Mathematics Branches, Topics, and Sub-Topics

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68Wxx Algorithms and complexity-related methods

This subtopic introduces the core ideas in algorithms and complexity-related methods, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.

Specific topics

68W01 General topics in algorithms

Overview

This topic examines general topics in algorithms within algorithms and complexity in computing, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Algorithm (Wikipedia)

Useful Links

Key Ideas

  • Design and analysis of efficient algorithms
  • Approximation quality and provable running-time bounds
  • Trade-offs between exactness, speed, and memory

Typical Uses

Used to choose, analyze, and improve algorithms for optimization, search, and data processing problems.

Applications

  • Optimization heuristics
  • Approximation methods
  • High-performance algorithm engineering

References

Recommended Textbooks

68W05 Nonnumerical algorithms

Overview

This topic examines nonnumerical algorithms within algorithms and complexity in computing, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Algorithm (Wikipedia)

Useful Links

Key Ideas

  • Design and analysis of efficient algorithms
  • Approximation quality and provable running-time bounds
  • Trade-offs between exactness, speed, and memory

Typical Uses

Used to choose, analyze, and improve algorithms for optimization, search, and data processing problems.

Applications

  • Optimization heuristics
  • Approximation methods
  • High-performance algorithm engineering

References

Recommended Textbooks

68W10 Parallel algorithms in computer science

Overview

This topic examines parallel algorithms in computer science within algorithms and complexity in computing, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Algorithm (Wikipedia)

Useful Links

Key Ideas

  • Design and analysis of efficient algorithms
  • Approximation quality and provable running-time bounds
  • Trade-offs between exactness, speed, and memory

Typical Uses

Used to choose, analyze, and improve algorithms for optimization, search, and data processing problems.

Applications

  • Optimization heuristics
  • Approximation methods
  • High-performance algorithm engineering

References

Recommended Textbooks

68W15 Distributed algorithms

Overview

This topic examines distributed algorithms within algorithms and complexity in computing, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Algorithm (Wikipedia)

Useful Links

Key Ideas

  • Design and analysis of efficient algorithms
  • Approximation quality and provable running-time bounds
  • Trade-offs between exactness, speed, and memory

Typical Uses

Used to choose, analyze, and improve algorithms for optimization, search, and data processing problems.

Applications

  • Optimization heuristics
  • Approximation methods
  • High-performance algorithm engineering

References

Recommended Textbooks

68W20 Randomized algorithms, average case analysis

Overview

This topic examines randomized algorithms, average case analysis within algorithms and complexity in computing, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Algorithm (Wikipedia)

Useful Links

Key Ideas

  • Design and analysis of efficient algorithms
  • Approximation quality and provable running-time bounds
  • Trade-offs between exactness, speed, and memory

Typical Uses

Used to choose, analyze, and improve algorithms for optimization, search, and data processing problems.

Applications

  • Optimization heuristics
  • Approximation methods
  • High-performance algorithm engineering

References

Recommended Textbooks

68W25 Approximation algorithms

Overview

This topic examines approximation algorithms within algorithms and complexity in computing, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Algorithm (Wikipedia)

Useful Links

Key Ideas

  • Design and analysis of efficient algorithms
  • Approximation quality and provable running-time bounds
  • Trade-offs between exactness, speed, and memory

Typical Uses

Used to choose, analyze, and improve algorithms for optimization, search, and data processing problems.

Applications

  • Optimization heuristics
  • Approximation methods
  • High-performance algorithm engineering

References

Recommended Textbooks

68W27 Online algorithms; streaming algorithms

Overview

This topic examines online algorithms; streaming algorithms within algorithms and complexity in computing, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Algorithm (Wikipedia)

Useful Links

Key Ideas

  • Design and analysis of efficient algorithms
  • Approximation quality and provable running-time bounds
  • Trade-offs between exactness, speed, and memory

Typical Uses

Used to choose, analyze, and improve algorithms for optimization, search, and data processing problems.

Applications

  • Optimization heuristics
  • Approximation methods
  • High-performance algorithm engineering

References

Recommended Textbooks

68W30 Symbolic computation and algebraic computation

Overview

This topic examines symbolic computation and algebraic computation within algorithms and complexity in computing, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Algorithm (Wikipedia)

Useful Links

Key Ideas

  • Design and analysis of efficient algorithms
  • Approximation quality and provable running-time bounds
  • Trade-offs between exactness, speed, and memory

Typical Uses

Used to choose, analyze, and improve algorithms for optimization, search, and data processing problems.

Applications

  • Optimization heuristics
  • Approximation methods
  • High-performance algorithm engineering

References

Recommended Textbooks

68W32 Algorithms on strings

Overview

This topic examines algorithms on strings within algorithms and complexity in computing, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Algorithm (Wikipedia)

Useful Links

Key Ideas

  • Design and analysis of efficient algorithms
  • Approximation quality and provable running-time bounds
  • Trade-offs between exactness, speed, and memory

Typical Uses

Used to choose, analyze, and improve algorithms for optimization, search, and data processing problems.

Applications

  • Optimization heuristics
  • Approximation methods
  • High-performance algorithm engineering

References

Recommended Textbooks

68W35 VLSI algorithms

Overview

This topic examines vlsi algorithms within algorithms and complexity in computing, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Algorithm (Wikipedia)

Useful Links

Key Ideas

  • Design and analysis of efficient algorithms
  • Approximation quality and provable running-time bounds
  • Trade-offs between exactness, speed, and memory

Typical Uses

Used to choose, analyze, and improve algorithms for optimization, search, and data processing problems.

Applications

  • Optimization heuristics
  • Approximation methods
  • High-performance algorithm engineering

References

Recommended Textbooks

68W40 Analysis of algorithms

Overview

This topic examines analysis of algorithms within algorithms and complexity in computing, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Algorithm (Wikipedia)

Useful Links

Key Ideas

  • Design and analysis of efficient algorithms
  • Approximation quality and provable running-time bounds
  • Trade-offs between exactness, speed, and memory

Typical Uses

Used to choose, analyze, and improve algorithms for optimization, search, and data processing problems.

Applications

  • Optimization heuristics
  • Approximation methods
  • High-performance algorithm engineering

References

Recommended Textbooks

68W50 Evolutionary algorithms, genetic algorithms, swarm intelligence

Overview

This topic examines evolutionary algorithms, genetic algorithms, swarm intelligence within algorithms and complexity in computing, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Algorithm (Wikipedia)

Useful Links

Key Ideas

  • Design and analysis of efficient algorithms
  • Approximation quality and provable running-time bounds
  • Trade-offs between exactness, speed, and memory

Typical Uses

Used to choose, analyze, and improve algorithms for optimization, search, and data processing problems.

Applications

  • Optimization heuristics
  • Approximation methods
  • High-performance algorithm engineering

References

Recommended Textbooks

68W60 Graph algorithms and data structures

Overview

This topic examines graph algorithms and data structures within algorithms and complexity in computing, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Algorithm (Wikipedia)

Useful Links

Key Ideas

  • Design and analysis of efficient algorithms
  • Approximation quality and provable running-time bounds
  • Trade-offs between exactness, speed, and memory

Typical Uses

Used to choose, analyze, and improve algorithms for optimization, search, and data processing problems.

Applications

  • Optimization heuristics
  • Approximation methods
  • High-performance algorithm engineering

References

Recommended Textbooks

68W99 None of the above

Overview

This topic examines none of the above within algorithms and complexity in computing, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Algorithm (Wikipedia)

Useful Links

Key Ideas

  • Design and analysis of efficient algorithms
  • Approximation quality and provable running-time bounds
  • Trade-offs between exactness, speed, and memory

Typical Uses

Used to choose, analyze, and improve algorithms for optimization, search, and data processing problems.

Applications

  • Optimization heuristics
  • Approximation methods
  • High-performance algorithm engineering

References

Recommended Textbooks