Abstract:Our object of study is the asymptotic growth of heaviest paths in a charged (weighted with signed weights) complete directed acyclic graph. Edge charges are i.i.d. random variables with common distribution F supported on [−∞, 1] with essential supremum equal to 1 (a charge of −∞ is understood as the absence of an edge). The asymptotic growth rate is a constant that we denote by C(F ). Even in the simplest case where F = pδ 1 + (1 − p)δ −∞ , corresponding to the longest path in the Barak-Erdős random graph, the… Show more
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