684 research outputs found

    Searching Polyhedra by Rotating Half-Planes

    Full text link
    The Searchlight Scheduling Problem was first studied in 2D polygons, where the goal is for point guards in fixed positions to rotate searchlights to catch an evasive intruder. Here the problem is extended to 3D polyhedra, with the guards now boundary segments who rotate half-planes of illumination. After carefully detailing the 3D model, several results are established. The first is a nearly direct extension of the planar one-way sweep strategy using what we call exhaustive guards, a generalization that succeeds despite there being no well-defined notion in 3D of planar "clockwise rotation". Next follow two results: every polyhedron with r>0 reflex edges can be searched by at most r^2 suitably placed guards, whereas just r guards suffice if the polyhedron is orthogonal. (Minimizing the number of guards to search a given polyhedron is easily seen to be NP-hard.) Finally we show that deciding whether a given set of guards has a successful search schedule is strongly NP-hard, and that deciding if a given target area is searchable at all is strongly PSPACE-hard, even for orthogonal polyhedra. A number of peripheral results are proved en route to these central theorems, and several open problems remain for future work.Comment: 45 pages, 26 figure

    On Heterogeneous Neighbor Discovery in Wireless Sensor Networks

    Full text link
    Neighbor discovery plays a crucial role in the formation of wireless sensor networks and mobile networks where the power of sensors (or mobile devices) is constrained. Due to the difficulty of clock synchronization, many asynchronous protocols based on wake-up scheduling have been developed over the years in order to enable timely neighbor discovery between neighboring sensors while saving energy. However, existing protocols are not fine-grained enough to support all heterogeneous battery duty cycles, which can lead to a more rapid deterioration of long-term battery health for those without support. Existing research can be broadly divided into two categories according to their neighbor-discovery techniques---the quorum based protocols and the co-primality based protocols.In this paper, we propose two neighbor discovery protocols, called Hedis and Todis, that optimize the duty cycle granularity of quorum and co-primality based protocols respectively, by enabling the finest-grained control of heterogeneous duty cycles. We compare the two optimal protocols via analytical and simulation results, which show that although the optimal co-primality based protocol (Todis) is simpler in its design, the optimal quorum based protocol (Hedis) has a better performance since it has a lower relative error rate and smaller discovery delay, while still allowing the sensor nodes to wake up at a more infrequent rate.Comment: Accepted by IEEE INFOCOM 201

    Guarding and Searching Polyhedra

    Get PDF
    Guarding and searching problems have been of fundamental interest since the early years of Computational Geometry. Both are well-developed areas of research and have been thoroughly studied in planar polygonal settings. In this thesis we tackle the Art Gallery Problem and the Searchlight Scheduling Problem in 3-dimensional polyhedral environments, putting special emphasis on edge guards and orthogonal polyhedra. We solve the Art Gallery Problem with reflex edge guards in orthogonal polyhedra having reflex edges in just two directions: generalizing a classic theorem by O'Rourke, we prove that r/2 + 1 reflex edge guards are sufficient and occasionally necessary, where r is the number of reflex edges. We also show how to compute guard locations in O(n log n) time. Then we investigate the Art Gallery Problem with mutually parallel edge guards in orthogonal polyhedra with e edges, showing that 11e/72 edge guards are always sufficient and can be found in linear time, improving upon the previous state of the art, which was e/6. We also give tight inequalities relating e with the number of reflex edges r, obtaining an upper bound on the guard number of 7r/12 + 1. We further study the Art Gallery Problem with edge guards in polyhedra having faces oriented in just four directions, obtaining a lower bound of e/6 - 1 edge guards and an upper bound of (e+r)/6 edge guards. All the previously mentioned results hold for polyhedra of any genus. Additionally, several guard types and guarding modes are discussed, namely open and closed edge guards, and orthogonal and non-orthogonal guarding. Next, we model the Searchlight Scheduling Problem, the problem of searching a given polyhedron by suitably turning some half-planes around their axes, in order to catch an evasive intruder. After discussing several generalizations of classic theorems, we study the problem of efficiently placing guards in a given polyhedron, in order to make it searchable. For general polyhedra, we give an upper bound of r^2 on the number of guards, which reduces to r for orthogonal polyhedra. Then we prove that it is strongly NP-hard to decide if a given polyhedron is entirely searchable by a given set of guards. We further prove that, even under the assumption that an orthogonal polyhedron is searchable, approximating the minimum search time within a small-enough constant factor to the optimum is still strongly NP-hard. Finally, we show that deciding if a specific region of an orthogonal polyhedron is searchable is strongly PSPACE-hard. By further improving our construction, we show that the same problem is strongly PSPACE-complete even for planar orthogonal polygons. Our last results are especially meaningful because no similar hardness theorems for 2-dimensional scenarios were previously known

    On Optimal Neighbor Discovery

    Full text link
    Mobile devices apply neighbor discovery (ND) protocols to wirelessly initiate a first contact within the shortest possible amount of time and with minimal energy consumption. For this purpose, over the last decade, a vast number of ND protocols have been proposed, which have progressively reduced the relation between the time within which discovery is guaranteed and the energy consumption. In spite of the simplicity of the problem statement, even after more than 10 years of research on this specific topic, new solutions are still proposed even today. Despite the large number of known ND protocols, given an energy budget, what is the best achievable latency still remains unclear. This paper addresses this question and for the first time presents safe and tight, duty-cycle-dependent bounds on the worst-case discovery latency that no ND protocol can beat. Surprisingly, several existing protocols are indeed optimal, which has not been known until now. We conclude that there is no further potential to improve the relation between latency and duty-cycle, but future ND protocols can improve their robustness against beacon collisions.Comment: Conference of the ACM Special Interest Group on Data Communication (ACM SIGCOMM), 201

    EASND: Energy Adaptive Secure Neighbour Discovery Scheme for Wireless Sensor Networks

    Get PDF
    Wireless Sensor Network (WSN) is defined as a distributed system of networking, which is enabled with set of resource constrained sensors, thus attempt to providing a large set of capabilities and connectivity interferences. After deployment nodes in the network must automatically affected heterogeneity of framework and design framework steps, including obtaining knowledge of neighbor nodes for relaying information. The primary goal of the neighbor discovery process is reducing power consumption and enhancing the lifespan of sensor devices. The sensor devices incorporate with advanced multi-purpose protocols, and specifically communication models with the pre-eminent objective of WSN applications. This paper introduces the power and security aware neighbor discovery for WSNs in symmetric and asymmetric scenarios. We have used different of neighbor discovery protocols and security models to make the network as a realistic application dependent model. Finally, we conduct simulation to analyze the performance of the proposed EASND in terms of energy efficiency, collisions, and security. The node channel utilization is exceptionally elevated, and the energy consumption to the discovery of neighbor nodes will also be significantly minimized. Experimental results show that the proposed model has valid accomplishment

    Automatic analysis (aa): efficient neuroimaging workflows and parallel processing using Matlab and XML.

    Get PDF
    Recent years have seen neuroimaging data sets becoming richer, with larger cohorts of participants, a greater variety of acquisition techniques, and increasingly complex analyses. These advances have made data analysis pipelines complicated to set up and run (increasing the risk of human error) and time consuming to execute (restricting what analyses are attempted). Here we present an open-source framework, automatic analysis (aa), to address these concerns. Human efficiency is increased by making code modular and reusable, and managing its execution with a processing engine that tracks what has been completed and what needs to be (re)done. Analysis is accelerated by optional parallel processing of independent tasks on cluster or cloud computing resources. A pipeline comprises a series of modules that each perform a specific task. The processing engine keeps track of the data, calculating a map of upstream and downstream dependencies for each module. Existing modules are available for many analysis tasks, such as SPM-based fMRI preprocessing, individual and group level statistics, voxel-based morphometry, tractography, and multi-voxel pattern analyses (MVPA). However, aa also allows for full customization, and encourages efficient management of code: new modules may be written with only a small code overhead. aa has been used by more than 50 researchers in hundreds of neuroimaging studies comprising thousands of subjects. It has been found to be robust, fast, and efficient, for simple-single subject studies up to multimodal pipelines on hundreds of subjects. It is attractive to both novice and experienced users. aa can reduce the amount of time neuroimaging laboratories spend performing analyses and reduce errors, expanding the range of scientific questions it is practical to address

    Randomized neighbor discovery protocols with collision detection for static multi-hop wireless ad hoc networks

    Full text link
    [EN] Neighbor discovery represents a first step after the deployment of wireless ad hoc networks, since the nodes that form them are equipped with limited-range radio transceivers, and they typically do not know their neighbors. In this paper two randomized neighbor discovery approaches, called CDH and CDPRR, based on collision detection for static multi-hop wireless ad hoc networks, are presented. Castalia 3.2 simulator has been used to compare our proposed protocols against two protocols chosen from the literature and used as reference: the PRR, and the Hello protocol. For the experiments, we chose five metrics: the neighbor discovery time, the number of discovered neighbors, the energy consumption, the throughput and the number of discovered neighbors versus packets sent ratio. According to the results obtained through simulation, we can conclude that our randomized proposals outperform both Hello and PRR protocols in the presence of collisions regarding all five metrics, for both one-hop and multi-hop scenarios. As novelty compared to the reference protocols, both proposals allow nodes to discover all their neighbors with probability 1, they are based on collision detection and know when to terminate the neighbor discovery process. Furthermore, qualitative comparisons of the existing protocols and the proposals are available in this paper. Moreover, CDPRR presents better results in terms of time, energy consumption and number of discovered neighbors versus packets sent ratio. We found that both proposals achieve to operate under more realistic assumptions. Furthermore, CDH does not need to know the number of nodes in the network.This work has been partially supported by the "Ministerio de Economia y Competitividad" in the "Programa Estatal de Fomento de la Investigacion Cientifica y Tecnica de Excelencia, Subprograma Estatal de Generacion de Conocimiento" within the project under Grant TIN2017-84802-C2-1-P. This work has also been partially supported by European Union through the ERANETMED (Euromediterranean Cooperation through ERANET joint activities and beyond) project ERANETMED3-227 SMARTWATIR.Sorribes, JV.; Peñalver Herrero, ML.; Tavares De Araujo Cesariny Calafate, CM.; Lloret, J. (2021). Randomized neighbor discovery protocols with collision detection for static multi-hop wireless ad hoc networks. Telecommunication Systems. 77(3):577-596. https://doi.org/10.1007/s11235-021-00763-457759677

    Mathematics for General Education: Another Rule of Three

    Get PDF
    • …
    corecore