Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An edge is a bisector of a simple path if it contains the middle point of the path. Let T=(V,E) be a tree. Given a source vertex s /spl isin/ V, the single-source tree bisector problem is to find, for every vertex /spl upsi/ /spl isin/ V, a bisector of the simple path from s to /spl upsi/. The all-pairs tree bisector problem is to find for, every pair of vertices u, /spl upsi/ /spl isin/ V, a bisector of the simple path from u to /spl upsi/. , it is first shown that solving the single-source tree bisector problem of a ighted tree has a time lor bound /spl Omega/(n log n) in the sequential case. Then, efficient parallel algorithms are proposed on the EREW PRAM for the single-source and all-pairs tree bisector problems. Two O(log n) time single-source algorithms are proposed. One uses O(n) work and is for unighted trees. The other uses O(n log n) work and is for ighted trees. Previous algorithms for the single-source problem could achieve the same time O(log n) and the same optimal work, O(n) for unighted trees and O(n log n) for ighted trees, on the CRCW PRAM. The contribution of our single-source algorithms is the improvement from CRCW to EREW. One all-pairs parallel algorithm is proposed. It requires O(log n) time using O(n/sup 2/) work. All the proposed algorithms are cost-optimal. Efficient tree bisector algorithms have practical applications to several location problems on trees. Using the proposed algorithms, efficient parallel solutions for those problems are also presented.
['Biing-Feng Wang', 'Shan-Chyun Ku', 'Keng-Hua Shil']
I am writing a research paper on a idea Cost-optimal parallel algorithms for the tree bisector and related problems
[{"from": "human", "value": "I am writing a research paper on a idea Cost-optimal parallel algorithms for the tree bisector and related problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An edge is a bisector of a simple path if it contains the middle point of the path. Let T=(V,E) be a tree. Given a source vertex s /spl isin/ V, the single-source tree bisector problem is to find, for every vertex /spl upsi/ /spl isin/ V, a bisector of the simple path from s to /spl upsi/. The all-pairs tree bisector problem is to find for, every pair of vertices u, /spl upsi/ /spl isin/ V, a bisector of the simple path from u to /spl upsi/. , it is first shown that solving the single-source tree bisector problem of a ighted tree has a time lor bound /spl Omega/(n log n) in the sequential case. Then, efficient parallel algorithms are proposed on the EREW PRAM for the single-source and all-pairs tree bisector problems. Two O(log n) time single-source algorithms are proposed. One uses O(n) work and is for unighted trees. The other uses O(n log n) work and is for ighted trees. Previous algorithms for the single-source problem could achieve the same time O(log n) and the same optimal work, O(n) for unighted trees and O(n log n) for ighted trees, on the CRCW PRAM. The contribution of our single-source algorithms is the improvement from CRCW to EREW. One all-pairs parallel algorithm is proposed. It requires O(log n) time using O(n/sup 2/) work. All the proposed algorithms are cost-optimal. Efficient tree bisector algorithms have practical applications to several location problems on trees. Using the proposed algorithms, efficient parallel solutions for those problems are also presented."}]