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A Randomly Weighted Minimum Arborescence with a Random Cost Constraint

Author

Listed:
  • Alan M. Frieze

    (Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

  • Tomasz Tkocz

    (Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

Abstract

We study the minimum spanning arborescence problem on the complete digraph K → n , where an edge e has a weight W e and a cost C e , each of which is an independent uniform random variable U s , where 0 < s ≤ 1 and U is uniform [ 0 , 1 ] . There is also a constraint that the spanning arborescence T must satisfy C ( T ) ≤ c 0 . We establish, for a range of values for c 0 , s , the asymptotic value of the optimum weight via the consideration of a dual problem.

Suggested Citation

  • Alan M. Frieze & Tomasz Tkocz, 2022. "A Randomly Weighted Minimum Arborescence with a Random Cost Constraint," Mathematics of Operations Research, INFORMS, vol. 47(2), pages 1664-1680, May.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:2:p:1664-1680
    DOI: 10.1287/moor.2021.1184
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