TY - GEN

T1 - Generalized edge-rankings of trees

AU - Zhou, Xiao

AU - Kashem, Md Abul

AU - Nishizeki, Takao

PY - 1997/12/1

Y1 - 1997/12/1

N2 - In this paper we newly define a generalized edge-ranking of a graph G as follows: for a positive integer c, a c-edge-ranking of G is a labeling (ranking) of the edges of G with integers such that, for any label i, deletion of all edges with labels > i leaves connected components, each having at most c edges with label i. The problem of finding an optimal c-edge-ranking of G, that is, a c-edge-ranking using the minimum number of ranks, has applications in scheduling the manufacture of complex multi-part products; it is equivalent to finding a c-edge-separator tree of G having the minimum height. We present an algorithm to find an optimal c-edge-ranking of a given tree T for any positive integer c in time 0(n2 log Δ), where n is the number of vertices in T and Δ is the maximum vertex-degree of T. Our algorithm is faster than the best algorithm known for the case c = 1.

AB - In this paper we newly define a generalized edge-ranking of a graph G as follows: for a positive integer c, a c-edge-ranking of G is a labeling (ranking) of the edges of G with integers such that, for any label i, deletion of all edges with labels > i leaves connected components, each having at most c edges with label i. The problem of finding an optimal c-edge-ranking of G, that is, a c-edge-ranking using the minimum number of ranks, has applications in scheduling the manufacture of complex multi-part products; it is equivalent to finding a c-edge-separator tree of G having the minimum height. We present an algorithm to find an optimal c-edge-ranking of a given tree T for any positive integer c in time 0(n2 log Δ), where n is the number of vertices in T and Δ is the maximum vertex-degree of T. Our algorithm is faster than the best algorithm known for the case c = 1.

KW - Algorithm

KW - Edge-ranking

KW - Separator tree

KW - Tree

UR - http://www.scopus.com/inward/record.url?scp=84896787035&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84896787035&partnerID=8YFLogxK

U2 - 10.1007/3-540-62559-3_31

DO - 10.1007/3-540-62559-3_31

M3 - Conference contribution

AN - SCOPUS:84896787035

SN - 3540625593

SN - 9783540625599

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 390

EP - 404

BT - Graph-Theoretic Concepts in Computer Science - 22nd International Workshop, WG 1996, Proceedings

T2 - 22nd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1996

Y2 - 12 June 1996 through 14 June 1996

ER -