Cascading divide-and-conquer: a technique for designing parallel algorithms
SIAM Journal on Computing
An introduction to parallel algorithms
An introduction to parallel algorithms
Computing Prüfer codes efficiently in parallel
Discrete Applied Mathematics
Introduction to Algorithms
Parallel Integer Sorting Is More Efficient Than Parallel Comparison Sorting on Exclusive Write PRAMs
SIAM Journal on Computing
A Parallel Algorithm for Constructing a Labeled Tree
IEEE Transactions on Parallel and Distributed Systems
Tree and Forest Volumes of Graphs
Tree and Forest Volumes of Graphs
Parallel graph algorithms for molecular conformation and tree codes
Parallel graph algorithms for molecular conformation and tree codes
Engineering Tree Labeling Schemes: A Case Study on Least Common Ancestors
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Parallel Algorithms for Dandelion-Like Codes
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
Unified parallel encoding and decoding algorithms for Dandelion-like codes
Journal of Parallel and Distributed Computing
Parallel algorithms for encoding and decoding blob code
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
| Hi-index | 5.23 |
We consider the problem of coding labeled trees by means of strings of node labels. Different codes have been introduced in the literature by Prüfer, Neville, and Deo and Micikevičius. For all of them, we show that both coding and decoding can be reduced to integer (radix) sorting, closing several open problems within a unified framework that can be applied both in a sequential and in a parallel setting. Our sequential coding and decoding schemes require optimal O(n) time when applied to n-node trees, yielding the first linear time decoding algorithm for a code presented by Neville. These schemes can be parallelized on the EREW PRAM model, so as to work in O(logn) time with cost O(n), , or O(nlogn), depending on the code and on the operation: in all cases, they either match or improve the performances of the best ad hoc approaches known so far.