Simplifying Activity-On-Edge Graphs

Authors David Eppstein, Daniel Frishberg , Elham Havvaei

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Author Details

David Eppstein
  • University of California, Irvine, CA, United States
Daniel Frishberg
  • University of California, Irvine, CA, United States
Elham Havvaei
  • University of California, Irvine, CA, United States

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David Eppstein, Daniel Frishberg, and Elham Havvaei. Simplifying Activity-On-Edge Graphs. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 24:1-24:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We formalize the simplification of activity-on-edge graphs used for visualizing project schedules, where the vertices of the graphs represent project milestones, and the edges represent either tasks of the project or timing constraints between milestones. In this framework, a timeline of the project can be constructed as a leveled drawing of the graph, where the levels of the vertices represent the time at which each milestone is scheduled to happen. We focus on the following problem: given an activity-on-edge graph representing a project, find an equivalent activity-on-edge graph—one with the same critical paths—that has the minimum possible number of milestone vertices among all equivalent activity-on-edge graphs. We provide an O(mn²)-time algorithm for solving this graph minimization problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • directed acyclic graph
  • activity-on-edge graph
  • critical path
  • project planning
  • milestone minimization
  • graph visualization


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