Concepts inOnline and incremental algorithms for facility location
Dynamic problem (algorithms)
Dynamic problems in computational complexity theory are problems stated in terms of the changing input data. In the most general form a problem in this category is usually stated as follows: Given a class of input objects, find efficient algorithms and data structures to answer a certain query about a set of input objects each time the input data is modified, i.e. , objects are inserted or deleted.
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Facility location
Facility location, also known as location analysis, is a branch of operations research and computational geometry concerning itself with mathematical modeling and solution of problems concerning optimal placement of facilities in order to minimize transportation costs, avoid placing hazardous materials near housing, outperform competitors' facilities, etc.
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Online and offline
The terms "online" and "offline" (also stylized as "on-line" and "off-line") have specific meanings in regard to computer technology and telecommunications. In general, "online" indicates a state of connectivity, while "offline" indicates a disconnected state. In common usage, "online" often refers to the Internet or the World-Wide Web.
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Competitive analysis (online algorithm)
Competitive analysis is a method invented for analyzing online algorithms, in which the performance of an online algorithm (which must satisfy an unpredictable sequence of requests, completing each request without being able to see the future) is compared to the performance of an optimal offline algorithm that can view the sequence of requests in advance. An algorithm is competitive if its competitive ratio¿the ratio between its performance and the offline algorithm's performance¿is bounded.
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Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions. These theories are often studied in the context of real numbers, complex numbers, and real and complex functions. Analysis may be conventionally distinguished from geometry.
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