Media type: E-Article Title: First‐passage percolation on a ladder graph, and the path cost in a VCG auction Contributor: Flaxman, Abraham; Gamarnik, David; Sorkin, Gregory B. Published: Wiley, 2011 Published in: Random Structures & Algorithms, 38 (2011) 3, Seite 350-364 Language: English DOI: 10.1002/rsa.20328 ISSN: 1042-9832; 1098-2418 Keywords: Applied Mathematics ; Computer Graphics and Computer-Aided Design ; General Mathematics ; Software Origination: Footnote: Description: AbstractThis paper studies the time constant for first‐passage percolation, and the Vickrey‐Clarke‐Groves (VCG) payment, for the shortest path on a ladder graph (a width‐2 strip) with random edge costs, treating both in a unified way based on recursive distributional equations.For first‐passage percolation where the edge costs are independent Bernoulli random variables we find the time constant exactly; it is a rational function of the Bernoulli parameter. For first‐passage percolation where the edge costs are uniform random variables we present a reasonably efficient means for obtaining arbitrarily close upper and lower bounds. Using properties of Harris chains we also show that the incremental cost to advance through the medium has a unique stationary distribution, and we compute stochastic lower and upper bounds. We rely on no special properties of the uniform distribution: the same methods could be applied to any well‐behaved, bounded cost distribution.For the VCG payment, with Bernoulli‐distributed costs the payment for an n‐long ladder, divided by n, tends to an explicit rational function of the Bernoulli parameter. Again, our methods apply more generally. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 38, 350‐364, 2011