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- W5012425 abstract "Combinatorial optimization problems from Theoretical Computer Sciences and certain magnetic alloys (called spin glasses) both consist of particles or variables which are coupled by a large number of competing interactions. This thesis deals with three such systems, for which determining an optimal state (also called ground state or solution) in which a maximal number of interaction is satisfied, is an algorithmically difficult problem.The difference between the ground state and the first excited state of 3-d Ising spin-glasses is studied using a substantially improved algorithm for finding ground states. The probability of a system wide excitation does not decrease with system size, in agreement with the predictions made by the mean-field model.The ground-state structure of the vertex-cover problem from Theoretical Computer Sciences is analyzed for a certain ensemble of random graphs using numerical clustering methods originally developed also for spin glasses. In a certain region of the characterizing parameter the ground state landscape consists only of a single cluster, which is in agreement with previously known analytical results. In the other region ground-states are organized in a hierarchical way which is compatible with continuous replica symmetry-breaking.For the random satisfiability problem the dynamics of an algorithm for finding solutions is described analytically. Two phases are identified: while solutions are found fast, i.e. in a time growing linear with system size, in one region, the solution time grows exponentially in the other. Qualitatively, the analytically predicted solution times agree with numerical simulations." @default.
- W5012425 created "2016-06-24" @default.
- W5012425 creator A5088411238 @default.
- W5012425 date "2022-02-20" @default.
- W5012425 modified "2023-09-23" @default.
- W5012425 title "Grundzustandsstruktur ungeordneter Systeme und Dynamik von Optimierungsalgorithmen" @default.
- W5012425 doi "https://doi.org/10.53846/goediss-2849" @default.
- W5012425 hasPublicationYear "2022" @default.
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