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Related Concept Videos

Range00:59

Range

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The range is one of the measures of variation. It can be defined as the difference between a dataset's highest and lowest values. For example, in the study of seven 16-ounce soda cans, the filled volume of soda was measured, thus producing the following amount (in ounces) of soda:
15.9; 16.1; 15.2; 14.8; 15.8; 15.9; 16.0; 15.5
Measurements of the amount of soda in a 16-ounce can vary since different subjects record these measurements or since the exact amount - 16 ounces of liquid, was not...
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Midrange01:07

Midrange

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A somewhat easy to compute quantitative estimate of a data set’s central tendency is its midrange, which is defined as the mean of the minimum and maximum values of an ordered data set.
Simply put, the midrange is half of the data set’s range. Similar to the mean, the midrange is sensitive to the extreme values and hence the prospective outliers. However, unlike the mean, the midrange is not sensitive to all the values of the data set that lie in the middle. Thus, it is prone to...
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Unusual Results01:16

Unusual Results

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Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In problems involving probability, unusual results can be observed in 2 instances – an unusually high number of successes or an unusually low number of successes.
According to the range rule of thumb, any value above or below two standard deviations, 2σ  from the mean, μ  is considered unusual.
Maximum unusual value =...
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Range Rule of Thumb to Interpret Standard Deviation01:13

Range Rule of Thumb to Interpret Standard Deviation

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The range rule of thumb in statistics helps us calculate a dataset's minimum and maximum values with known standard deviation. This rule is based on the concept that 95% of all values in a dataset lie within two standard deviations from the mean.
For instance, the range rule of thumb can be used to find the tallest and the shortest student in a class, given the mean student height and standard deviation. If the mean student height is 1.6 m and the standard deviation, s is 0.05 m, the height...
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Absolute and Local Extreme Values01:22

Absolute and Local Extreme Values

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The highest and lowest values of a function, relative to a reference axis, are known as extreme values. These include absolute maximum and absolute minimum values, which represent the highest and lowest points the function reaches across its entire domain. Within a restricted portion of the function, the highest and lowest values are referred to as local maximum and local minimum values, respectively.Periodic functions, such as sine and cosine, show extreme values at infinitely many points due...
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Wald-Wolfowitz Runs Test I01:17

Wald-Wolfowitz Runs Test I

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The Wald-Wolfowitz test, also known as the runs test, is a nonparametric statistical test used to assess the randomness of a sequence of two different types of elements (e.g., positive/negative values, successes/failures). It examines whether the order of the elements in a sequence is random or if there is a pattern or trend present. This nonparametric test applies to any ordered data despite the population and sample data distribution, even if a higher sample size is available.
The test works...
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Updated: May 1, 2026

Executing Complexity-Increasing Queries in Relational MySQL and NoSQL MongoDB and EXist Size-Growing ISO/EN 13606 Standardized EHR Databases
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Encoding range minima and range top-2 queries.

Pooya Davoodi1, Gonzalo Navarro, Rajeev Raman

  • 1Computer Science and Engineering, New York University Polytechnic School of Engineering, , Brooklyn, NY 11201, USA.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|April 23, 2014
PubMed
Summary
This summary is machine-generated.

We developed a data structure for efficient range minimum queries (RMQs) using optimal space and constant query time. This method also improves encoding for random arrays and extends to range top-2 queries.

Keywords:
Cartesian treerange minimum queryrepresentations of ordinal treesuccinct data structuretransformation

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Area of Science:

  • Data Structures and Algorithms
  • Information Theory
  • Computational Complexity

Background:

  • Range Minimum Queries (RMQs) are fundamental in computer science.
  • Efficiently answering RMQs without array access requires specialized data structures.
  • Existing methods achieve optimal space and time but can be complex or lack expected performance on random data.

Purpose of the Study:

  • To develop a novel data structure for encoding Range Minimum Queries (RMQs).
  • To achieve asymptotically optimal space usage and constant worst-case query time.
  • To extend the approach to the Range Top-2 Query (RT2Q) problem and analyze its performance.

Main Methods:

  • Design of a new data structure for RMQ encoding.
  • Analysis of space complexity (2n+o(n) bits) and query time (O(1)).
  • Extension to RT2Q with a data structure using 3.272n+o(n) bits and constant query time.

Main Results:

  • Achieved asymptotically optimal 2n+o(n) bits space for RMQ encoding.
  • Guaranteed O(1) worst-case time for RMQ answering.
  • Demonstrated expected space of 1.919n+o(n) bits for RMQs on random arrays.
  • Developed a constant-time RT2Q data structure with 3.272n+o(n) bits.

Conclusions:

  • The proposed RMQ data structure is efficient and offers a more natural approach.
  • The method provides improved expected space complexity for random arrays.
  • The generalization to RT2Q offers a practical solution for finding top-k elements efficiently.