136 research outputs found

    Weighted Coverings and Packings

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    In this paper we introduce a generalization of the concepts of coverings and packings in Hamming space called weighted coverings and packings. This allows us to formulate a number of well-known coding theoretical problems in a uniform manner. We study the existence of perfect weighted codes, discuss connections between weighted coverings and packings, and present many constructions for them

    Covering Radius 1985-1994

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    We survey important developments in the theory of covering radius during the period 1985-1994. We present lower bounds, constructions and upper bounds, the linear and nonlinear cases, density and asymptotic results, normality, specific classes of codes, covering radius and dual distance, tables, and open problems

    Partitioning a Polygon Into Small Pieces

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    We study the problem of partitioning a given simple polygon PP into a minimum number of polygonal pieces, each of which has bounded size. We give algorithms for seven notions of `bounded size,' namely that each piece has bounded area, perimeter, straight-line diameter, geodesic diameter, or that each piece must be contained in a unit disk, an axis-aligned unit square or an arbitrarily rotated unit square. A more general version of the area problem has already been studied. Here we are, in addition to PP, given positive real values a1,,aka_1,\ldots,a_k such that the sum i=1kai\sum_{i=1}^k a_i equals the area of PP. The goal is to partition PP into exactly kk pieces Q1,,QkQ_1,\ldots,Q_k such that the area of QiQ_i is aia_i. Such a partition always exists, and an algorithm with running time O(nk)O(nk) has previously been described, where nn is the number of corners of PP. We give an algorithm with optimal running time O(n+k)O(n+k). For polygons with holes, we get running time O(nlogn+k)O(n\log n+k). For the other problems, it seems out of reach to compute optimal partitions for simple polygons; for most of them, even in extremely restricted cases such as when PP is a square. We therefore develop O(1)O(1)-approximation algorithms for these problems, which means that the number of pieces in the produced partition is at most a constant factor larger than the cardinality of a minimum partition. Existing algorithms do not allow Steiner points, which means that all corners of the produced pieces must also be corners of PP. This has the disappointing consequence that a partition does often not exist, whereas our algorithms always produce useful partitions. Furthermore, an optimal partition without Steiner points may require Ω(n)\Omega(n) pieces for polygons where a partition consisting of just 22 pieces exists when Steiner points are allowed.Comment: 32 pages, 24 figure

    Quality of Service Aware Data Stream Processing for Highly Dynamic and Scalable Applications

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    Huge amounts of georeferenced data streams are arriving daily to data stream management systems that are deployed for serving highly scalable and dynamic applications. There are innumerable ways at which those loads can be exploited to gain deep insights in various domains. Decision makers require an interactive visualization of such data in the form of maps and dashboards for decision making and strategic planning. Data streams normally exhibit fluctuation and oscillation in arrival rates and skewness. Those are the two predominant factors that greatly impact the overall quality of service. This requires data stream management systems to be attuned to those factors in addition to the spatial shape of the data that may exaggerate the negative impact of those factors. Current systems do not natively support services with quality guarantees for dynamic scenarios, leaving the handling of those logistics to the user which is challenging and cumbersome. Three workloads are predominant for any data stream, batch processing, scalable storage and stream processing. In this thesis, we have designed a quality of service aware system, SpatialDSMS, that constitutes several subsystems that are covering those loads and any mixed load that results from intermixing them. Most importantly, we natively have incorporated quality of service optimizations for processing avalanches of geo-referenced data streams in highly dynamic application scenarios. This has been achieved transparently on top of the codebases of emerging de facto standard best-in-class representatives, thus relieving the overburdened shoulders of the users in the presentation layer from having to reason about those services. Instead, users express their queries with quality goals and our system optimizers compiles that down into query plans with an embedded quality guarantee and leaves logistic handling to the underlying layers. We have developed standard compliant prototypes for all the subsystems that constitutes SpatialDSMS

    LIPIcs, Volume 258, SoCG 2023, Complete Volume

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    LIPIcs, Volume 258, SoCG 2023, Complete Volum

    Geometry and Topology in Memory and Navigation

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    Okinawa Institute of Science and Technology Graduate UniversityDoctor of PhilosophyGeometry and topology offer rich mathematical worlds and perspectives with which to study and improve our understanding of cognitive function. Here I present the following examples: (1) a functional role for inhibitory diversity in associative memories with graph- ical relationships; (2) improved memory capacity in an associative memory model with setwise connectivity, with implications for glial and dendritic function; (3) safe and effi- cient group navigation among conspecifics using purely local geometric information; and (4) enhancing geometric and topological methods to probe the relations between neural activity and behaviour. In each work, tools and insights from geometry and topology are used in essential ways to gain improved insights or performance. This thesis contributes to our knowledge of the potential computational affordances of biological mechanisms (such as inhibition and setwise connectivity), while also demonstrating new geometric and topological methods and perspectives with which to deepen our understanding of cognitive tasks and their neural representations.doctoral thesi

    The deep space network

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    Various ongoing projects within the Deep Space Network are discussed, including mission support, communications, data processing, and network operations

    Proactive-reactive, robust scheduling and capacity planning of deconstruction projects under uncertainty

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    A project planning and decision support model is developed and applied to identify and reduce risk and uncertainty in deconstruction project planning. It allows calculating building inventories based on sensor information and construction standards and it computes robust project plans for different scenarios with multiple modes, constrained renewable resources and locations. A reactive and flexible planning element is proposed in the case of schedule infeasibility during project execution
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