New and simple algorithms for stable flow problems

Stable flows generalize the well-known concept of stable matchings to markets in which transactions may involve several agents, forwarding flow from one to another. An instance of the problem consists of a capacitated directed network, in which vertices express their preferences over their incident edges. A network flow is stable if there is no group of vertices that all could benefit from rerouting the flow along a walk. Fleiner established that a stable flow always exists by reducing it to the stable allocation problem. We present an augmenting-path algorithm for computing a stable flow, the first algorithm that achieves polynomial running time for this problem without using stable allocation as a black-box subroutine. We further consider the problem of finding a stable flow such that the flow value on every edge is within a given interval. For this problem, we present an elegant graph transformation and based on this, we devise a simple and fast algorithm, which also can be used to find a solution to the stable marriage problem with forced and forbidden edges. Finally, we study the stable multicommodity flow model introduced by Kir\'{a}ly and Pap. The original model is highly involved and allows for commodity-dependent preference lists at the vertices and commodity-specific edge capacities. We present several graph-based reductions that show equivalence to a significantly simpler model. We further show that it is NP-complete to decide whether an integral solution exists

Stable marriage and roommates problems with restricted edges: complexity and approximability

In the Stable Marriage and Roommates problems, a set of agents is given, each of them having a strictly ordered preference list over some or all of the other agents. A matching is a set of disjoint pairs of mutually acceptable agents. If any two agents mutually prefer each other to their partner, then they block the matching, otherwise, the matching is said to be stable. We investigate the complexity of finding a solution satisfying additional constraints on restricted pairs of agents. Restricted pairs can be either forced or forbidden. A stable solution must contain all of the forced pairs, while it must contain none of the forbidden pairs. Dias et al. (2003) gave a polynomial-time algorithm to decide whether such a solution exists in the presence of restricted edges. If the answer is no, one might look for a solution close to optimal. Since optimality in this context means that the matching is stable and satisfies all constraints on restricted pairs, there are two ways of relaxing the constraints by permitting a solution to: (1) be blocked by as few as possible pairs, or (2) violate as few as possible constraints n restricted pairs. Our main theorems prove that for the (bipartite) Stable Marriage problem, case (1) leads to View the MathML source-hardness and inapproximability results, whilst case (2) can be solved in polynomial time. For non-bipartite Stable Roommates instances, case (2) yields an View the MathML source-hard but (under some cardinality assumptions) 2-approximable problem. In the case of View the MathML source-hard problems, we also discuss polynomially solvable special cases, arising from restrictions on the lengths of the preference lists, or upper bounds on the numbers of restricted pairs

On Generalizations of Network Design Problems with Degree Bounds

Iterative rounding and relaxation have arguably become the method of choice in dealing with unconstrained and constrained network design problems. In this paper we extend the scope of the iterative relaxation method in two directions: (1) by handling more complex degree constraints in the minimum spanning tree problem (namely, laminar crossing spanning tree), and (2) by incorporating `degree bounds' in other combinatorial optimization problems such as matroid intersection and lattice polyhedra. We give new or improved approximation algorithms, hardness results, and integrality gaps for these problems.Comment: v2, 24 pages, 4 figure

Dynamical masses, absolute radii and 3D orbits of the triply eclipsing star HD 181068 from Kepler photometry

HD 181068 is the brighter of the two known triply eclipsing hierarchical triple stars in the Kepler field. It has been continuously observed for more than 2 yr with the Kepler space telescope. Of the nine quarters of the data, three have been obtained in short-cadence mode, that is one point per 58.9 s. Here we analyse this unique data set to determine absolute physical parameters (most importantly the masses and radii) and full orbital configuration using a sophisticated novel approach. We measure eclipse timing variations (ETVs), which are then combined with the single-lined radial velocity measurements to yield masses in a manner equivalent to double-lined spectroscopic binaries. We have also developed a new light-curve synthesis code that is used to model the triple, mutual eclipses and the effects of the changing tidal field on the stellar surface and the relativistic Doppler beaming. By combining the stellar masses from the ETV study with the simultaneous light-curve analysis we determine the absolute radii of the three stars. Our results indicate that the close and the wide subsystems revolve in almost exactly coplanar and prograde orbits. The newly determined parameters draw a consistent picture of the system with such details that have been beyond reach before

Distance and the pattern of intra-European trade

Given an undirected graph G = (V, E) and subset of terminals T ⊆ V, the element-connectivity κ ′ G (u, v) of two terminals u, v ∈ T is the maximum number of u-v paths that are pairwise disjoint in both edges and non-terminals V \ T (the paths need not be disjoint in terminals). Element-connectivity is more general than edge-connectivity and less general than vertex-connectivity. Hind and Oellermann [21] gave a graph reduction step that preserves the global element-connectivity of the graph. We show that this step also preserves local connectivity, that is, all the pairwise element-connectivities of the terminals. We give two applications of this reduction step to connectivity and network design problems. • Given a graph G and disjoint terminal sets T1, T2,..., Tm, we seek a maximum number of elementdisjoint Steiner forests where each forest connects each Ti. We prove that if each Ti is k element k connected then there exist Ω( log hlog m) element-disjoint Steiner forests, where h = | i Ti|. If G is planar (or more generally, has fixed genus), we show that there exist Ω(k) Steiner forests. Our proofs are constructive, giving poly-time algorithms to find these forests; these are the first non-trivial algorithms for packing element-disjoint Steiner Forests. • We give a very short and intuitive proof of a spider-decomposition theorem of Chuzhoy and Khanna [12] in the context of the single-sink k-vertex-connectivity problem; this yields a simple and alternative analysis of an O(k log n) approximation. Our results highlight the effectiveness of the element-connectivity reduction step; we believe it will find more applications in the future

Evaluation of Hungarian Wines for Resveratrol by Overpressured Layer Chromatography

A method, including solid phase extraction sample preparation, overpressured layer chromatographic separation and subsequent densitometric evaluation, was developed for measurement of total resveratrol (cis- and trans-isomers) content of wine. The amount of resveratrol was determined in wine samples from different winemaking regions of Hungary. The total resveratrol was high in Hungarian red wines (3.6–11 mg/L), and much lower in white ones (0.04–1.5 mg/L)

Confirmation of the Chinese version of the Problematic Internet Use Questionnaire Short Form (PIUQ-SF)

Although an increasing number of studies have focused on problematic Internet use, numerous measures exist with only modest investigation into their reliability and validity, both within and across different cultures (Király et al. 2015). The most frequently used questionnaire is the Internet Addiction Test (Young 1998). However, its factor structure appears to be unstable (e.g., Fernandez-Villa et al. 2015; Pontesetal. 2014). Koronczai et al. (2011) suggested that a suitable measure should fit six basic requirements. More specifically, it should be (i) comprehensive, that is examining more, possibly all, aspects of problematic Internet use; (ii) as concise as possible, in order to be able to assess the more impulsive population, and to use in time-limited surveys (or having different forms with different length). Such a measure should be (iii) reliable and valid for different methods of data collection (e.g. online, paper-and-pencil self-rating, face-to-face); as well as (iv) for different age groups (e.g. adolescents and adults), and (v) in different cultural settings. Finally, (vi) cut-off scores should be defined on the basis of clinical examination. The Problematic Internet Use Questionnaire (PIUQ) (Demetrovics et al. 2008) fulfills several of the aforementioned criteria. The 18-item PIUQ is a comprehensive measure that assesses three basic aspects of problematic Internet use (i.e., obsession, neglect, and control disorder). The 18-item and the shorter 9-item versions of the PIUQ have a reliable structure, and are suitable for time-limited surveys and have proved to be valid across various methods of data collection (i.e., online as well as paper-pencil) and age groups (Demetrovics et al. 2008; Koronczai et al. 2011). However, its implementation has so far mostly taken place in Western individualistic cultures (Kelley and Gruber 2010, 2013; Koronczai et al. 2011; Zahodne et al. 2011. To date, the PIUQ has also been applied in a survey in Iran with good Cronbach’s alpha coefficients and subscales (Mazhari 2012a, 2012b). Consequently, validation of the questionnaire in a culture that is significantly different from the Western culture is needed. Accordingly, the aim of the present study was the validation of the 9-item PIUQ among the Chinese population

Toddlers favor communicatively presented information over statistical reliability in learning about artifacts

Observed associations between events can be validated by statistical information of reliability or by testament of communicative sources. We tested whether toddlers learn from their own observation of efficiency, assessed by statistical information on reliability of interventions, or from communicatively presented demonstration, when these two potential types of evidence of validity of interventions on a novel artifact are contrasted with each other. Eighteen-month-old infants observed two adults, one operating the artifact by a method that was more efficient (2/3 probability of success) than that of the other (1/3 probability of success). Compared to the Baseline condition, in which communicative signals were not employed, infants tended to choose the less reliable method to operate the artifact when this method was demonstrated in a communicative manner in the Experimental condition. This finding demonstrates that, in certain circumstances, communicative sanctioning of reliability may override statistical evidence for young learners. Such a bias can serve fast and efficient transmission of knowledge between generations