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Distance Measurements by Taping01:18

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Tapes are essential in surveying for accurate, durable, and short-distance measurements. Made from lightweight, nylon-coated steel, they offer flexibility and strength for rugged outdoor use. The nylon coating protects against rust and wear, extending the tape's life. Standard lengths, around 30 meters, are marked in meters and millimeters for precision.Surveyors select tapes based on site conditions and accuracy needs. Lightweight, nylon-coated tapes are commonly used for ease of handling and...
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Related Experiment Video

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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Recognizing distance-count matrices.

Paolo Boldi1, Chiara Prezioso1, Flavio Furia1

  • 1Computer Science Department, Università degli Studi, Milano, Italy.

Plos One
|July 8, 2026
PubMed
Summary
This summary is machine-generated.

Recognizing distance-count matrices (DCMs) for graphs is computationally hard. However, constructing DCMs is efficient for graphs built using specific operations, enabling tractable compositional theories.

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Area of Science:

  • Graph theory
  • Network analysis
  • Computational complexity

Background:

  • Axiomatizing centrality measures often requires counterexamples.
  • Geometric centrality counterexamples necessitate graphs with specific distance counts.
  • Distance-count matrices (DCMs) encode these distance counts.

Purpose of the Study:

  • To determine the computational complexity of recognizing distance-count matrices (DCMs).
  • To investigate the tractability of constructing DCMs under graph operations.

Main Methods:

  • Proving the strong NP-completeness of recognizing DCMs for undirected graphs.
  • Analyzing the algorithmic behavior of DCM construction under graph operations (DCM-stable operations).

Main Results:

  • Deciding if a matrix is a DCM is strongly NP-complete.
  • Constructing DCMs is computationally intractable in general.
  • DCM construction is algorithmically well-behaved for DCM-stable graph operations.

Conclusions:

  • The inverse problem of constructing DCMs is generally intractable.
  • Distance-count matrices possess a tractable compositional theory for structured graph classes generated by DCM-stable operations.