A Randomly Weighted Minimum Arborescence with a Random Cost Constraint

Alan M. Frieze () and Tomasz Tkocz ()
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Alan M. Frieze: Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Tomasz Tkocz: Carnegie Mellon University, Pittsburgh, Pennsylvania 15213

Mathematics of Operations Research, 2022, vol. 47, issue 2, 1664-1680

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.

Keywords: Primary and secondary: 05C80; 90C27; random minimum spanning arborescence; cost constraint (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:2:p:1664-1680

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