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Related Concept Videos

Graphs of Equations in Two Variables01:30

Graphs of Equations in Two Variables

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An equation with two variables, typically written in the form y = f(x) or Ax + By = C, describes a relationship between quantities represented by x and y. Each solution to such an equation is an ordered pair (x, y) that satisfies the equation when substituted. These pairs can be represented graphically to understand the variables' relationship visually.A common technique for constructing the graph of a two-variable equation is to create a value table. Begin by choosing several values for the...
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Graphs of functions provide a visual representation of how output values change in response to varying inputs. Each point on the graph corresponds to an ordered pair, where the x-coordinate (independent variable) determines the horizontal position and the y-coordinate (dependent variable) determines the vertical position. Linear functions like y = x give a straight line, indicating a constant rate of change.Nonlinear functions display more complex behaviors. Even power functions generate...
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The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
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A Y-connected synchronous generator, grounded through a neutral impedance, is designed to produce balanced internal phase voltages with only positive-sequence components. The generator's sequence networks include a source voltage that is exclusively in the positive-sequence network. The sequence components of line-to-ground voltages at the generator terminals illustrate this configuration.
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The graph of the equation where y equals x squared forms a curve known as a parabola. This curve acts as a boundary in the coordinate plane, dividing it into distinct regions based on the relative position of points.When the equality sign in the equation is replaced with an inequality—such as greater than, less than, greater than or equal to, or less than or equal to—the graphical representation changes from a single curve into a broader shaded area that signifies the set of all...
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An ogive graph is sometimes called a cumulative frequency polygon. It is one type of frequency polygon that shows cumulative frequency. In other words, the cumulative percentages are added to the graph from left to right. An ogive graph plots cumulative frequency on the vertical y-axis and class boundaries along the horizontal x-axis. It’s very similar to a histogram; only instead of rectangles, an ogive displays a single point where the top right of the rectangle would be. Creating this...
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Related Experiment Video

Updated: Mar 9, 2026

A Knowledge Graph Approach to Elucidate the Role of Organellar Pathways in Disease via Biomedical Reports
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EmptyHeaded: A Relational Engine for Graph Processing.

Christopher R Aberger1, Susan Tu1, Kunle Olukotun1

  • 1Stanford University.

Proceedings. ACM-SIGMOD International Conference on Management of Data
|January 13, 2017
PubMed
Summary
This summary is machine-generated.

EmptyHeaded is a new high-level graph processing engine that matches low-level performance. It offers an easier-to-use query language while achieving speeds comparable to specialized graph engines.

Keywords:
GHDH.2 [Information Systems]: Database Management System EnginesSIMDWorst-case optimal joingeneralized hypertree decompositiongraph processingsingle instruction multiple data

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Area of Science:

  • Computer Science
  • Database Systems
  • Graph Analytics

Background:

  • High-performance graph processing engines are typically categorized as low-level or high-level.
  • Low-level engines offer performance but require complex user coding, while high-level engines are user-friendly but significantly slower.

Purpose of the Study:

  • To introduce EmptyHeaded, a novel high-level graph processing engine.
  • To achieve performance comparable to low-level engines while maintaining ease of use.

Main Methods:

  • Developed a new class of join algorithms with theoretical guarantees.
  • Designed a novel join engine architecture featuring a query optimizer and SIMD-parallel data layouts.
  • Implemented a rich datalog-like query language.

Main Results:

  • EmptyHeaded significantly outperforms existing high-level approaches (up to 3 orders of magnitude) on graph pattern queries, PageRank, and SSSP.
  • Achieved performance comparable to the best low-level engine (Galois) on PageRank and competitive performance on SSSP.

Conclusions:

  • EmptyHeaded bridges the gap between usability and performance in graph processing.
  • The engine demonstrates the potential of novel join algorithms and architecture for high-performance graph analytics.