On an edge ranking problem of trees and graphs

Ananth V. Iyer; H. Donald Ratliff; Gopalakrishnan Vijayan

doi:10.1016/0166-218X(91)90012-L

On an edge ranking problem of trees and graphs

Ananth V. Iyer
, H. Donald Ratliff
, Gopalakrishnan Vijayan

MGT Dean's Office Administration

Georgia Institute of Technology
IBM

Research output: Contribution to journal › Article › peer-review

63 Scopus citations

Abstract

A k-edge ranking of an undirected graph is a labeling of the edges of the graph with integers 1, 2, ..., k, with the property that all paths between two edges with the same label i contain an edge with label j[rang]i. The edge ranking problem is that of finding the smallest k for which a graph has a k-edge ranking. This problem is useful in the optimization of the number of parallel stages required to assemble a product from its components. The problem is also related to that of finding minimum height edge partition trees of graphs. The main result in the paper is an O(n log n) time approximation algorithm for edge ranking of trees, which has a worst case performance ratio of 2.

Original language	English
Pages (from-to)	43-52
Number of pages	10
Journal	Discrete Applied Mathematics
Volume	30
Issue number	1
DOIs	https://doi.org/10.1016/0166-218X(91)90012-L
State	Published - Jan 7 1991

Access to Document

10.1016/0166-218X(91)90012-L

Cite this

@article{4eca9580fe9b45bdb7316f60c38610fa,

title = "On an edge ranking problem of trees and graphs",

abstract = "A k-edge ranking of an undirected graph is a labeling of the edges of the graph with integers 1, 2, ..., k, with the property that all paths between two edges with the same label i contain an edge with label j[rang]i. The edge ranking problem is that of finding the smallest k for which a graph has a k-edge ranking. This problem is useful in the optimization of the number of parallel stages required to assemble a product from its components. The problem is also related to that of finding minimum height edge partition trees of graphs. The main result in the paper is an O(n log n) time approximation algorithm for edge ranking of trees, which has a worst case performance ratio of 2.",

author = "Iyer, \{Ananth V.\} and Ratliff, \{H. Donald\} and Gopalakrishnan Vijayan",

year = "1991",

month = jan,

day = "7",

doi = "10.1016/0166-218X(91)90012-L",

language = "English",

volume = "30",

pages = "43--52",

journal = "Discrete Applied Mathematics",

issn = "0166-218X",

publisher = "Elsevier B.V.",

number = "1",

}

TY - JOUR

T1 - On an edge ranking problem of trees and graphs

AU - Iyer, Ananth V.

AU - Ratliff, H. Donald

AU - Vijayan, Gopalakrishnan

PY - 1991/1/7

Y1 - 1991/1/7

N2 - A k-edge ranking of an undirected graph is a labeling of the edges of the graph with integers 1, 2, ..., k, with the property that all paths between two edges with the same label i contain an edge with label j[rang]i. The edge ranking problem is that of finding the smallest k for which a graph has a k-edge ranking. This problem is useful in the optimization of the number of parallel stages required to assemble a product from its components. The problem is also related to that of finding minimum height edge partition trees of graphs. The main result in the paper is an O(n log n) time approximation algorithm for edge ranking of trees, which has a worst case performance ratio of 2.

AB - A k-edge ranking of an undirected graph is a labeling of the edges of the graph with integers 1, 2, ..., k, with the property that all paths between two edges with the same label i contain an edge with label j[rang]i. The edge ranking problem is that of finding the smallest k for which a graph has a k-edge ranking. This problem is useful in the optimization of the number of parallel stages required to assemble a product from its components. The problem is also related to that of finding minimum height edge partition trees of graphs. The main result in the paper is an O(n log n) time approximation algorithm for edge ranking of trees, which has a worst case performance ratio of 2.

UR - https://www.scopus.com/pages/publications/0008447567

U2 - 10.1016/0166-218X(91)90012-L

DO - 10.1016/0166-218X(91)90012-L

M3 - Article

AN - SCOPUS:0008447567

SN - 0166-218X

VL - 30

SP - 43

EP - 52

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 1

ER -

On an edge ranking problem of trees and graphs

Abstract

Access to Document

Other files and links

Fingerprint

Cite this