# DSA 2 at Technische Universität Graz

## Flashcards and summaries for DSA 2 at the Technische Universität Graz

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### Exemplary flashcards for DSA 2 at the Technische Universität Graz on StudySmarter:

Triangulation of a point set S in the plain is ...

### Exemplary flashcards for DSA 2 at the Technische Universität Graz on StudySmarter:

Triangulation of a Polygon P is ...

### Exemplary flashcards for DSA 2 at the Technische Universität Graz on StudySmarter:

Plane Straight-Line Graph is

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### Exemplary flashcards for DSA 2 at the Technische Universität Graz on StudySmarter:

Maximal Plane Straight-Line Graph is

### Exemplary flashcards for DSA 2 at the Technische Universität Graz on StudySmarter:

How many edges and triangles can a triangulation of a pointset S with n points have?

### Exemplary flashcards for DSA 2 at the Technische Universität Graz on StudySmarter:

How many edges and triangles can a triangulation of a polygon P with n vertices have?

### Exemplary flashcards for DSA 2 at the Technische Universität Graz on StudySmarter:

What can triangulations be used for?

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### Exemplary flashcards for DSA 2 at the Technische Universität Graz on StudySmarter:

A triangulation for an n-point set can be constructed in

### Exemplary flashcards for DSA 2 at the Technische Universität Graz on StudySmarter:

A directed Graph is called ... if it has no loops

### Exemplary flashcards for DSA 2 at the Technische Universität Graz on StudySmarter:

Simplepath contains ...

### Exemplary flashcards for DSA 2 at the Technische Universität Graz on StudySmarter:

Length in weighted graphs is  ...

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### Exemplary flashcards for DSA 2 at the Technische Universität Graz on StudySmarter:

An undirected graph is a forest if

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## Exemplary flashcards for DSA 2 at the Technische Universität Graz on StudySmarter:

DSA 2

Triangulation of a point set S in the plain is ...

a partition of the convex hull of it into interior-disjoint triangles, whose edges are segments spanned by the points of S.
Also no point of S lies inside a segment or a triangle.

DSA 2

Triangulation of a Polygon P is ...

the maximal plane straight-line graph on S inside P

DSA 2

Plane Straight-Line Graph is

a set of points in the plain and the set of edges spend by this points, such that no two edges cross in their interior

DSA 2

Maximal Plane Straight-Line Graph is

one where we can't add any edge without crossing another edge.

-> We can obtain a Maximal Plane Straight-Line Graph by adding edges, that are not crossing the other edges, as long as possible (the result is always a TRIANGULATION)

DSA 2

How many edges and triangles can a triangulation of a pointset S with n points have?

e = 3n−3−h   edges

t = 2n−2−h    triangles
h -> extreme points

DSA 2

How many edges and triangles can a triangulation of a polygon P with n vertices have?

e = 2n−3   edges

t = n−2     triangles

-> The number of edges and triangles is linear in the number of vertices

DSA 2

What can triangulations be used for?

• modelling surfaces
• triangular networks in cartography
• 3D modeling
• Computer Graphics
• simulation of fluid flows
• proving time bounds
• finding shortest path inside a polygon
• combinatorics
• ...

DSA 2

A triangulation for an n-point set can be constructed in

O(n log n) time

Θ(n) space

DSA 2

A directed Graph is called ... if it has no loops

simple

DSA 2

Simplepath contains ...

every vertex in V at most once

DSA 2

Length in weighted graphs is  ...

the sum of the edge weights

DSA 2

An undirected graph is a forest if

if it is acyclic

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