The classic result by Fortune, Hopcroft, and Wyllie [TCS ’80] states that the directed disjoint paths problem is NP-complete even for two pairs of terminals. Extending this well-known result, we show that the directed disjoint paths problem is NP-complete for any constant congestion \(c \ge 1\) and \(k \ge 3c - 1\) pairs of terminals. This refutes a conjecture by Giannopoulou et al. [SODA ’22], which says that the directed disjoint paths problem with congestion two is polynomial-time solvable for any constant number \(k\) of terminal pairs. We then consider the cases that are not covered by this hardness result. The first nontrivial case is \(c = 2\) and \(k = 3\). Our second main result is to show that this case is polynomial-time solvable.

The present study aims at improving the predictive power of the use of pronouns in computational modeling of the risk of Alzheimer's dementia (AD) by (i) further determining the onset of increased pronoun use in AD and (ii) providing insights into the linguistic contexts affected by the increase early on. Pronoun use was compared longitudinally between subjects who either stayed cognitively intact (CTR-group, n = 5) or who had developed AD upon follow-up after 10–12 years (AD-group, n = 5). Data were taken from semi-structured biographical interviews, which stem from the Interdisciplinary Longitudinal Study on Adult Development and Aging (ILSE). The first interview (baseline) was conducted when all participants were still cognitively healthy. Analyses concerned the proportional distribution of 12 pronoun types and linguistic contexts of increased use. Already at baseline, the AD-group produced a significantly higher proportion of D-pronouns (der, die, das, etc.) than the CTR-group. The increase in D-pronouns did not affect linguistic contexts favoring the use of personal pronouns. Instead, we found a significantly higher proportion of D-pronouns referring to family members and a significantly higher proportion of personal pronouns referring to non-family humans in the AD-group than in the CTR-group. Our results suggest that the predictive power of the use of pronouns can be significantly improved in computational modeling of the risk of AD by assessing language material that induces the use of pronouns in linguistic contexts affected by the increase.

Alzheimer's disease is a progressive incurable condition for which the success of any symptomatic therapy depends crucially on the starting time. Ideally it starts before the disease has caused any cognitive impairments. Our work aims at developing speech-based dementia screening methods that detect dementia as early as possible. Here, we aim to predict the outbreak even before clinical screening tests can diagnose the disease. Using the longitudinal ILSE study, we automatically extract features from biographic interviews and predict the development of dementia 5 and 12 years into the future. Our prediction system achieves results of 73.3% and 75.7% unweighted average recall (UAR), respectively, which clearly outperform a prediction based on prior diagnoses or disease prevalence. Thus, the automated analysis of spoken interviews offers a highly effective prediction procedure that allows for easy-to-use, cost-effective casual testing.