Computer Science – Discrete Mathematics
Scientific paper
2008-09-11
Computer Science
Discrete Mathematics
30 pages, use pgf/tikz
Scientific paper
Sturmian words are infinite binary words with many equivalent definitions: They have a minimal factor complexity among all aperiodic sequences; they are balanced sequences (the labels 0 and 1 are as evenly distributed as possible) and they can be constructed using a mechanical definition. All this properties make them good candidates for being extremal points in scheduling problems over two processors. In this paper, we consider the problem of generalizing Sturmian words to trees. The problem is to evenly distribute labels 0 and 1 over infinite trees. We show that (strongly) balanced trees exist and can also be constructed using a mechanical process as long as the tree is irrational. Such trees also have a minimal factor complexity. Therefore they bring the hope that extremal scheduling properties of Sturmian words can be extended to such trees, as least partially. Such possible extensions are illustrated by one such example.
Gast Nicolas
Gaujal Bruno
No associations
LandOfFree
Distributing Labels on Infinite Trees does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Distributing Labels on Infinite Trees, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Distributing Labels on Infinite Trees will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-473976