rules for escalation in response to continued pushy behaviour from a male manager may indicate that it is most effective for a female subordinate to acquiesce. However, the female subordinate may choose to violate social rules and risk being perceived as inappropriate and damaging the relationship, to achieve a super-ordinate goal or for personal satisfaction. Conversely, the social rules and responses developed in the current research program have implications for professional effectiveness in the workplace by providing guidelines for dealing with dominating behaviour.

A mobile ad-hoc network (MANET) is a collection of wireless mobile nodes forming a temporary network without the support of any established infrastructure or centralized administration. There are many potential applications based the techniques of MANETs, such as disaster rescue, personal area networking, wireless conference, military applications, etc. MANETs face a number of challenges for designing a scalable routing protocol due to their natural characteristics. Guaranteeing delivery and the capability to handle dynamic connectivity are the most important issues for routing protocols in MANETs. In this dissertation, we will propose four algorithms that address different aspects of routing problems in MANETs. Firstly, in position based routing protocols to design a scalable location management scheme is inherently difficult. Enhanced Scalable Location management Service (EnSLS) is proposed to improve the scalability of existing location management services, and a mathematical model is proposed to compare the performance of the classical location service, GLS, and our protocol, EnSLS. The analytical model shows that EnSLS has better scalability compared with that of GLS. Secondly, virtual backbone routing can reduce communication overhead and speedup the routing process compared with many existing on-demand routing protocols for routing detection. In many studies, Minimum Connected Dominating Set (MCDS) is used to approximate virtual backbones in a unit-disk graph. However finding a MCDS is an NP-hard problem. In the dissertation, we develop two new pure localized protocols for calculating the CDS. One emphasizes forming a small size initial near-optimal CDS via marking process, and the other uses an iterative synchronized method to avoid illegal simultaneously removal of dominating nodes. Our new protocols largely reduce the number of nodes in CDS compared with existing methods. We show the efficiency of our approach through both theoretical analysis and simulation experiments. Finally, using multiple redundant paths for routing is a promising solution. However, selecting an optimal path set is an NP hard problem. We propose the Genetic Fuzzy Multi-path Routing Protocol (GFMRP), which is a multi-path routing protocol based on fuzzy set theory and evolutionary computing.

This thesis has two parts. In the first part, we study some graph covering problems with a non-local covering rule that allows a "remote" node to be covered by repeatedly applying the covering rule. In the second part, we provide some results on the packing of Steiner trees. In the Propagation problem we are given a graph $G$ and the goal is to find a minimum-sized set of nodes $S$ that covers all of the nodes, where a node $v$ is covered if (1) $v$ is in $S$, or (2) $v$ has a neighbor $u$ such that $u$ and all of its neighbors except $v$ are covered. Rule (2) is called the propagation rule, and it is applied iteratively. Throughout, we use $n$ to denote the number of nodes in the input graph. We prove that the path-width parameter is a lower bound for the optimal value. We show that the Propagation problem is NP-hard in planar weighted graphs. We prove that it is NP-hard to approximate the optimal value to within a factor of $2^{\log^{1-\epsilon}{n}}$ in weighted (general) graphs. The second problem that we study is the Power Dominating Set problem. This problem has two covering rules. The first rule is the same as the domination rule as in the Dominating Set problem, and the second rule is the same propagation rule as in the Propagation problem. We show that it is hard to approximate the optimal value to within a factor of $2^{\log^{1-\epsilon}{n}}$ in general graphs. We design and analyze an approximation algorithm with a performance guarantee of $O(\sqrt{n})$ on planar graphs. We formulate a common generalization of the above two problems called the General Propagation problem. We reformulate this general problem as an orientation problem, and based on this reformulation we design a dynamic programming algorithm. The algorithm runs in linear time when the graph has tree-width $O(1)$. Motivated by applications, we introduce a restricted version of the problem that we call the $\ell$-round General Propagation problem. We give a PTAS for the $\ell$-round General Propagation problem on planar graphs, for small values of $\ell$. Our dynamic programming algorithms and the PTAS can be extended to other problems in networks with similar propagation rules. As an example we discuss the extension of our results to the Target Set Selection problem in the threshold model of the diffusion processes. In the second part of the thesis, we focus on the Steiner Tree Packing problem. In this problem, we are given a graph $G$ and a subset of terminal nodes $R\subseteq V(G)$. The goal in this problem is to find a maximum cardinality set of disjoint trees that each spans $R$, that is, each of the trees should contain all terminal nodes. In the edge-disjoint version of this problem, the trees have to be edge disjoint. In the element-disjoint version, the trees have to be node disjoint on non-terminal nodes and edge-disjoint on edges adjacent to terminals. We show that both problems are NP-hard when there are only $3$ terminals. Our main focus is on planar instances of these problems. We show that the edge-disjoint version of the problem is NP-hard even in planar graphs with $3$ terminals on the same face of the embedding. Next, we design an algorithm that achieves an approximation guarantee of $\frac{1}{2}-\frac{1}{k}$, given a planar graph that is $k$ element-connected on the terminals; in fact, given such a graph the algorithm returns $k/2-1$ element-disjoint Steiner trees. Using this algorithm we get an approximation algorithm with guarantee of (almost) $4$ for the edge-disjoint version of the problem in planar graphs. We also show that the natural LP relaxation of the edge-disjoint Steiner Tree Packing problem has an integrality ratio of $2-\epsilon$ in planar graphs.

This thesis has two parts. In the first part, we study some graph covering problems with a non-local covering rule that allows a "remote" node to be covered by repeatedly applying the covering rule. In the second part, we provide some results on the packing of Steiner trees. In the Propagation problem we are given a graph $G$ and the goal is to find a minimum-sized set of nodes $S$ that covers all of the nodes, where a node $v$ is covered if (1) $v$ is in $S$, or (2) $v$ has a neighbor $u$ such that $u$ and all of its neighbors except $v$ are covered. Rule (2) is called the propagation rule, and it is applied iteratively. Throughout, we use $n$ to denote the number of nodes in the input graph. We prove that the path-width parameter is a lower bound for the optimal value. We show that the Propagation problem is NP-hard in planar weighted graphs. We prove that it is NP-hard to approximate the optimal value to within a factor of $2^{\log^{1-\epsilon}{n}}$ in weighted (general) graphs. The second problem that we study is the Power Dominating Set problem. This problem has two covering rules. The first rule is the same as the domination rule as in the Dominating Set problem, and the second rule is the same propagation rule as in the Propagation problem. We show that it is hard to approximate the optimal value to within a factor of $2^{\log^{1-\epsilon}{n}}$ in general graphs. We design and analyze an approximation algorithm with a performance guarantee of $O(\sqrt{n})$ on planar graphs. We formulate a common generalization of the above two problems called the General Propagation problem. We reformulate this general problem as an orientation problem, and based on this reformulation we design a dynamic programming algorithm. The algorithm runs in linear time when the graph has tree-width $O(1)$. Motivated by applications, we introduce a restricted version of the problem that we call the $\ell$-round General Propagation problem. We give a PTAS for the $\ell$-round General Propagation problem on planar graphs, for small values of $\ell$. Our dynamic programming algorithms and the PTAS can be extended to other problems in networks with similar propagation rules. As an example we discuss the extension of our results to the Target Set Selection problem in the threshold model of the diffusion processes. In the second part of the thesis, we focus on the Steiner Tree Packing problem. In this problem, we are given a graph $G$ and a subset of terminal nodes $R\subseteq V(G)$. The goal in this problem is to find a maximum cardinality set of disjoint trees that each spans $R$, that is, each of the trees should contain all terminal nodes. In the edge-disjoint version of this problem, the trees have to be edge disjoint. In the element-disjoint version, the trees have to be node disjoint on non-terminal nodes and edge-disjoint on edges adjacent to terminals. We show that both problems are NP-hard when there are only $3$ terminals. Our main focus is on planar instances of these problems. We show that the edge-disjoint version of the problem is NP-hard even in planar graphs with $3$ terminals on the same face of the embedding. Next, we design an algorithm that achieves an approximation guarantee of $\frac{1}{2}-\frac{1}{k}$, given a planar graph that is $k$ element-connected on the terminals; in fact, given such a graph the algorithm returns $k/2-1$ element-disjoint Steiner trees. Using this algorithm we get an approximation algorithm with guarantee of (almost) $4$ for the edge-disjoint version of the problem in planar graphs. We also show that the natural LP relaxation of the edge-disjoint Steiner Tree Packing problem has an integrality ratio of $2-\epsilon$ in planar graphs.

Un code identifiant est un ensemble de sommets d'un graphe tel que, d'une part, chaque sommet hors du code a un voisin dans le code (propriété de domination) et, d'autre part, tous les sommets ont un voisinage distinct à l'intérieur du code (propriété de séparation). Dans cette thèse, nous nous intéressons à des aspects combinatoires et algorithmiques relatifs aux codes identifiants.Pour la partie combinatoire, nous étudions tout d'abord des questions extrémales en donnant une caractérisation complète des graphes non-orientés finis ayant comme taille minimum de code identifiant leur ordre moins un. Nous caractérisons également les graphes dirigés finis, les graphes non-orientés infinis et les graphes orientés infinis ayant pour seul code identifiant leur ensemble de sommets. Ces résultats répondent à des questions ouvertes précédemment étudiées dans la littérature.Puis, nous étudions la relation entre la taille minimum d'un code identifiant et le degré maximum d'un graphe, en particulier en donnant divers majorants pour ce paramètre en fonction de l'ordre et du degré maximum. Ces majorants sont obtenus via deux techniques. L'une est basée sur la construction d'ensembles indépendants satisfaisant certaines propriétés, et l'autre utilise la combinaison de deux outils de la méthode probabiliste : le lemme local de Lovasz et une borne de Chernoff. Nous donnons également des constructions de familles de graphes en relation avec ce type de majorants, et nous conjecturons que ces constructions sont optimales à une constante additive près.Nous présentons également de nouveaux minorants et majorants pour la cardinalité minimum d'un code identifiant dans des classes de graphes particulières. Nous étudions les graphes de maille au moins 5 et de degré minimum donné en montrant que la combinaison de ces deux paramètres influe fortement sur la taille minimum d'un code identifiant. Nous appliquons ensuite ces résultats aux graphes réguliers aléatoires. Puis, nous donnons des minorants pour la taille d'un code identifiant des graphes d'intervalles et des graphes d'intervalles unitaires. Enfin, nous donnons divers minorants et majorants pour cette quantité lorsque l'on se restreint aux graphes adjoints. Cette dernière question est abordée via la notion nouvelle de codes arête-identifiants.Pour la partie algorithmique, il est connu que le problème de décision associés à la notion de code identifiant est NP-complet même pour des classes de graphes restreintes. Nous étendons ces résultats à d'autres classes de graphes telles que celles des graphes split, des co-bipartis, des adjoints ou d'intervalles. Pour cela nous proposons des réductions polynomiales depuis divers problèmes algorithmiques classiques. Ces résultats montrent que dans beaucoup de classes de graphes, le problème des codes identifiants est algorithmiquement plus difficile que des problèms liés (tel que le problème des ensembles dominants).Par ailleurs, nous complétons les connaissances relatives à l'approximabilité du problème d'optimisation associé aux codes identifiants. Nous étendons le résultat connu de NP-difficulté pour l'approximation de ce problème avec un facteur sous-logarithmique (en fonction de la taille du graphe instance) aux graphes bipartis, split et co-bipartis, respectivement. Nous étendons également le résultat connu d'APX-complétude pour les graphes de degré maximum donné à une sous-classe des graphes split, aux graphes bipartis de degré maximum 4 et aux graphes adjoints. Enfin, nous montrons l'existence d'un algorithme de type PTAS pour les graphes d'intervalles unitaires. / An identifying code is a set of vertices of a graph such that, on the one hand, each vertex out of the code has a neighbour in the code (domination property), and, on the other hand, all vertices have a distinct neighbourhood within the code (separation property). In this thesis, we investigate combinatorial and algorithmic aspects of identifying codes.For the combinatorial part, we first study extremal questions by giving a complete characterization of all finite undirected graphs having their order minus one as minimum size of an identifying code. We also characterize finite directed graphs, infinite undirected graphs and infinite oriented graphs having their whole vertex set as unique identifying code. These results answer open questions that were previously studied in the literature.We then study the relationship between the minimum size of an identifying code and the maximum degree of a graph. In particular, we give several upper bounds for this parameter as a function of the order and the maximum degree. These bounds are obtained using two techniques. The first one consists in the construction of independent sets satisfying certain properties, and the second one is the combination of two tools from the probabilistic method: the Lovasz local lemma and a Chernoff bound. We also provide constructions of graph families related to this type of upper bounds, and we conjecture that they are optimal up to an additive constant.We also present new lower and upper bounds for the minimum cardinality of an identifying code in specific graph classes. We study graphs of girth at least 5 and of given minimum degree by showing that the combination of these two parameters has a strong influence on the minimum size of an identifying code. We apply these results to random regular graphs. Then, we give lower bounds on the size of a minimum identifying code of interval and unit interval graphs. Finally, we prove several lower and upper bounds for this parameter when considering line graphs. The latter question is tackled using the new notion of an edge-identifying code.For the algorithmic part, it is known that the decision problem associated to the notion of an identifying code is NP-complete, even for restricted graph classes. We extend the known results to other classes such as split graphs, co-bipartite graphs, line graphs or interval graphs. To this end, we propose polynomial-time reductions from several classical hard algorithmic problems. These results show that in many graph classes, the identifying code problem is computationally more difficult than related problems (such as the dominating set problem).Furthermore, we extend the knowledge of the approximability of the optimization problem associated to identifying codes. We extend the known result of NP-hardness of approximating this problem within a sub-logarithmic factor (as a function of the instance graph) to bipartite, split and co-bipartite graphs, respectively. We also extendthe known result of its APX-hardness for graphs of given maximum degree to a subclass of split graphs, bipartite graphs of maximum degree 4 and line graphs. Finally, we show the existence of a PTAS algorithm for unit interval graphs.