On the Number of Topological Types Occurring in a Parameterized Family of Arrangements

Let be an o-minimal structure over ℝ, a closed definable set, and

Two hardness results for core stability in hedonic coalition formation games

We establish NP-completeness of two problems on core stable coalitions in hedonic games. In the first problem every player has only two acceptable coalitions in his preference list, and in the second problem the preference structures arise from the distances in an underlying metric space.     

The projected newton method for solving inverse eigenvalue problems - the case of multiple eigenvaues

This paper deals with the optimal solution of ill-posed linear problems, i.e..linear problems for which the solution operator is unbounded. We consider worst-case ar,and averagecase settings. Our main result is that algorithms having finite error (for a given setting) exist if and only if the solution operator is bounded (in that setting). In the worst-case setting, this means that there is no algorithm for solving ill-posed problems having finite error. In the average-case setting, this means that algorithms having finite error exist if and only lf the solution operator is bounded on the average. If the solution operator is bounded on the average, we find average-case optimal information of cardinality n and optimal algorithms using this information, and show that the average error of these algorithms tends to zero as n→∞. These results are then used to determine the [euro]-complexity, i.e., the minimal costof finding an [euro]-accurate approximation. In the worst-case setting, the [euro]comp1exity of an illposed problem is infinite for all [euro]>0; that is, we cannot find an approximation having finite error and finite cost. In the average-case setting, the [euro]-complexity of an ill-posed problem is infinite for all [euro]>0 iff the solution operator is not bounded on the average, moreover, if the the solutionoperator is bounded on the average, then the [euro]-complexity is finite for all [euro]>0.     

On cover-structure graphs

Motivated by a problem in communication complexity, we study cover-structure graphs (cs-graphs), defined as intersection graphs of maximal monochromatic rectangles in a matrix. We show that not every graph is a cs-graph. Especially, squares and odd holes are not cs-graphs.It is natural to look at graphs (beautiful graphs) having the property that each induced subgraph is a cs-graph. They form a new class of Berge graphs. We make progress towards their characterization by showing that every square-free bipartite graph is beautiful, and that beautiful line graphs of square-free bipartite graphs are just Path-or-Even-Cycle-of-Cliques graphs.     

Nonlinear and adaptive frame approximation schemes for elliptic PDEs: Theory and numerical experiments

This article is concerned with adaptive numerical frame methods for elliptic operator equations. We show how specific noncanonical frame expansions on domains can be constructed. Moreover, we study the approximation order of best n‐term frame approximation, which serves as the benchmark for the performance of adaptive schemes. We also discuss numerical experiments for second order elliptic boundary value problems in polygonal domains where the discretization is based on recent constructions of boundary adapted wavelet bases on the interval. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

The property of being polynomial for Mal’tsev constraint satisfaction problems

A combinatorial constraint satisfaction problem aims at expressing in unified terms a wide spectrum of problems in various branches of mathematics, computer science, and AI. The generalized satisfiability problem is NP-complete, but many of its restricted versions can be solved in a polynomial time. It is known that the computational complexity of a restricted constraint satisfaction problem depends only on a set of polymorphisms of relations which are admitted to be used in the problem. For the case where a set of such relations is invariant under some Mal’tsev operation, we show that the corresponding constraint satisfaction problem can be solved in a polynomial time. __________ Translated from Algebra i Logika, Vol. 45, No. 6, pp. 655–686, November–December, 2006.     

Some Notes on the Linear Complexity of Sidel’nikov-Lempel-Cohn-Eastman Sequences

We continue the study of the linear complexity of binary sequences, independently introduced by Sidel’nikov and Lempel, Cohn, and Eastman. These investigations were originated by Helleseth and Yang and extended by Kyureghyan and Pott. We determine the exact linear complexity of several families of these sequences using well-known results on cyclotomic numbers. Moreover, we prove a general lower bound on the linear complexity profile for all of these sequences.     

On the Linear Complexity Profile of Nonlinear Congruential Pseudorandom Number Generators with Dickson Polynomials

Linear complexity and linear complexity profile are important characteristics of a sequence for applications in cryptography and Monte-Carlo methods. The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. Recently, a weak lower bound on the linear complexity profile of a general nonlinear congruential pseudorandom number generator was proven by Gutierrez, Shparlinski and the first author. For most nonlinear generators a much stronger lower bound is expected. Here, we obtain a much stronger lower bound on the linear complexity profile of nonlinear congruential pseudorandom number generators with Dickson polynomials.     

关于一些凸规划问题的复杂性研究结果

目前,已发表了大量研究各类不同凸规划的低复杂度的障碍函数方法的文章. 利用自和谐理论,对不同的几类凸规划问题构造相应的对数障碍函数,通过两个引理证明这些凸规划问题相应的对数障碍函数都满足自和谐,根据Nesterov 和Nemirovsky的工作证明了所给问题的内点算法具有多项式复杂性.