Approximation algorithms for the mobile piercing set problem with applications to clustering,

Abstract. The main contributions of this paper are two-fold. First, we present a simple, general framework for obtaining efficient constantfactor approximation algorithms for the mobile piercing set (MPS) problem on unit-disks for standard metrics in fixed dimension vector spaces. More specifically, we provide low constant approximations for L 1 and L ∞ norms on a d-dimensional space, for any fixed d > 0, and for the L 2 norm on two-and three-dimensional spaces. Our framework provides a family of fully-distributed and decentralized algorithms, which adapt (asymptotically) optimally to the mobility of disks, at the expense of a low degradation on the best known approximation factors of the respective centralized algorithms: Our algorithms take O(1) time to update the piercing set maintained, per movement of a disk. We also present a family of fully-distributed algorithms for the MPS problem which either match or improve the best known approximation bounds of centralized algorithms for the respective norms and space dimensions. Second, we show how the proposed algorithms can be directly applied to provide theoretical performance analyses for two popular 1-hop clustering algorithms in ad-hoc networks: the lowest-id algorithm and the Least Cluster Change (LCC) algorithm. More specifically, we formally prove that the LCC algorithm adapts in constant time to the mobility of the network nodes, and minimizes (up to low constant factors) the number of 1-hop clusters maintained. While there is a vast literature on simulation results for the LCC and the lowest-id algorithms, these had not been formally analyzed prior to this work. We also present an O(log n)-approximation algorithm for the mobile piercing set problem for nonuniform disks (i.e., disks that may have different radii), with constant update time

Approximating Minimum Independent Dominating Sets in Wireless Networks

We present the first polynomial-time approximation scheme (PTAS) for the Minimum Independent Dominating Set problem in graphs of polynomially bounded growth. Graphs of bounded growth are used to characterize wireless communication networks, and this class of graph includes many models known from the literature, e.g. (Quasi) Unit Disk Graphs. An independent dominating set is a dominating set in a graph that is also independent. It thus combines the advantages of both structures, and there are many applications that rely on these two structures e.g. in the area of wireless ad hoc networks. The presented approach yields a robust algorithm, that is, the algorithm accepts any undirected graph as input, and returns a (1+")- pproximate minimum dominating set, or a certificate showing that the input graph does not reflect a wireless network

Clustering and Hybrid Routing in Mobile Ad Hoc Networks

This dissertation focuses on clustering and hybrid routing in Mobile Ad Hoc Networks (MANET). Specifically, we study two different network-layer virtual infrastructures proposed for MANET: the explicit cluster infrastructure and the implicit zone infrastructure. In the first part of the dissertation, we propose a novel clustering scheme based on a number of properties of diameter-2 graphs to provide a general-purpose virtual infrastructure for MANET. Compared to virtual infrastructures with central nodes, our virtual infrastructure is more symmetric and stable, but still light-weight. In our clustering scheme, cluster initialization naturally blends into cluster maintenance, showing the unity between these two operations. We call our algorithm tree-based since cluster merge and split operations are performed based on a spanning tree maintained at some specific nodes. Extensive simulation results have shown the effectiveness of our clustering scheme when compared to other schemes proposed in the literature. In the second part of the dissertation, we propose TZRP (Two-Zone Routing Protocol) as a hybrid routing framework that can balance the tradeoffs between pure proactive, fuzzy proactive, and reactive routing approaches more effectively in a wide range of network conditions. In TZRP, each node maintains two zones: a Crisp Zone for proactive routing and efficient bordercasting, and a Fuzzy Zone for heuristic routing using imprecise locality information. The perimeter of the Crisp Zone is the boundary between pure proactive routing and fuzzy proactive routing, and the perimeter of the Fuzzy Zone is the boundary between proactive routing and reactive routing. By adjusting the sizes of these two zones, a reduced total routing control overhead can be achieved

Mobile backbone architecture for wireless ad-hoc networks : algorithms and performance analysis

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2007.Includes bibliographical references (p. 181-189).In this thesis, we study a novel hierarchical wireless networking approach in which some of the nodes are more capable than others. In such networks, the more capable nodes can serve as Mobile Backbone Nodes and provide a backbone over which end-to-end communication can take place. The main design problem considered in this thesis is that of how to (i) Construct such Mobile Backbone Networks so as to optimize a network performance metric, and (ii) Maintain such networks under node mobility. In the first part of the thesis, our approach consists of controlling the mobility of the Mobile Backbone Nodes (MBNs) in order to maintain network connectivity for the Regular Nodes (RNs). We formulate this problem subject to minimizing the number of MBNs and refer to it as the Connected Disk Cover (CDC) problem. We show that it can be decomposed into the Geometric Disk Cover (GDC) problem and the Steiner Tree Problem with Minimum Number of Steiner Points (STP-MSP). We prove that if these subproblems are solved separately by y- and 5-approximation algorithms, the approximation ratio of the joint solution is y1+6. Then, we focus on the two subproblems and present a number of distributed approximation algorithms that maintain a solution to the GDC problem under mobility. A new approach to the solution of the STP-MSP is also described. We show that this approach can be extended in order to obtain a joint approximate solution to the CDC problem. Finally, we evaluate the performance of the algorithms via simulation and show that the proposed GDC algorithms perform very well under mobility and that the new approach for the joint solution can significantly reduce the number of Mobile Backbone Nodes.(cont.) In the second part of the thesis, we address the the joint problem of placing a fixed number K MBNs in the plane, and assigning each RN to exactly one MBN. In particular, we formulate and solve two problems under a general communications model. The first is the Maximum Fair Placement and Assignment (MFPA) problem in which the objective is to maximize the throughput of the minimum throughput RN. The second is the Maximum Throughput Placement and Assignment (MTPA) problem, in which the objective is to maximize the aggregate throughput of the RNs. Due to the change in model (e.g. fixed number of MBNs,general communications model) from the first part of the thesis, the problems of this part of the thesis require a significantly different approach and solution methodology. Our main result is a novel optimal polynomial time algorithm for the MFPA problem for fixed K. For a restricted version of the MTPA problem, we develop an optimal polynomial time algorithm for K < 2. We also develop two heuristic algorithms for both problems, including an approximation algorithm for which we bound the worst case performance loss. Finally, we present simulation results comparing the performance of the various algorithms developed in the paper. In the third part of the thesis, we consider the problem of placing the Mobile Backbone Nodes over a finite time horizon. In particular, we assume complete a-priori knowledge of each of the RNs' trajectories over a finite time interval, and consider the problem of determining the optimal MBN path over that time interval. We consider the path planning of a single MBN and aim to maximize the time-average system throughput. We also assume that the velocity of the MBN factors into the performance objective (e.g. as a constraint/penalty).(cont.) Our first approach is a discrete one, for which our main result is a dynamic programming based approximation algorithm for the path planning problem. We provide worst case analysis of the performance of the algorithm. Additionally, we develop an optimal algorithm for the 1-step velocity constrained path planning problem. Using this as a sub-routine, we develop a greedy heuristic algorithm for the overall path planning problem. Next, we approach the path-planning problem from a continuous perspective. We formulate the problem as an optimal control problem, and develop interesting insights into the structure of the optimal solution. Finally, we discuss extensions of the base discrete and continuous formulations and compare the various developed approaches via simulation.by Anand Srinivas.Ph.D

Artificial Intelligence and civil liability

This study – commissioned by the Policy Department C at the request of the Committee on Legal Affairs – analyses the notion of AI-technologies and the applicable legal framework for civil liability. It demonstrates how technology regulation should be technologyspecific, and presents a Risk Management Approach, where the party who is best capable of controlling and managing a technology-related risk is held strictly liable, as a single entry point for litigation. It then applies such approach to four case-studies, to elaborate recommendations

Algorithms for Geometric Covering and Piercing Problems

This thesis involves the study of a range of geometric covering and piercing problems, where the unifying thread is approximation using disks. While some of the problems addressed in this work are solved exactly with polynomial time algorithms, many problems are shown to be at least NP-hard. For the latter, approximation algorithms are the best that we can do in polynomial time assuming that P is not equal to NP. One of the best known problems involving unit disks is the Discrete Unit Disk Cover (DUDC) problem, in which the input consists of a set of points P and a set of unit disks in the plane D, and the objective is to compute a subset of the disks of minimum cardinality which covers all of the points. Another perspective on the problem is to consider the centre points (denoted Q) of the disks D as an approximating set of points for P. An optimal solution to DUDC provides a minimal cardinality subset Q*, a subset of Q, so that each point in P is within unit distance of a point in Q*. In order to approximate the general DUDC problem, we also examine several restricted variants. In the Line-Separable Discrete Unit Disk Cover (LSDUDC) problem, P and Q are separated by a line in the plane. We write that l^- is the half-plane defined by l containing P, and l^+ is the half-plane containing Q. LSDUDC may be solved exactly in O(m^2n) time using a greedy algorithm. We augment this result by describing a 2-approximate solution for the Assisted LSDUDC problem, where the union of all disks centred in l^+ covers all points in P, but we consider using disks centred in l^- as well to try to improve the solution. Next, we describe the Within-Strip Discrete Unit Disk Cover (WSDUDC) problem, where P and Q are confined to a strip of the plane of height h. We show that this problem is NP-complete, and we provide a range of approximation algorithms for the problem with trade-offs between the approximation factor and running time. We outline approximation algorithms for the general DUDC problem which make use of the algorithms for LSDUDC and WSDUDC. These results provide the fastest known approximation algorithms for DUDC. As with the WSDUDC results, we present a set of algorithms in which better approximation factors may be had at the expense of greater running time, ranging from a 15-approximate algorithm which runs in O(mn + m log m + n log n) time to a 18-approximate algorithm which runs in O(m^6n+n log n) time. The next problems that we study are Hausdorff Core problems. These problems accept an input polygon P, and we seek a convex polygon Q which is fully contained in P and minimizes the Hausdorff distance between P and Q. Interestingly, we show that this problem may be reduced to that of computing the minimum radius of disk, call it k_opt, so that a convex polygon Q contained in P intersects all disks of radius k_opt centred on the vertices of P. We begin by describing a polynomial time algorithm for the simple case where P has only a single reflex vertex. On general polygons, we provide a parameterized algorithm which performs a parametric search on the possible values of k_opt. The solution to the decision version of the problem, i.e. determining whether there exists a Hausdorff Core for P given k_opt, requires some novel insights. We also describe an FPTAS for the decision version of the Hausdorff Core problem. Finally, we study Generalized Minimum Spanning Tree (GMST) problems, where the input consists of imprecise vertices, and the objective is to select a single point from each imprecise vertex in order to optimize the weight of the MST over the points. In keeping with one of the themes of the thesis, we begin by using disks as the imprecise vertices. We show that the minimization and maximization versions of this problem are NP-hard, and we describe some parameterized and approximation algorithms. Finally, we look at the case where the imprecise vertices consist of just two vertices each, and we show that the minimization version of the problem (which we call 2-GMST) remains NP-hard, even in the plane. We also provide an algorithm to solve the 2-GMST problem exactly if the combinatorial structure of the optimal solution is known. We identify a number of open problems in this thesis that are worthy of further study. Among them: Is the Assisted LSDUDC problem NP-complete? Can the WSDUDC results be used to obtain an improved PTAS for DUDC? Are there classes of polygons for which the determination of the Hausdorff Core is easy? Is there a PTAS for the maximum weight GMST problem on (unit) disks? Is there a combinatorial approximation algorithm for the 2-GMST problem (particularly with an approximation factor under 4)

Intelligent, Item-Based Stereotype Recommender System

Recommender systems (RS) have become key components driving the success of e-commerce, and other platforms where revenue and customer satisfaction is dependent on the user’s ability to discover desirable items in large catalogues. As the number of users and items on a platform grows, the computational complexity, the vastness of the data, and the sparsity problem constitute important challenges for any recommendation algorithm. In addition, the most widely studied filtering-based RS, while effective in providing suggestions for established users and items, are known for their poor performance for the new user and new item (cold start) problems. Stereotypical modelling of users and items is a promising approach to solving these problems. A stereotype represents an aggregation of the characteristics of the items or users which can be used to create general user or item classes. This work propose a set of methodologies for the automatic generation of stereotypes during the cold-starts. The novelty of the proposed approach rests on the findings that stereotypes built independently of the user-to-item ratings improve both recommendation metrics and computational performance during cold-start phases. The resulting RS can be used with any machine learning algorithm as a solver, and the improved performance gains due to rate-agnostic stereotypes are orthogonal to the gains obtained using more sophisticated solvers. Recommender Systems using the primitive metadata features (baseline systems) as well as factorisation-based systems are used as benchmarks for state-of-the-art methodologies to assess the results of the proposed approach under a wide range of recommendation quality metrics. The results demonstrate how such generic groupings of the metadata features, when performed in a manner that is unaware and independent of the user’s community preferences, may greatly reduce the dimension of the recommendation model, and provide a framework that improves the quality of recommendations in the cold start

Vision-Based Autonomous Control in Robotic Surgery

Robotic Surgery has completely changed surgical procedures. Enhanced dexterity, ergonomics, motion scaling, and tremor filtering, are well-known advantages introduced with respect to classical laparoscopy. In the past decade, robotic plays a fundamental role in Minimally Invasive Surgery (MIS) in which the da Vinci robotic system (Intuitive Surgical Inc., Sunnyvale, CA) is the most widely used system for robot-assisted laparoscopic procedures. Robots also have great potentiality in Microsurgical applications, where human limits are crucial and surgical sub-millimetric gestures could have enormous benefits with motion scaling and tremor compensation. However, surgical robots still lack advanced assistive control methods that could notably support surgeon's activity and perform surgical tasks in autonomy for a high quality of intervention. In this scenario, images are the main feedback the surgeon can use to correctly operate in the surgical site. Therefore, in view of the increasing autonomy in surgical robotics, vision-based techniques play an important role and can arise by extending computer vision algorithms to surgical scenarios. Moreover, many surgical tasks could benefit from the application of advanced control techniques, allowing the surgeon to work under less stressful conditions and performing the surgical procedures with more accuracy and safety. The thesis starts from these topics, providing surgical robots the ability to perform complex tasks helping the surgeon to skillfully manipulate the robotic system to accomplish the above requirements. An increase in safety and a reduction in mental workload is achieved through the introduction of active constraints, that can prevent the surgical tool from crossing a forbidden region and similarly generate constrained motion to guide the surgeon on a specific path, or to accomplish robotic autonomous tasks. This leads to the development of a vision-based method for robot-aided dissection procedure allowing the control algorithm to autonomously adapt to environmental changes during the surgical intervention using stereo images elaboration. Computer vision is exploited to define a surgical tools collision avoidance method that uses Forbidden Region Virtual Fixtures by rendering a repulsive force to the surgeon. Advanced control techniques based on an optimization approach are developed, allowing multiple tasks execution with task definition encoded through Control Barrier Functions (CBFs) and enhancing haptic-guided teleoperation system during suturing procedures. The proposed methods are tested on a different robotic platform involving da Vinci Research Kit robot (dVRK) and a new microsurgical robotic platform. Finally, the integration of new sensors and instruments in surgical robots are considered, including a multi-functional tool for dexterous tissues manipulation and different visual sensing technologies