Optimal path in two and three dimensions

Nehemia Schwartz, Alexander L. Nazaryev, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


We apply the Dijkstra algorithm to generate optimal paths between two given sites on a lattice representing a disordered energy landscape. We study the geometrical and energetic scaling properties of the optimal path where the energies are taken from a uniform distribution. Our numerical results for both two and three dimensions suggest that the optimal path for random uniformly distributed energies is in the same universality class as the directed polymers. We present physical realizations of polymers in a disordered energy landscape for which this result is relevant.

Original languageEnglish
Pages (from-to)7642-7644
Number of pages3
JournalPhysical Review E
Issue number6
StatePublished - 1998


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