17 research outputs found

    A Massively Parallel Dynamic Programming for Approximate Rectangle Escape Problem

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    Sublinear time complexity is required by the massively parallel computation (MPC) model. Breaking dynamic programs into a set of sparse dynamic programs that can be divided, solved, and merged in sublinear time. The rectangle escape problem (REP) is defined as follows: For nn axis-aligned rectangles inside an axis-aligned bounding box BB, extend each rectangle in only one of the four directions: up, down, left, or right until it reaches BB and the density kk is minimized, where kk is the maximum number of extensions of rectangles to the boundary that pass through a point inside bounding box BB. REP is NP-hard for k>1k>1. If the rectangles are points of a grid (or unit squares of a grid), the problem is called the square escape problem (SEP) and it is still NP-hard. We give a 22-approximation algorithm for SEP with k2k\geq2 with time complexity O(n3/2k2)O(n^{3/2}k^2). This improves the time complexity of existing algorithms which are at least quadratic. Also, the approximation ratio of our algorithm for k3k\geq 3 is 3/23/2 which is tight. We also give a 88-approximation algorithm for REP with time complexity O(nlogn+nk)O(n\log n+nk) and give a MPC version of this algorithm for k=O(1)k=O(1) which is the first parallel algorithm for this problem

    LIPIcs, Volume 258, SoCG 2023, Complete Volume

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    LIPIcs, Volume 258, SoCG 2023, Complete Volum

    Smart Wireless Sensor Networks

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    The recent development of communication and sensor technology results in the growth of a new attractive and challenging area - wireless sensor networks (WSNs). A wireless sensor network which consists of a large number of sensor nodes is deployed in environmental fields to serve various applications. Facilitated with the ability of wireless communication and intelligent computation, these nodes become smart sensors which do not only perceive ambient physical parameters but also be able to process information, cooperate with each other and self-organize into the network. These new features assist the sensor nodes as well as the network to operate more efficiently in terms of both data acquisition and energy consumption. Special purposes of the applications require design and operation of WSNs different from conventional networks such as the internet. The network design must take into account of the objectives of specific applications. The nature of deployed environment must be considered. The limited of sensor nodes� resources such as memory, computational ability, communication bandwidth and energy source are the challenges in network design. A smart wireless sensor network must be able to deal with these constraints as well as to guarantee the connectivity, coverage, reliability and security of network's operation for a maximized lifetime. This book discusses various aspects of designing such smart wireless sensor networks. Main topics includes: design methodologies, network protocols and algorithms, quality of service management, coverage optimization, time synchronization and security techniques for sensor networks

    Scalable Control Strategies and a Customizable Swarm Robotic Platform for Boundary Coverage and Collective Transport Tasks

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    abstract: Swarms of low-cost, autonomous robots can potentially be used to collectively perform tasks over large domains and long time scales. The design of decentralized, scalable swarm control strategies will enable the development of robotic systems that can execute such tasks with a high degree of parallelism and redundancy, enabling effective operation even in the presence of unknown environmental factors and individual robot failures. Social insect colonies provide a rich source of inspiration for these types of control approaches, since they can perform complex collective tasks under a range of conditions. To validate swarm robotic control strategies, experimental testbeds with large numbers of robots are required; however, existing low-cost robots are specialized and can lack the necessary sensing, navigation, control, and manipulation capabilities. To address these challenges, this thesis presents a formal approach to designing biologically-inspired swarm control strategies for spatially-confined coverage and payload transport tasks, as well as a novel low-cost, customizable robotic platform for testing swarm control approaches. Stochastic control strategies are developed that provably allocate a swarm of robots around the boundaries of multiple regions of interest or payloads to be transported. These strategies account for spatially-dependent effects on the robots' physical distribution and are largely robust to environmental variations. In addition, a control approach based on reinforcement learning is presented for collective payload towing that accommodates robots with heterogeneous maximum speeds. For both types of collective transport tasks, rigorous approaches are developed to identify and translate observed group retrieval behaviors in Novomessor cockerelli ants to swarm robotic control strategies. These strategies can replicate features of ant transport and inherit its properties of robustness to different environments and to varying team compositions. The approaches incorporate dynamical models of the swarm that are amenable to analysis and control techniques, and therefore provide theoretical guarantees on the system's performance. Implementation of these strategies on robotic swarms offers a way for biologists to test hypotheses about the individual-level mechanisms that drive collective behaviors. Finally, this thesis describes Pheeno, a new swarm robotic platform with a three degree-of-freedom manipulator arm, and describes its use in validating a variety of swarm control strategies.Dissertation/ThesisDoctoral Dissertation Mechanical Engineering 201

    Theoretical and computational advances in finite-size facility placement and assignment problems

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    The goal of this research is to develop fundamental theory and exact solution methods for the optimal placement of multiple, finite-size, rectangular facilities in presence of existing rectangular facilities, in a plane. Applications of this research can be found in facility layout (re)design in manufacturing, distribution systems, services (retail outlets, hospital floors, etc.), and printed circuit board design; where designing an efficient layout can save millions of dollars in operational costs. Main difficulty of this optimization problem lies in its continuous non-convex/non-concave feasible space, which makes it tough to escape local optimality. Through this research, novel approaches will be proposed which can be used to distill this continuous space into a finite set of candidate solutions, making it amenable to search for the global optimum. The first two parts of this research deal with establishing a unified theory for the finite-size facility placement problem and establishing the theory of dominance for pruning the sub-optimal solutions. Traditionally, the facility location/layout problems are modeled as the Quadratic Assignment Problem (QAP), which is strongly NP-hard. Also, for getting strong lower bounds in the dominance procedure, we may need to solve an instance of the NP-hard Quadratic Semi-Assignment Problem (QSAP). To this end, the third part of this research deals with investigating parallel and High Performance Computing (HPC) methods for solving the Linear Assignment Problem (LAP), which is an important sub-problem of the QAP. The final part of this research deals with investigating parallel and HPC methods for obtaining strong lower bounds and possibly solving large QAPs. Since QAP is known to be a computationally intensive problem, it should be noted that large in this context means problem instances with up to 30 facilities and locations
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