Abstract
We consider the problem of optimizing the locations of source nodes in transportationnetworks. A reduction of the fraction of surplus nodes induces a glassy transition. Incontrast to most constraint satisfaction problems involving discrete variables, ourproblem involves continuous variables which lead to cavity fields in the form offunctions. The one-step replica symmetry breaking (1RSB) solution involves solving astable distribution of functionals, which is in general infeasible. In this paper, weobtain small closed sets of functional cavity fields and demonstrate how functionalrecursions are converted to simple recursions of probabilities which make the 1RSBsolution feasible. The physical results in the replica symmetric (RS) and the 1RSBframeworks are thus derived and the stabilities of the RS and 1RSB solutions areexamined.
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