metric space
- noun
- /ˈmɛtrɪk speɪs/
- Specialized
:
espacio métrico
- In a metric space, the distance between any two points must satisfy the triangle inequality.
- point in the metric space
Examples
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This approach is used to derive simple memoryless algorithms for two types of online problems. We derive a simple algorithm, which is memoryless and randomized, for the k-server problem in a metric space with n points.
Academic text (1994) -
Each time you calculate distances, you are working within a metric space defined by certain properties.
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We simply map points in our metric space to a function.
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But if your metric space is connected, let me state it that way.
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So let X be a metric space and YA subset of X.
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After a request has been served, there is at least one point in the metric space where both Harmonic and the adversary have a server.
Academic text (1994) -
At every step, the two servers managed by Harmonic and the two managed by the adversary occupy (up to) four points in the metric space.
Academic text (1994) -
Even without the Lazy Adversary Conjecture, we can bound the performance of the Harmonic algorithm in an arbitrary metric space for the case M = 2.
Academic text (1994) -
Lamar thought, Maurice Fréchet came up with the idea of metric space in the year 1906.
Fiction book (1999) -
Later, Grove 19 proved that Harmonic achieves a competitive ratio that is O(M²M) in any metric space and for all M.
Academic text (1994)
Surface Forms
Morphology
The compound is directly compositional: 'metric' (a distance-defining function) modifies 'space', so a learner who knows both words can infer it means a space that has a metric (i.e. a notion of distance). Although the term is technical and 'space' here is an abstract mathematical set rather than a physical area, the overall meaning is derivable from the constituents and follows common noun-modifier logic.
Etymology
The term metric space comes from the words metric (a rule to 'measure') and space (a set of points). It means a set where you can give a 'distance' between any two points, so the name says it is a space with a metric.
