lecture_18

# lecture_18 - Introduction to Algorithms 6.046J/18.401...

This preview shows pages 1–7. Sign up to view the full content.

Introduction to Algorithms 6.046J/18.401 Lecture 1 7 Prof. Piotr Indyk

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Computational Geometry ctd. Segment intersection problem: – Given: a set of n distinct segments s 1 …s n , represented by coordinates of endpoints – Detection : detect if there is any pair s i s j that intersects – Reporting : report all pairs of intersecting segments © 2003 by Piotr Indyk Introduction to Algorithms November 15, 2004 L18.2
Segment intersection Easy to solve in O(n 2 ) time Is it possible to get a better algorithm for the reporting problem ? •N O (in the worst-case) However: – We will see we can do better for the detection problem – Moreover, the number of intersections P is usually small. Then, we would like an output sensitive algorithm, whose running time is low if P is small . © 2003 by Piotr Indyk Introduction to Algorithms November 15, 2004 L18.3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Result We will show: – O(n log n) time for detection – O( (n +P) log n) time for reporting We will use … … (no, not divide and conquer) Binary Search Trees Specifically: Line sweep approach © 2003 by Piotr Indyk Introduction to Algorithms November 15, 2004 L18.4
Orthogonal segments V-segment All segments are either horizontal or vertical H-segment Assumption: all coordinates are distinct Therefore, only vertical- horizontal intersections exist © 2003 by Piotr Indyk Introduction to Algorithms November 15, 2004 L18.5

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Orthogonal segments Sweep line: –A vertical line sweeps the plane from left to right – It “stops” at all “important” x-coordinates, i.e., when it hits a V-segment or endpoints of an H-segment
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 04/10/2008 for the course CSE 6.046J/18. taught by Professor Piotrindykandcharlese.leiserson during the Fall '04 term at MIT.

### Page1 / 19

lecture_18 - Introduction to Algorithms 6.046J/18.401...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online