Introduction to algorithms
Approximating the minimum degree spanning tree to within one from the optimal degree
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Distributed computing: fundamentals, simulations and advanced topics
Distributed computing: fundamentals, simulations and advanced topics
Distributed Algorithms
Tree exploration with little memory
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Bounded Degree Spanning Trees (Extended Abstract)
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Label-guided graph exploration by a finite automaton
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Oracle size: a new measure of difficulty for communication tasks
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Local MST computation with short advice
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Communication algorithms with advice
Journal of Computer and System Sciences
Distributed computing with advice: information sensitivity of graph coloring
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Hi-index | 0.00 |
This paper deals with compact label-based representations for trees. Consider an n-node undirected connected graph G with a predefined numbering on the ports of each node. The all-ports tree labeling ${\mathcal L}_{all}$ gives each node v of G a label containing the port numbers of all the tree edges incident to v. The upward tree labeling ${\mathcal L}_{up}$ labels each node v by the number of the port leading from v to its parent in the tree. Our measure of interest is the worst case and total length of the labels used by the scheme, denoted Mup(T) and Sup(T) for ${\mathcal L}_{up}$ and Mall(T) and Sall(T) for ${\mathcal L}_{all}$. The problem studied in this paper is the following: Given a graph G and a predefined port labeling for it, with the ports of each node v numbered by 0,...,deg(v) – 1, select a rooted spanning tree for G minimizing (one of) these measures. We show that the problem is polynomial for Mup(T), Sup(T) and Sall(T) but NP-hard for Mall(T) (even for 3-regular planar graphs). We show that for every graph G and port numbering there exists a spanning tree T for which Sup(T) = O(n log log n). We give a tight bound of O(n) in the cases of complete graphs with arbitrary labeling and arbitrary graphs with symmetric port assignments. We conclude by discussing some applications for our tree representation schemes.