We give a complexity dichotomy for the Quantified Constraint Satisfaction Problem \( \mathrm{QCSP}(\mathrm{H}) \) when \( \mathrm{H} \) is a reflexive tournament. It is well known that reflexive tournaments can be split into a sequence of strongly connected components \( \mathrm{H}_1,\ldots ,\mathrm{H}_n \) so that there exists an edge from every vertex of \( \mathrm{H}_i \) to every vertex of \( \mathrm{H}_j \) if and only if \( i\lt j \) . We prove that if \( \mathrm{H} \) has both its initial and final strongly connected component (possibly equal) of size 1, then \( \mathrm{QCSP}(\mathrm{H}) \) is in \( \mathsf {NL} \) and otherwise \( \mathrm{QCSP}(\mathrm{H}) \) is \( \mathsf {NP} \) -hard.

We give a complexity dichotomy for the Quantified Constraint Satisfaction Problem QCSP(H) when H is a reflexive tournament. It is well-known that reflexive tournaments can be split into a sequence of strongly connected components H₁,…,H_n so that there exists an edge from every vertex of H_i to every vertex of H_j if and only if i < j. We prove that if H has both its initial and final strongly connected component (possibly equal) of size 1, then QCSP(H) is in NL and otherwise QCSP(H) is NP-hard.

Descriptive data analysis is used for mining spatial and temporal patterns from ski lift entrance data. The data, collected through radio-frequency identification scanners, cover one skiing season with approximately 1.2 million recorded ski lift transportations. Cluster analysis was performed on ten subsamples, and the obtained clusters were cross-validated. Several types of skier behavior were found. Temporal clustering revealed that skier patterns differ according to time of maximal performance and length of stay in the ski lift transportation system. Spatial clustering revealed that it is reasonable to have as many clusters as ski lifts in a ski resort, since skiers tend to choose a dominant ski lift during a skier-day. The detected patterns reveal valuable information that can be used for potential improvement of products and services offered by ski resorts.

We study the (non-uniform) quantified constraint satisfaction problem QCSP( H ) as H ranges over semicomplete digraphs. We obtain a complexity-theoretic trichotomy: QCSP( H ) is either in P, is NP-complete, or is Pspace-complete. The largest part of our work is the algebraic classification of precisely which semicomplete digraphs enjoy only essentially unary polymorphisms, which is combinatorially interesting in its own right.

A constraint language $\Gamma$ on a finite set A has been called polynomially expressive if the number of n-ary relations expressible by $\exists\wedge$-atomic formulas over $\Gamma$ is bounded by $\exp(O(n^k))$ for some constant k. It has recently been discovered that this property is characterized by the existence of a $(k+1)$-ary polymorphism satisfying certain identities; such polymorphisms are called k-edge operations and include Mal'cev and near-unanimity operations as special cases. We prove that if $\Gamma$ is any constraint language which, for some $k>1$, has a k-edge operation as a polymorphism, then the constraint satisfaction problem for $\langle\Gamma\rangle$ (the closure of $\Gamma$ under $\exists\wedge$-atomic expressibility) is globally tractable. We also show that the set of relations definable over $\Gamma$ using quantified generalized formulas is polynomially exactly learnable using improper equivalence queries.

A k-edge operation \varphi on a finite set A is a k + 1-ary operation that satisfies the identities \begin{gathered} \varphi (x,x,y,...,y) \approx \varphi (x,y,x,y,...,y) \approx y, \hfill \\ \varphi (y,y,y,x,y,...,y) \approx \varphi (y,y,y,y,x,y,...,y) \approx ... \hfill \\ ... \approx \varphi (y,y,y,...,y,x) \approx y. \hfill \\ \end{gathered} We prove that any constraint language .. that, for some k \ge 1, has a k-edge operation as a polymorphism is globally tractable. We also show that the set of relations definable over .. using quantified generalized formulas is polynomially exactly learnable using improper equivalence queries. Special instances of k-edge operations are Mal'cev and near-unanimity operations and so this class of constraint languages includes many well known examples.