ps3sol

# ps3sol - 6.889 Algorithms for Planar Graphs and Beyond...

This preview shows pages 1–2. Sign up to view the full content.

6.889: Algorithms for Planar Graphs and Beyond September 28, 2011 Problem Set 3 This problem set is due Wednesday, October 5 at noon. 1. Let P := { p 1 ,...,p k } be points in the plane and { Q 1 ,...,Q t } be a partition of P into t sets. Argue (informally) that there exist disjoint curves in the plane, C 1 ,...,C t , such that for i = 1 ,...,t , Q i C i . Deduce (informally) that there is a suitable function g , such that for every k , the planar grid graph G of size g ( k ) × g ( k ) has the following property: if u 1 ,...,u k V ( G ) are suﬃciently far apart from each other and from the boundary (i.e. their pairwise distance and distance to the boundary is at least f ( k ) for a suitable function f ) and { Q 1 ,...,Q t } is a partition of { u 1 ,...,u k } , then there exist disjoint trees T 1 ,...,T t in G such that for i = 1 ,...,t , Q i T i . Solution: Let Π be the plane and observe that if F is a ﬁnite set of points in Π then Π - F is still connected. So for any two given points

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

ps3sol - 6.889 Algorithms for Planar Graphs and Beyond...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online