Counting Popular Matchings in House Allocation Problems

We study the problem of counting the number of popular matchings in a given instance. A popular matching instance consists of agents A and houses H, where each agent ranks a subset of houses according to their preferences. A matching is an assignment of agents to houses. A matching M is more popular than matching M' if the number of agents that prefer M to M' is more than the number of people that prefer M' to M. A matching M is called popular if there exists no matching more popular than M. McDermid and Irving gave a poly-time algorithm for counting the number of popular matchings when the preference lists are strictly ordered. We first consider the case of ties in preference lists. Nasre proved that the problem of counting the number of popular matching is #P-hard when there are ties. We give an FPRAS for this problem. We then consider the popular matching problem where preference lists are strictly ordered but each house has a capacity associated with it. We give a switching graph characterization of popular matchings in this case. Such characterizations were studied earlier for the case of strictly ordered preference lists (McDermid and Irving) and for preference lists with ties (Nasre). We use our characterization to prove that counting popular matchings in capacitated case is #P-hard

Popular matchings with two-sided preferences and one-sided ties

We are given a bipartite graph $G = (A \cup B, E)$ where each vertex has a preference list ranking its neighbors: in particular, every $a \in A$ ranks its neighbors in a strict order of preference, whereas the preference lists of $b \in B$ may contain ties. A matching $M$ is popular if there is no matching $M'$ such that the number of vertices that prefer $M'$ to $M$ exceeds the number of vertices that prefer $M$ to~$M'$. We show that the problem of deciding whether $G$ admits a popular matching or not is NP-hard. This is the case even when every $b \in B$ either has a strict preference list or puts all its neighbors into a single tie. In contrast, we show that the problem becomes polynomially solvable in the case when each $b \in B$ puts all its neighbors into a single tie. That is, all neighbors of $b$ are tied in $b$'s list and $b$ desires to be matched to any of them. Our main result is an $O(n^2)$ algorithm (where $n = |A \cup B|$) for the popular matching problem in this model. Note that this model is quite different from the model where vertices in $B$ have no preferences and do not care whether they are matched or not.Comment: A shortened version of this paper has appeared at ICALP 201

Matroid and Knapsack Center Problems

In the classic $k$-center problem, we are given a metric graph, and the objective is to open $k$ nodes as centers such that the maximum distance from any vertex to its closest center is minimized. In this paper, we consider two important generalizations of $k$-center, the matroid center problem and the knapsack center problem. Both problems are motivated by recent content distribution network applications. Our contributions can be summarized as follows: 1. We consider the matroid center problem in which the centers are required to form an independent set of a given matroid. We show this problem is NP-hard even on a line. We present a 3-approximation algorithm for the problem on general metrics. We also consider the outlier version of the problem where a given number of vertices can be excluded as the outliers from the solution. We present a 7-approximation for the outlier version. 2. We consider the (multi-)knapsack center problem in which the centers are required to satisfy one (or more) knapsack constraint(s). It is known that the knapsack center problem with a single knapsack constraint admits a 3-approximation. However, when there are at least two knapsack constraints, we show this problem is not approximable at all. To complement the hardness result, we present a polynomial time algorithm that gives a 3-approximate solution such that one knapsack constraint is satisfied and the others may be violated by at most a factor of $1+\epsilon$. We also obtain a 3-approximation for the outlier version that may violate the knapsack constraint by $1+\epsilon$.Comment: A preliminary version of this paper is accepted to IPCO 201

Which game narratives do adolescents of different gameplay and sociodemographic backgrounds prefer? a mixed-methods analysis

OBJECTIVE: The aim of this study was to investigate which narrative elements of digital game narratives are preferred by the general adolescent population, and to examine associations with gender, socioeconomic status (SES), and gameplay frequency. Further, the study aims to discuss how results can be translated to serious digital games. MATERIALS AND METHODS: Adolescents were recruited through school to complete a survey on narrative preferences in digital games. The survey included questions on sociodemographic information, frequency of gameplay, and an open-ended question on what could be an appealing narrative for them. Data were analyzed in a mixed-methods approach, using thematic analysis and chi-square analyses to determine narrative preferences and the associations between game narrative elements and player characteristics (gender, SES, and frequency of gameplay). RESULTS: The sample consisted of 446 adolescents (12-15 years old) who described 30 narrative subthemes. Preferences included human characters as protagonists; nonhuman characters only as antagonists; realistic settings, such as public places or cities; and a strong conflict surrounding crime, catastrophe, or war. Girls more often than boys defined characters by their age, included avatars, located the narrative in private places, developed profession-related skills, and included a positive atmosphere. Adolescents of nonacademic education more often than adolescents of academic education defined characters by criminal actions. Infrequent players more often included human characters defined by their age than frequent players. After performing a Bonferroni correction, narrative preferences for several gender differences remained. CONCLUSION: Different narrative elements related to subgroups of adolescents by gender, SES, and frequency of gameplay. Customization of narratives in serious digital health games should be warranted for boys and girls; yet, further research is needed to specify how to address girls in particular

Writing product and process in children with English as an additional language

Children draw on limited cognitive resources to write and these resources are under more demand when writing in English as an additional language (EAL). This study investigated the relationship between writing process measures along with two language measures, phonological awareness and lexical retrieval, and measures of writing product. Thirty-nine EAL children took part in the study and their writing was digitised so that execution speed, burst length, and the pattern of pauses were available for analysis. The results found that lexical retrieval was significantly associated, indirectly through execution speed and burst length, with the number of words, lexical richness, and writing quality. The results are discussed in the context of common underlying proficiency theory and lexical retrieval as part of the translation process of writing

High school boys' and girls' writing conceptions and writing self-efficacy beliefs : what is their role in writing performance?

ABSTRACT: This study investigated the conceptions about writing and writing self-efficacy beliefs held by high school students in relation to the students’ gender as well as their associations with writing achievement. The results show that female students have more sophisticated writing conceptions than their male counterparts but no gender differences were found in writing self-efficacy beliefs. In addition, results reveal that writing self-efficacy beliefs and gender play an important role in predicting writing performance and that writing performance is moderated by students’ writing conceptions. Educational implications and further research are discussed

The Effect of Keyboard-Based Word Processing on Students With Different Working Memory Capacity During the Process of Academic Writing

This study addresses the current debate about the beneficial effects of text processing software on students with different working memory (WM) during the process of academic writing, especially with regard to the ability to display higher-level conceptual thinking. A total of 54 graduate students (15 male, 39 female) wrote one essay by hand and one by keyboard. Our results show a beneficial effect of text processing software, in terms of both the qualitative and quantitative writing output. A hierarchical cluster analysis was used to detect distinct performance groups in the sample. These performance groups mapped onto three differing working memory profiles. The groups with higher mean WM scores manifested superior writing complexity using a keyboard, in contrast to the cluster with the lowest mean WM. The results also point out that more revision during the writing process itself does not inevitably reduce the quality of the final output