Layered upward embedding of acyclic digraphs

Authors:
Nassim Sohaee
Affiliations:
University of Texas at Dallas, Department of Computer Science and Engineering, Richardson, Texas
Venue:
MATH'08 Proceedings of the 13th WSEAS international conference on Applied mathematics
Year:
2008

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Abstract

A layered upward drawing of a directed acyclic graph is a plane drawing of the digraph in which nodes are embedded in parallel horizontal lines, called layers, and each directed edge is represented as a line segments increasing in the vertical direction. In this papers, first we prove that the minimum number of layers for layered upward embedding of a st-graph is one more than the length of longest path from source node s to sink node t. Then, we will discuss about the edge insertion process to find a super st-graph of any upward embeddable graph. Finally we will prove that minimum number of layers in layered upward embedding of any upward embeddable graph is one less than the length of longest path from s to t in its super st-graph.