This House Proves that Debating is Harder than Soccer

During the last twenty years, a lot of research was conducted on the sport elimination problem: Given a sports league and its remaining matches, we have to decide whether a given team can still possibly win the competition, i.e., place first in the league at the end. Previously, the computational complexity of this problem was investigated only for games with two participating teams per game. In this paper we consider Debating Tournaments and Debating Leagues in the British Parliamentary format, where four teams are participating in each game. We prove that it is NP-hard to decide whether a given team can win a Debating League, even if at most two matches are remaining for each team. This contrasts settings like football where two teams play in each game since there this case is still polynomial time solvable. We prove our result even for a fictitious restricted setting with only three teams per game. On the other hand, for the common setting of Debating Tournaments we show that this problem is fixed parameter tractable if the parameter is the number of remaining rounds $k$. This also holds for the practically very important question of whether a team can still qualify for the knock-out phase of the tournament and the combined parameter $k + b$ where $b$ denotes the threshold rank for qualifying. Finally, we show that the latter problem is polynomial time solvable for any constant $k$ and arbitrary values $b$ that are part of the input.Comment: 18 pages, to appear at FUN 201

Die Baumkronenspinnen (Araneae) des Leipziger Auwaldes

The canopy spiders of the floodplain forest in Leipzig have become a focus of ecological studies in recent years. In 2006 we sampled 30 tree canopies in the ‘Burgaue’ nature reserve with pyrethrum knock-down fogging, recording 502 adult spiders belonging to 48 species and 11 families. Based on these data and the results of a previous fogging study, the studied spider community was dominated by forest and forest-edge species with a preference for the shrub and canopy strata as well as by spiders of the web spider feeding guild. The community structure was typical for arboreal spider communities from northern temperate forests but very different from communities in the tropics. Species richness and evenness were similar to the old growth near-primary Białowieża Forest in Poland. The checklist of 96 canopy spider species of the floodplain forest of Leipzig includes 54 additions to the spider fauna of Leipzig and vicinity by recent canopy studies and eight first canopy records for Leipzig from our field work. The theridiid Dipoena torva (Thorell, 1875) was recorded for the first time in Saxony. The floodplain forest of Leipzig sustains a large and species-rich arboreal spider community and is thus a valuable habitat for a large proportion of endangered species (12%).Die Spinnen der Baumkronen des Leipziger Auwaldes wurden in den vergangenen Jahren ein Schwerpunkt ökologischer Forschung. Im Jahr 2006 untersuchten wir 30 Baumkronen im Naturschutzgebiet „Burgaue“ mithilfe der Insektizid-Baumkronenbenebelung und erhielten dabei 502 adulte Spinnen aus 48 Arten und 11 Familien. Basierend auf diesen Daten und Ergebnissen einer früheren Benebelungsstudie fanden wir, dass die untersuchte Spinnengemeinschaft von Wald- und Waldrandarten mit Präferenz für die Strauch- und Kronenschicht dominiert war. Auf Gildenniveau dominierten die Netzspinnen. Die Gemeinschaftsstruktur war typisch für eine arboreale Spinnengemeinschaft der nördlichen temperaten Wälder aber sehr verschieden von Gemeinschaften in den Tropen. Artenvielfalt und Evenness waren ähnlich dem Urwald von Białowieża in Polen. Aufgrund der Baumkronenforschungen in Leipzig beinhaltet die Baumkronen-Checkliste der 96 Spinnenarten des Leipziger Auwaldes 54 Erstnachweise für Leipzig und Umgebung. Acht Arten wurden erstmals durch unsere neuen Feldarbeiten in Leipzig nachgewiesen, die Kugelspinne Dipoena torva (Thorell, 1875) dabei erstmals in Sachsen. Der Leipziger Auwald beherbergt eine große und artenreiche arboreale Spinnengemeinschaft und ist ein wertvolles Habitat für einen großen Anteil gefährdeter Arten (12 %)