A parametric critical path problem and an application for cyclic scheduling

Eugene Levner, Vladimir Kats

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


The paper addresses a problem of finding critical paths in PERT networks (digraphs) with variable arc lengths depending on a parameter. By equipping the Bellman-Ford label-correcting algorithm with variable vectorial labels depending on the parameter, we derive its version that solves the problem in O(mn2) time, for all possible parameter values (where m stands for the number of arcs, and n is the number of nodes in the digraph). An application related to cyclic scheduling of tasks in a robotic cell is considered.

Original languageEnglish
Pages (from-to)149-158
Number of pages10
JournalDiscrete Applied Mathematics
Issue number1-3
StatePublished - 5 Oct 1998
Externally publishedYes


  • Analysis of algorithms, distance algorithms, critical-path algorithms
  • Cyclic scheduling, robotic scheduling
  • Networks/graphs, parametric shortest path problem


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