Collaborative Learning of Stochastic Bandits over a Social Network

We consider a collaborative online learning paradigm, wherein a group of agents connected through a social network are engaged in playing a stochastic multi-armed bandit game. Each time an agent takes an action, the corresponding reward is instantaneously observed by the agent, as well as its neighbours in the social network. We perform a regret analysis of various policies in this collaborative learning setting. A key finding of this paper is that natural extensions of widely-studied single agent learning policies to the network setting need not perform well in terms of regret. In particular, we identify a class of non-altruistic and individually consistent policies, and argue by deriving regret lower bounds that they are liable to suffer a large regret in the networked setting. We also show that the learning performance can be substantially improved if the agents exploit the structure of the network, and develop a simple learning algorithm based on dominating sets of the network. Specifically, we first consider a star network, which is a common motif in hierarchical social networks, and show analytically that the hub agent can be used as an information sink to expedite learning and improve the overall regret. We also derive networkwide regret bounds for the algorithm applied to general networks. We conduct numerical experiments on a variety of networks to corroborate our analytical results.Comment: 14 Pages, 6 Figure

Constant memory routing in quasi-planar and quasi-polyhedral graphs

AbstractWe address the problem of online route discovery for a class of graphs that can be embedded either in two or in three-dimensional space. In two dimensions we propose the class of quasi-planar graphs and in three dimensions the class of quasi-polyhedral graphs. In the former case such graphs are geometrically embedded in R2 and have an underlying backbone that is planar with convex faces; however within each face arbitrary edges (with arbitrary crossings) are allowed. In the latter case, these graphs are geometrically embedded in R3 and consist of a backbone of convex polyhedra and arbitrary edges within each polyhedron. In both cases we provide a routing algorithm that guarantees delivery. Our algorithms need only “remember” the source and destination nodes and one (respectively, two) reference nodes used to store information about the underlying face (respectively, polyhedron) currently being traversed. The existence of the backbone is used only in proofs of correctness of the routing algorithm; the particular choice is irrelevant and does not affect the behaviour of the algorithm

Connectivity, Coverage and Placement in Wireless Sensor Networks

Wireless communication between sensors allows the formation of flexible sensor networks, which can be deployed rapidly over wide or inaccessible areas. However, the need to gather data from all sensors in the network imposes constraints on the distances between sensors. This survey describes the state of the art in techniques for determining the minimum density and optimal locations of relay nodes and ordinary sensors to ensure connectivity, subject to various degrees of uncertainty in the locations of the nodes

Determining Distributions of Security Means for WSNs based on the Model of a Neighbourhood Watch

Neighbourhood watch is a concept that allows a community to distribute a complex security task in between all members. Members of the community carry out individual security tasks to contribute to the overall security of it. It reduces the workload of a particular individual while securing all members and allowing them to carry out a multitude of security tasks. Wireless sensor networks (WSNs) are composed of resource-constraint independent battery driven computers as nodes communicating wirelessly. Security in WSNs is essential. Without sufficient security, an attacker is able to eavesdrop the communication, tamper monitoring results or deny critical nodes providing their service in a way to cut off larger network parts. The resource-constraint nature of sensor nodes prevents them from running full-fledged security protocols. Instead, it is necessary to assess the most significant security threats and implement specialised protocols. A neighbourhood-watch inspired distributed security scheme for WSNs has been introduced by Langend\"orfer. Its goal is to increase the variety of attacks a WSN can fend off. A framework of such complexity has to be designed in multiple steps. Here, we introduce an approach to determine distributions of security means on large-scale static homogeneous WSNs. Therefore, we model WSNs as undirected graphs in which two nodes connected iff they are in transmission range. The framework aims to partition the graph into $n$ distinct security means resulting in the targeted distribution. The underlying problems turn out to be NP hard and we attempt to solve them using linear programs (LPs). To evaluate the computability of the LPs, we generate large numbers of random {\lambda}-precision unit disk graphs (UDGs) as representation of WSNs. For this purpose, we introduce a novel {\lambda}-precision UDG generator to model WSNs with a minimal distance in between nodes

Domination problems in social networks

The thesis focuses on domination problems in social networks. Domination problems are one of the classical types of problems in computer science. Domination problems are fundamental and widely studied problems in algorithms and complexity theory. They have been extensively studied and adopted in many real-life applications. In general, a set D of vertices of a simple (no loops or multiple edges), undirected graph G = (V,E) is called dominating if each vertex in V −D is adjacent to some vertex in D. The computational problem of computing a dominating set of minimum size is known as “the dominating set problem”. The dominating set problem is NP-hard in general graphs. A social network - the graph of relationships and interactions within a group of individuals - plays a fundamental role as a medium for the spread of information, ideas, and influence among its members. In a social network, people, who have problems such as drinking, smoking and drug use related issues, can have both positive and negative impact on each other and a person can take and move among different roles since they are affected by their peers. As an example, positive impacts of intervention and education programs on a properly selected set of initial individuals can diffuse widely into society via various social contacts: face to face, phone calls, email, social networks and so on. Exploiting the relationships and influences among individuals in social networks might offer considerable benefit to both the economy and society. In order to deal with social problems, the positive influence dominating set (PIDS) is a typical one to help people to alleviate these social problems. However, existing PIDS algorithms are usually greedy and finding approximation solutions that are inefficient for the growing social networks. By now these proposed algorithms can deal with social problems only in undirected social networks with uniform weight value. To overcome the shortcomings of the existing PIDS model, a novel domination model namely weight positive influence dominating set (WPIDS) is presented. A main contribution of the thesis is that the proposed WPIDS model can be applied in weighted directed social networks. It considers the direction and degree of users’ influence in social networks in which the PIDS model does not. The experimental results have revealed that the WPIDS model is more effective than the PIDS model. At the same time, thanks to the publication of Dijkstra’s pioneering paper, a lot of self-stabilizing algorithms for computing minimal dominating sets have been proposed, such as the self-stabilizing algorithms for minimal single dominating sets and minimal k-dominating sets (MKDS). However, for the MKDS problem, so far there is no self-stabilizing algorithm that works in arbitrary graphs. The proposed algorithms for the MKDS either work for tree graphs or find a minimal 2-dominating set. So, in the thesis, for the MKDS problem, two self-stabilizing algorithms are presented that can operate on general graphs. For the weighted dominating set (WDS) problem, most of the proposed algorithms find approximation solutions to a WDS. For the non-uniform WDS problem, there is no self-stabilizing algorithm for the WDS. In the thesis, self-stabilizing algorithms for the minimal weighted dominating set (MWDS) and minimal positive influence dominating set (MPIDS) are presented when operating in any general network. The worst case convergence time of the two algorithms from any arbitrary initial state are also proved. Finally, in order to reduce cost in an education/intervention programme arising from the PIDS problem, two cooperative cost games about PIDS problem are constructed