TY - GEN

T1 - Finding optimal edge-rankings of trees

AU - Zhou, Xiao

AU - Nishizeki, Takao

PY - 1995/1/22

Y1 - 1995/1/22

N2 - An edge-ranking of an undirected graph G is a labeling of the edges of G with integers such that every path between two edges with the same label i contains an edge with label j > i. An edge-ranking using a minimum number of ranks is called an optimal edge-ranking. The problem of finding an optimal edge-ranking of G has applications in scheduling the manufacture of complex multi-part products; it is equivalent to finding the minimum height edge separator tree of G. Polynomial-time algorithms for the problem on trees have been obtained, which find an optimal edge-ranking of a tree T in time O(n3 log n) where n is the number of vertices in T. In our previous paper we have given a simple O(n2) algorithm. This paper presents a more efficient algorithm, which finds an optimal edge-ranking of a tree in time O(n log n).

AB - An edge-ranking of an undirected graph G is a labeling of the edges of G with integers such that every path between two edges with the same label i contains an edge with label j > i. An edge-ranking using a minimum number of ranks is called an optimal edge-ranking. The problem of finding an optimal edge-ranking of G has applications in scheduling the manufacture of complex multi-part products; it is equivalent to finding the minimum height edge separator tree of G. Polynomial-time algorithms for the problem on trees have been obtained, which find an optimal edge-ranking of a tree T in time O(n3 log n) where n is the number of vertices in T. In our previous paper we have given a simple O(n2) algorithm. This paper presents a more efficient algorithm, which finds an optimal edge-ranking of a tree in time O(n log n).

UR - http://www.scopus.com/inward/record.url?scp=0040823897&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040823897&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0040823897

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 122

EP - 131

BT - Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995

PB - Association for Computing Machinery

T2 - 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995

Y2 - 22 January 1995 through 24 January 1995

ER -