Towards a Megamodel to Model Software Evolution Through Transformations

Model Driven Engineering is a promizing approach that could lead to the emergence of a new paradigm for software evolution, namely Model Driven Software Evolution. Models, Metamodels and Transformations are the cornerstones of this approach. Combining these concepts leads to very complex structures which revealed to be very difficult to understand especially when different technological spaces are considered such as XMLWare (the technology based on XML), Grammarware and BNF, Modelware and UML, Dataware and SQL, etc. The concepts of model, metamodel and transformation are usually ill-defined in industrial standards like the MDA or XML. This paper provides a conceptual framework, called a megamodel, that aims at modelling large-scale software evolution processes. Such processes are modeled as graphs of systems linked with well-defined set of relations such as RepresentationOf (μ), ConformsTo (χ) and IsTransformedIn (τ).  

Computational complexity and approximability of social welfare optimization in multiagent resource allocation

A central task in multiagent resource allocation, which provides mechanisms to allocate (bundles of) resources to agents, is to maximize social welfare. We assume resources to be indivisible and nonshareable and agents to express their utilities over bundles of resources, where utilities can be represented in the bundle form, the $k$ -additive form, and as straight-line programs. We study the computational complexity of social welfare optimization in multiagent resource allocation, where we consider utilitarian and egalitarian social welfare and social welfare by the Nash product. Solving some of the open problems raised by Chevaleyre et al. (2006) and confirming their conjectures, we prove that egalitarian social welfare optimization is $\mathrm{NP}$ -complete for the bundle form, and both exact utilitarian and exact egalitarian social welfare optimization are $\mathrm{DP}$ -complete, each for both the bundle and the $2$ -additive form, where $\mathrm{DP}$ is the second level of the boolean hierarchy over  $\mathrm{NP}$ . In addition, we prove that social welfare optimization by the Nash product is $\mathrm{NP}$ -complete for both the bundle and the $1$ -additive form, and that the exact variants are $\mathrm{DP}$ -complete for the bundle and the $3$ -additive form. For utility functions represented as straight-line programs, we show $\mathrm{NP}$ -completeness for egalitarian social welfare optimization and social welfare optimization by the Nash product. Finally, we show that social welfare optimization by the Nash product in the $1$ -additive form is hard to approximate, yet we also give fully polynomial-time approximation schemes for egalitarian and Nash product social welfare optimization in the $1$ -additive form with a fixed number of agents.  

Supervised term weighting centroid-based classifiers for text categorization

In this paper, we study the theoretical properties of the class feature centroid (CFC) classifier by considering the rate of change of each prototype vector with respect to individual dimensions (terms). We show that CFC is inherently biased toward the larger (dominant majority) classes, which invariably leads to poor performance on class-imbalanced data. CFC also aggressively prune terms that appear across all classes, discarding some non-exclusive but useful terms. To overcome these CFC limitations while retaining its intrinsic and worthy design goals, we propose an improved centroid-based classifier that uses precise term-class distribution properties instead of presence or absence of terms in classes. Specifically, terms are weighted based on the Kullback–Leibler (KL) divergence measure between pairs of class-conditional term probabilities; we call this the CFC–KL centroid classifier. We then generalize CFC–KL to handle multi-class data by replacing the KL measure with the multi-class Jensen–Shannon (JS) divergence, called CFC–JS. Our proposed supervised term weighting schemes have been evaluated on 5 datasets; KL and JS weighted classifiers consistently outperformed baseline CFC and unweighted support vector machines (SVM). We also devise a word cloud visualization approach to highlight the important class-specific words picked out by our KL and JS term weighting schemes, which were otherwise obscured by unsupervised term weighting. The experimental and visualization results show that KL and JS term weighting not only notably improve centroid-based classifiers, but also benefit SVM classifiers as well.  

Approximation and complexity of the optimization and existence problems for maximin share,proportional share,and minimax share allocation of indivisible goods

This paper is concerned with various types of allocation problems in fair division of indivisible goods, aiming at maximin share, proportional share, and minimax share allocations. However, such allocations do not always exist, not even in very simple settings with two or three agents. A natural question is to ask, given a problem instance, what is the largest value c for which there is an allocation such that every agent has utility of at least c times her fair share. We first prove that the decision problem of checking if there exists a minimax share allocation for a given problem instance is \(\mathrm {NP}\)-hard when the agents’ utility functions are additive. We then show that, for each of the three fairness notions, one can approximate c by a polynomial-time approximation scheme, assuming that the number of agents is fixed. Next, we investigate the restricted cases when utility functions have values in \(\{0,1\}\) only or are defined based on scoring vectors (Borda and lexicographic vectors), and we obtain several tractability results for these cases. Interestingly, we show that maximin share allocations can always be found efficiently with Borda utilities, which cannot be guaranteed for general additive utilities. In the nonadditive setting, we show that there exists a problem instance for which there is no c-maximin share allocation, for any constant c. We explore a class of symmetric submodular utilities for which there exists a tight \(\frac{1}{2}\)-maximin share allocation, and show how it can be approximated to within a factor of \(\nicefrac {1}{4}\).  

Positional scoring-based allocation of indivisible goods

We define a family of rules for dividing m indivisible goods among agents, parameterized by a scoring vector and a social welfare aggregation function. We assume that agents’ preferences over sets of goods are additive, but that the input is ordinal: each agent reports her preferences simply by ranking single goods. Similarly to positional scoring rules in voting, a scoring vector \(s = (s_1, \ldots , s_m)\) consists of m nonincreasing, nonnegative weights, where \(s_i\) is the score of a good assigned to an agent who ranks it in position i. The global score of an allocation for an agent is the sum of the scores of the goods assigned to her. The social welfare of an allocation is the aggregation of the scores of all agents, for some aggregation function \(\star \) such as, typically, \(+\) or \(\min \). The rule associated with s and \(\star \) maps a profile to (one of) the allocation(s) maximizing social welfare. After defining this family of rules, and focusing on some key examples, we investigate some of the social-choice-theoretic properties of this family of rules, such as various kinds of monotonicity, and separability. Finally, we focus on the computation of winning allocations, and on their approximation: we show that for commonly used scoring vectors and aggregation functions this problem is NP-hard and we exhibit some tractable particular cases.