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

Social Welfare in One-sided Matching Markets without Money

We study social welfare in one-sided matching markets where the goal is to efficiently allocate n items to n agents that each have a complete, private preference list and a unit demand over the items. Our focus is on allocation mechanisms that do not involve any monetary payments. We consider two natural measures of social welfare: the ordinal welfare factor which measures the number of agents that are at least as happy as in some unknown, arbitrary benchmark allocation, and the linear welfare factor which assumes an agent's utility linearly decreases down his preference lists, and measures the total utility to that achieved by an optimal allocation. We analyze two matching mechanisms which have been extensively studied by economists. The first mechanism is the random serial dictatorship (RSD) where agents are ordered in accordance with a randomly chosen permutation, and are successively allocated their best choice among the unallocated items. The second mechanism is the probabilistic serial (PS) mechanism of Bogomolnaia and Moulin [8], which computes a fractional allocation that can be expressed as a convex combination of integral allocations. The welfare factor of a mechanism is the infimum over all instances. For RSD, we show that the ordinal welfare factor is asymptotically 1/2, while the linear welfare factor lies in the interval [.526, 2/3]. For PS, we show that the ordinal welfare factor is also 1/2 while the linear welfare factor is roughly 2/3. To our knowledge, these results are the first non-trivial performance guarantees for these natural mechanisms

Recommendations and requirements for slaughtering plants : constuction, operation

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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

Popular matchings in the marriage and roommates problems

Popular matchings have recently been a subject of study in the context of the so-called House Allocation Problem, where the objective is to match applicants to houses over which the applicants have preferences. A matching M is called popular if there is no other matching M′ with the property that more applicants prefer their allocation in M′ to their allocation in M. In this paper we study popular matchings in the context of the Roommates Problem, including its special (bipartite) case, the Marriage Problem. We investigate the relationship between popularity and stability, and describe efficient algorithms to test a matching for popularity in these settings. We also show that, when ties are permitted in the preferences, it is NP-hard to determine whether a popular matching exists in both the Roommates and Marriage cases

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

Inner Speech during Silent Reading Reflects the Reader's Regional Accent

While reading silently, we often have the subjective experience of inner speech. However, there is currently little evidence regarding whether this inner voice resembles our own voice while we are speaking out loud. To investigate this issue, we compared reading behaviour of Northern and Southern English participants who have differing pronunciations for words like ‘glass’, in which the vowel duration is short in a Northern accent and long in a Southern accent. Participants' eye movements were monitored while they silently read limericks in which the end words of the first two lines (e.g., glass/class) would be pronounced differently by Northern and Southern participants. The final word of the limerick (e.g., mass/sparse) then either did or did not rhyme, depending on the reader's accent. Results showed disruption to eye movement behaviour when the final word did not rhyme, determined by the reader's accent, suggesting that inner speech resembles our own voice

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