The Best-or-Worst and the Postdoc problems

We consider two variants of the secretary problem, the\emph{ Best-or-Worst} and the \emph{Postdoc} problems, which are closely related. First, we prove that both variants, in their standard form with binary payoff 1 or 0, share the same optimal stopping rule. We also consider additional cost/perquisites depending on the number of interviewed candidates. In these situations the optimal strategies are very different. Finally, we also focus on the Best-or-Worst variant with different payments depending on whether the selected candidate is the best or the worst

Machine Covering in the Random-Order Model

In the Online Machine Covering problem jobs, defined by their sizes, arrive one by one and have to be assigned to $m$ parallel and identical machines, with the goal of maximizing the load of the least-loaded machine. In this work, we study the Machine Covering problem in the recently popular random-order model. Here no extra resources are present, but instead the adversary is weakened in that it can only decide upon the input set while jobs are revealed uniformly at random. It is particularly relevant to Machine Covering where lower bounds are usually associated to highly structured input sequences. We first analyze Graham's Greedy-strategy in this context and establish that its competitive ratio decreases slightly to $\Theta\left(\frac{m}{\log(m)}\right)$ which is asymptotically tight. Then, as our main result, we present an improved $\tilde{O}(\sqrt[4]{m})$-competitive algorithm for the problem. This result is achieved by exploiting the extra information coming from the random order of the jobs, using sampling techniques to devise an improved mechanism to distinguish jobs that are relatively large from small ones. We complement this result with a first lower bound showing that no algorithm can have a competitive ratio of $O\left(\frac{\log(m)}{\log\log(m)}\right)$ in the random-order model. This lower bound is achieved by studying a novel variant of the Secretary problem, which could be of independent interest

Random grant allocation from the researchers’ perspective: Introducing the distinction into legitimate and illegitimate problems in Bourdieu’s field theory

Discussions about funding research grants by lottery have centered on weighing the pros and cons of peer review, but this focus does not fully account for how an idea comes across in the field of science to those researchers directly dependent on research funding. Not only do researchers have personal perspectives, but they are also shaped by their experiences and the positions they occupy in the field of science. Applying Bourdieu’s field theory, the authors explore the question of which field-specific problems and conflicts scientists identify and for which they could imagine using a grant lottery in the allocation of research funding. Under what conditions does such a solution, which is external to the field of science, seem justified to them? The results show that different areas of application are conceivable for a lottery mechanism in the field of science but that its use seems justifiable only for legitimate field-specific quandaries

Teaching, Research and Academic Careers

This open access book evaluates research quality, quality of teaching and the relationship between the two through sound statistical methods, and in a comparative perspective with other European countries. In so doing, it covers an increasingly important topic for universities that affects university funding. It discusses whether university evaluation should be limited to a single factor or consider multiple dimensions of research, since academic careers, teaching and awarding degrees are intertwined. The chapters included in the book evaluate teaching and research, also taking the gender dimension into account, in order to understand where and when gender discrimination occurs in assessment. Divided into five sections, the book analyses the administrative data on the determinants of career completion of university students; increasing precariousness of academic careers, especially of young researchers; methods designed to assess research productivity when co-authorship and team production are becoming the standard practice; and interrelations between students’ achievements and teachers’ careers driven by research assessment. It brings together contributions from a large group of economists, statisticians and social scientists working under a project sponsored by ANVUR, the Italian agency for the evaluation of teaching and research of academic institutions. From an international perspective, the findings in this book are particularly interesting because despite low tuition costs, tertiary education in Italy has relatively low enrolment rates and even lower completion rates compared to those in other European and American countries. This book is of interest to researchers of the sociology of education, education policy, public administration, economics and statistics of education, and to administrators and policy makers working in the area of higher education

Online Independent Set Beyond the Worst-Case: Secretaries, Prophets, and Periods

We investigate online algorithms for maximum (weight) independent set on graph classes with bounded inductive independence number like, e.g., interval and disk graphs with applications to, e.g., task scheduling and spectrum allocation. In the online setting, it is assumed that nodes of an unknown graph arrive one by one over time. An online algorithm has to decide whether an arriving node should be included into the independent set. Unfortunately, this natural and practically relevant online problem cannot be studied in a meaningful way within a classical competitive analysis as the competitive ratio on worst-case input sequences is lower bounded by $\Omega(n)$. As a worst-case analysis is pointless, we study online independent set in a stochastic analysis. Instead of focussing on a particular stochastic input model, we present a generic sampling approach that enables us to devise online algorithms achieving performance guarantees for a variety of input models. In particular, our analysis covers stochastic input models like the secretary model, in which an adversarial graph is presented in random order, and the prophet-inequality model, in which a randomly generated graph is presented in adversarial order. Our sampling approach bridges thus between stochastic input models of quite different nature. In addition, we show that our approach can be applied to a practically motivated admission control setting. Our sampling approach yields an online algorithm for maximum independent set with competitive ratio $O(\rho^2)$ with respect to all of the mentioned stochastic input models. for graph classes with inductive independence number $\rho$. The approach can be extended towards maximum-weight independent set by losing only a factor of $O(\log n)$ in the competitive ratio with $n$ denoting the (expected) number of nodes