Violator Spaces: Structure and Algorithms

Sharir and Welzl introduced an abstract framework for optimization problems, called LP-type problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a proper generalization of LP-type problems. We show that Clarkson's randomized algorithms for low-dimensional linear programming work in the context of violator spaces. For example, in this way we obtain the fastest known algorithm for the P-matrix generalized linear complementarity problem with a constant number of blocks. We also give two new characterizations of LP-type problems: they are equivalent to acyclic violator spaces, as well as to concrete LP-type problems (informally, the constraints in a concrete LP-type problem are subsets of a linearly ordered ground set, and the value of a set of constraints is the minimum of its intersection).Comment: 28 pages, 5 figures, extended abstract was presented at ESA 2006; author spelling fixe

Experimental study of geometric t-spanners : a running time comparison

The construction of t-spanners of a given point set has received a lot of attention, especially from a theoretical perspective. We experimentally study the performance of the most common construction algorithms for points in the Euclidean plane. In a previous paper [10] we considered the properties of the produced graphs from five common algorithms. We consider several additional algorithms and focus on the running times. This is the first time an extensive comparison has been made between the running times of construction algorithms of t-spanners

The Five Factor Model of personality and evaluation of drug consumption risk

The problem of evaluating an individual's risk of drug consumption and misuse is highly important. An online survey methodology was employed to collect data including Big Five personality traits (NEO-FFI-R), impulsivity (BIS-11), sensation seeking (ImpSS), and demographic information. The data set contained information on the consumption of 18 central nervous system psychoactive drugs. Correlation analysis demonstrated the existence of groups of drugs with strongly correlated consumption patterns. Three correlation pleiades were identified, named by the central drug in the pleiade: ecstasy, heroin, and benzodiazepines pleiades. An exhaustive search was performed to select the most effective subset of input features and data mining methods to classify users and non-users for each drug and pleiad. A number of classification methods were employed (decision tree, random forest, $k$-nearest neighbors, linear discriminant analysis, Gaussian mixture, probability density function estimation, logistic regression and na{\"i}ve Bayes) and the most effective classifier was selected for each drug. The quality of classification was surprisingly high with sensitivity and specificity (evaluated by leave-one-out cross-validation) being greater than 70\% for almost all classification tasks. The best results with sensitivity and specificity being greater than 75\% were achieved for cannabis, crack, ecstasy, legal highs, LSD, and volatile substance abuse (VSA).Comment: Significantly extended report with 67 pages, 27 tables, 21 figure

A Nearly Linear-Time PTAS for Explicit Fractional Packing and Covering Linear Programs

We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual solutions whose costs are within a factor of 1+eps of the optimal cost in time O((r+c)log(n)/eps^2 + n).Comment: corrected version of FOCS 2007 paper: 10.1109/FOCS.2007.62. Accepted to Algorithmica, 201

A Faster Algorithm for Two-Variable Integer Programming

We show that a 2-variable integer program, defined by $m$ constraints involving coefficients with at most $\varphi$ bits can be solved with $O(m + \varphi)$ arithmetic operations on rational numbers of size~$O(\varphi)$. This result closes the gap between the running time of two-variable integer programming with the sum of the running times of the Euclidean algorithm on $\varphi$-bit integers and the problem of checking feasibility of an integer point for $m$~constraints

Guaranteed and randomized methods for stability analysis of uncertain metabolic networks

A persistent problem hampering our understanding of the dynamics of large-scale metabolic networks is the lack of experimentally determined kinetic parameters that are necessary to build computationalmodels of biochemical processes. To overcome some of the limitations imposed by absent or incomplete kinetic data, structural kinetic modeling (SKM) was proposed recently as an intermediate approach between stoichiometric analysis and a full kinetic description. SKM extends stationary flux-balance analysis (FBA) by a local stability analysis utilizing an appropriate parametrization of the Jacobian matrix. To characterize the Jacobian, we utilize results from robust control theory to determine subintervals of the Jacobian’ entries that correspond to asymptotically stable metabolic states. Furthermore, we propose an efficient sampling scheme in combination with methods from computational geometry to sketch the stability region. A glycolytic pathway model comprising 12 uncertain parameters is used to assess the feasibility of the method