Maximum Flows and Critical Vertices in AND/OR Graphs

Extended Abstract
  • Yvo Desmedt
  • Yongge Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2387)


We will study this problem and present an algorithm for finding the minimum-time-cost solution graph in an AND/OR graph. We will also study the following problems which often appear in industry when using AND/OR graphs to model manufacturing processes or to model problem solving processes: finding maximum (additive and non-additive) flows and critical vertices in an AND/OR graph. Though there are well known polynomial time algorithms for the corresponding problems in the traditional graph theory, we will show that generally it is NP-hard to find a non-additive maximum flow in an AND/OR graph, and it is both NP-hard and coNP-hard to find a set of critical vertices in an AND/OR graph. We will also present a polynomial time algorithm for finding a maximum additive flow in an AND/OR graph, and discuss the relative complexity of these problems.


Polynomial Time Maximum Flow Polynomial Time Algorithm Incoming Edge Solution Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Yvo Desmedt
    • 1
    • 2
  • Yongge Wang
    • 3
  1. 1.Computer ScienceFlorida State UniversityTallahasseeUSA
  2. 2.Department of Mathematics, Royal HollowayUniversity of LondonUK
  3. 3.Department of Software and Information SystemsUniversity of North Carolina at CharlotteCharlotte

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