On the complexity of strongly connected components in directed hypergraphs

We study the complexity of some algorithmic problems on directed hypergraphs and their strongly connected components (SCCs). The main contribution is an almost linear time algorithm computing the terminal strongly connected components (i.e. SCCs which do not reach any components but themselves). "Almost linear" here means that the complexity of the algorithm is linear in the size of the hypergraph up to a factor alpha(n), where alpha is the inverse of Ackermann function, and n is the number of vertices. Our motivation to study this problem arises from a recent application of directed hypergraphs to computational tropical geometry. We also discuss the problem of computing all SCCs. We establish a superlinear lower bound on the size of the transitive reduction of the reachability relation in directed hypergraphs, showing that it is combinatorially more complex than in directed graphs. Besides, we prove a linear time reduction from the well-studied problem of finding all minimal sets among a given family to the problem of computing the SCCs. Only subquadratic time algorithms are known for the former problem. These results strongly suggest that the problem of computing the SCCs is harder in directed hypergraphs than in directed graphs.Comment: v1: 32 pages, 7 figures; v2: revised version, 34 pages, 7 figure

Brand advertising competition across economic cycles’

This study investigates how brands’ responses to competitors’ advertising actions change over the business cycle. In an empirical analysis of advertising activity by 105 brands in six consumer packaged goods categories over 10 years in a market that experienced severe economic swings, we show that managers become more aggressive in contractions. Brands respond not only more often to competitors’ advertising but also more intensely. Different brands react in contractions. Brand leaders respond less often and intensely in bad times; by contrast, premium-tier brands seem to avoid competition in good times but aggressively defend their position in bad times, especially against cheaper competitors, which are more popular in contractions. We corroborate the validity of our findings through in-depth interviews with executives and introduce two useful metrics, aggressivity and receptivity, to map changes in brand competition in an industry when economic conditions change. Collectively, the findings show how managers can better anticipate competitive advertising reactions in good and bad economic times

An Investigation into EFL Learners’ Perspectives Towards Dynamic Assessment

This chapter reports on a study that examines English-as-a-foreign-language (EFL) learners’ perspectives towards Dynamic Assessment (DA) and their engagement with it in a university setting in Turkey. Learning-oriented assessment approaches have lately received growing attention, and DA which embeds learning into the assessment is one of them. Some influential studies examined L2 learners’ development over time, and a few studies demonstrated either learners’ or teachers’ perspectives on DA. Yet, more studies examining learner engagement with DA in different writing contexts are warranted. Driven by this gap, twenty-five EFL university students taking a Writing Skills course were recruited for this qualitative study. Each student was provided one-on-one interactive DA two times a week for ten weeks. For this chapter, we draw on audio recordings during DA/mediation sessions and semi-structured focused group interviews conducted in five groups in Turkish to explore students’ perspectives on DA and illustrate their engagement with DA. The preliminary moment-to-moment analysis of dialogic interactions revealed that mediational moves diverged according to each learner’s needs. The interview data also revealed three main themes consisting of several sub-themes. Notably, these themes that illustrated the students’ perspectives towards adopting DA in an EFL writing setting had a bidirectional relationship between teaching and assessment. The chapter will also highlight challenges faced while applying DA and implications for EFL writing teachers