Original title: Statistická fyzika složitých optimalizačních problémů
Translated title: Statistical Physics of Hard Optimization Problems
Authors: Zdeborová, Lenka ; Janiš, Václav (advisor) ; Mertens, Stephan (referee) ; Zecchina, Riccardo (referee)
Document type: Doctoral theses
Year: 2008
Language: eng
Abstract: Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the NP-complete class are particularly dicult, it is believed that the number of operations required to minimize the cost function is in the most dicult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this thesis is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named "locked" constraint...

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/16402

Permalink: http://www.nusl.cz/ntk/nusl-292739


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Doctoral theses