The complexity of searching implicit graphs

AbstractThe standard complexity classes of complexity theory do not allow for direct classification of most of the problems solved by heuristic search algorithms. The reason is that, almost always, these are defined in terms of implicit graphs of state or problem reduction spaces, while the standard definitions of all complexity classes are specifically tailored to explicit inputs.To allow for more precise comparisons with standard complexity classes, we introduce here a model for the analysis of algorithms on graphs given by vertex expansion procedures. It is based on previously studied concepts of “succinct representation” techniques, and allows us to prove PSPACE-completeness or EXPTIME-completeness of specific, natural problems on implicit graphs, such as those solved by A∗, AO∗, and other best-first search strategies

Anyone but Him: The Complexity of Precluding an Alternative

Preference aggregation in a multiagent setting is a central issue in both human and computer contexts. In this paper, we study in terms of complexity the vulnerability of preference aggregation to destructive control. That is, we study the ability of an election's chair to, through such mechanisms as voter/candidate addition/suppression/partition, ensure that a particular candidate (equivalently, alternative) does not win. And we study the extent to which election systems can make it impossible, or computationally costly (NP-complete), for the chair to execute such control. Among the systems we study--plurality, Condorcet, and approval voting--we find cases where systems immune or computationally resistant to a chair choosing the winner nonetheless are vulnerable to the chair blocking a victory. Beyond that, we see that among our studied systems no one system offers the best protection against destructive control. Rather, the choice of a preference aggregation system will depend closely on which types of control one wishes to be protected against. We also find concrete cases where the complexity of or susceptibility to control varies dramatically based on the choice among natural tie-handling rules.Comment: Preliminary version appeared in AAAI '05. Also appears as URCS-TR-2005-87

Abstracts of Ph.D. theses in mathematics

summary:Leischner, Pavel: Spatial imagination development of the secondary school pupils. Mašíček, Libor: Diagnostics and sensitivity of robust models. Duintjer Tebbens, Erik Jurjen: Modern methods for solving linear problems. Matonoha, Ctirad: Numerical realization of trust region methods. Duda, Jakub: Delta convexity, metric projection and negligible sets. Smrčka, Michael: Choquet's theory in function spaces. Hanika, Jiří: Search problems and bounded arithmetic. Pawlas, Zbyněk: Asymptotics in stochastic geometry. Bodlák, Karel: Methods of stereology and spatial statistics in applications. Čapek, Václav: M-smoothers Zvára, Petr: Prediction in non-linear autoregressive processes. Blanda, Jiří: Pricing of life insurance products Finfrle, Pavel: Model for calculation of liability value arising from life insurance. Finěk Václav: Orthonormal wavelets and their applications. Stanovský David : Left distributive left quasigroups. Koblížková, Michaela: Polyhedra and secondary school mathematics. Krýsl, Svatopluk: Invariant differential operators for projective contact geometries. Šmíd, Dalibor: Properties of invariant differential operators. Šmíd, Martin: Notes on approximation of stochastic programming problems. Komárková, Lenka: Change point problem for censored data. Kechlibar, Marian: Commutative algebra and cryptography