Combinatorial Voter Control in Elections

Voter control problems model situations such as an external agent trying to affect the result of an election by adding voters, for example by convincing some voters to vote who would otherwise not attend the election. Traditionally, voters are added one at a time, with the goal of making a distinguished alternative win by adding a minimum number of voters. In this paper, we initiate the study of combinatorial variants of control by adding voters: In our setting, when we choose to add a voter~$v$, we also have to add a whole bundle $\kappa(v)$ of voters associated with $v$. We study the computational complexity of this problem for two of the most basic voting rules, namely the Plurality rule and the Condorcet rule.Comment: An extended abstract appears in MFCS 201

Graph editing to a given degree sequence

We investigate the parameterized complexity of the graph editing problem called Editing to a Graph with a Given Degree Sequence where the aim is to obtain a graph with a given degree sequence σ by at most k vertex deletions, edge deletions and edge additions. We show that the problem is W[1]-hard when parameterized by k for any combination of the allowed editing operations. From the positive side, we show that the problem can be solved in time 2O(k(Δ⁎+k)2)n2log⁡n for n -vertex graphs, where Δ⁎=max⁡σ, i.e., the problem is FPT when parameterized by k+Δ⁎. We also show that Editing to a Graph with a Given Degree Sequence has a polynomial kernel when parameterized by k+Δ⁎ if only edge additions are allowed, and there is no polynomial kernel unless NP⊆co-NP/poly for all other combinations of the allowed editing operations

Synthesen von 4,5-disubstituierten Pyrimidinen und ihre Umsetzung zu Purinen, Oxazolo- und Pyrazolopyrimidinen (Synthesen in der heterocyclischen Reihe ; 2)

Aus 4-Chlor-5-carbäthoxy-pyrimidin erhält man mit Aminen, Alkoholaten und Mercaptiden Substituentenaustausch am C-4. 8-Hydroxy-purin läßt sich aus 4-Amino-pyrimidin-carbonsäure-(5)-amid bzw. -hydrazid einstufig durch Hofmann'schen bzw. Curtius'schen Abbau darstellen. Analog erhält man aus 4-Hydroxy-pyrimidin-carbonsäure-(5)-hydrazid das 2-Hydroxy-oxazolo [5.4-d]pyrimidin. Zu 3-Hydroxy-pyrazolo[3.4-d] pyrimidinen kommt man durch Ringschlußreaktionen von 4-Chlor-5-carbäthoxy-pyrimidin mit Hydrazinen

Neue Synthesen 5-monosubstituierter Pyrimidine (Synthesen in der heterocyclischen Reihe ; 1)

5-Monosubstituierte Pyrimidine werden aus 2-substituierten 1.1.3.3-Tetraalkoxypropanen mit Formamid erhalten. aus dem leicht zugänglichen 4-ydroxy-5-carbäthoxy-pyrimidin läßt sich die 4-Chlor-Verbindung darstellen, deren katalytische Hydrierung zu 5-Carbäthoxy-pyrimidin führt. Daraus erhält man mit Ammoniak bzw. Hydrazin Pyrimidin-carbonsäure-(5)-amid bzw.-hydrazid, deren Abbaureaktionen 5-Amino-pyrimidin ergeben