ALGORITHMS

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ALGORITHMS
Mark de Berg TU Eindhoven
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Algorithms research

• Try to find (the most) efficient solutions to
  computational problems
• fast
• small storage
• Example given a source s and destination t in a
  network, what is the fastest way to compute the
  shortest path from s to t ?

t
s
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Algorithms and efficiency

• Data sets are getting larger and larger
• Optimizing code or fast hardware help to speed up
  algorithms, but only to a limited extent

scale-up behavior is crucial
code optimization
10 n2
n2/10 50 n log n (factor 1000 gain
for n106)
different approach with better scale-up behavior
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Our specialty algorithms for spatial data

• Many areas of computer science deal with spatial
  data
• geographic information systems
• CAD/CAM
• robotics
• We study algorithmic aspects of problems arising
  in such areas.

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Geographic Information Systems
Dot map set of points in the plane representing
population density, etc.
How can we compute a dot map with half the number
of dots that represents the same distribution?
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Shape matching
How can we store a collection of shapes such that
we can quickly find the ones that resemble a
query shape most closely?
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CAD/CAM
Design for manufacturing Can a given design be
manufactured with a certain technology?
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Visualization

• How can we compute a representation of a terrain
  at a lower level of detail?
• How can we generate a representation with a
  mixed resolution high level of detail near the
  viewer, low level of detail far away?

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Motion planning and collision detection
How do we compute whether a given part can be
transported out of an industrial installation?
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Doing a research project in algorithms

• Theory
• Develop new algorithms and data structures
• Prove that they work
• Analyze efficiency
• Experiments
• Compare new solution experimentally with
  existing solutions
• Fine-tune the algorithm to get the best
  performance
• Balance between theoretical and experimental work
  depends
• on personal preference of the student.

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Recommended courses
I/O

• I/O-efficient algorithms
• (1st trimester)
• Computer graphics
• (1st trimester)
• Probabilistic algorithms
• (2nd semester)
• Geometric algorithms
• (3rd trimester)

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The Algorithms Group
Mohammad Farshi
Otfried Cheong
Yuval Nir
Mohammad Abam
Chris Gray
Mark Schroders
Sheung-Hung Poon
Micha Streppel
Xavier Goaoc