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The complexity of variants of 3-SAT and Not-All-Equal 3-SAT is well studied. However, in contrast, very little is known about the complexity of the problems' quantified counterparts. In the first part of this paper, we show that $\forall \exists$ 3-SAT is $\Pi_2^P$-complete even if (1) each variable appears exactly twice unnegated and exactly twice negated, (2) each clause is a disjunction of exactly three distinct variables, and (3) the number of universal variables is equal to the number of existential variables. Furthermore, we show that the problem remains $\Pi_2^P$-complete if (1a) each universal variable appears exactly once unnegated and exactly once negated, (1b) each existential variable appears exactly twice unnegated and exactly twice negated, and (2) and (3) remain unchanged. On the other hand, the problem becomes NP-complete for certain variants in which each universal variable appears exactly once. In the second part of the paper, we establish $\Pi_2^P$-completeness for $\forall \exists$ Not-All-Equal 3-SAT even if (1') the Boolean formula is linear and monotone, (2') each universal variable appears exactly once and each existential variable appears exactly three times, and (3') each clause is a disjunction of exactly three distinct variables that contains at most one universal variable. On the positive side, we uncover variants of $\forall \exists$ Not-All-Equal 3-SAT that are co-NP-complete or solvable in polynomial time., Comment: 36 pages; reference corrected in introduction (the result of Karpinski and Piecuch establishes NP-completeness of Not-All-Equal 3-SAT if each variable appears *at most* four times)

We consider the following control problem on fair allocation of indivisible goods. Given a set $I$ of items and a set of agents, each having strict linear preference over the items, we ask for a minimum subset of the items whose deletion guarantees the existence of a proportional allocation in the remaining instance; we call this problem Proportionality by Item Deletion (PID). Our main result is a polynomial-time algorithm that solves PID for three agents. By contrast, we prove that PID is computationally intractable when the number of agents is unbounded, even if the number $k$ of item deletions allowed is small, since the problem turns out to be W[3]-hard with respect to the parameter $k$. Additionally, we provide some tight lower and upper bounds on the complexity of PID when regarded as a function of $|I|$ and $k$., Comment: This is the authors' self-archived copy of a paper that appeared in the proceedings of the 5th International Conference on Algorithmic Decision Theory (ADT 2017)

We show NP-completeness for several planar variants of the monotone satisfiability problem with bounded variable appearances. With one exception the presented variants have an associated bipartite graph where the vertex degree is bounded by at most four. Hence, a planar and orthogonal drawing for these graphs can be computed efficiently, which may turn out to be useful in reductions using these variants as a starting point for proving some decision problem to be NP-hard., Comment: 8 pages, 4 figures

We study the complexity of the destructive bribery problem---an external agent tries to prevent a disliked candidate from winning by bribery actions---in voting over combinatorial domains, where the set of candidates is the Cartesian product of several issues. This problem is related to the concept of the margin of victory of an election which constitutes a measure of robustness of the election outcome and plays an important role in the context of electronic voting. In our setting, voters have conditional preferences over assignments to these issues, modelled by CP-nets. We settle the complexity of all combinations of this problem based on distinctions of four voting rules, five cost schemes, three bribery actions, weighted and unweighted voters, as well as the negative and the non-negative scenario. We show that almost all of these cases are NP-complete or NP-hard for weighted votes while approximately half of the cases can be solved in polynomial time for unweighted votes., Comment: 22 pages

We continue previous work by Mattei et al. (Mattei, N., Pini, M., Rossi, F., Venable, K.: Bribery in voting with CP-nets. Ann. of Math. and Artif. Intell. pp. 1--26 (2013)) in which they study the computational complexity of bribery schemes when voters have conditional preferences that are modeled by CP-nets. For most of the cases they considered, they could show that the bribery problem is solvable in polynomial time. Some cases remained open---we solve two of them and extend the previous results to the case that voters are weighted. Moreover, we consider negative (weighted) bribery in CP-nets, when the briber is not allowed to pay voters to vote for his preferred candidate., Comment: improved readability; identified Cheapest Subsets to be the enumeration variant of K.th Largest Subset, so we renamed it to K-Smallest Subsets and point to the literatur; some more typos fixed

We consider a linear transport equation on the edges of a network with time-varying coefficients. Using methods for non-autonomous abstract Cauchy problems, we obtain well-posedness of the problem and describe the asymptotic profile of the solutions under certain natural conditions on the network. We further apply our theory to a model used for air traffic flow management.

We consider the computational complexity of a problem modeling bribery in the context of voting systems. In the scenario of Swap Bribery, each voter assigns a certain price for swapping the positions of two consecutive candidates in his preference ranking. The question is whether it is possible, without exceeding a given budget, to bribe the voters in a way that the preferred candidate wins in the election. We initiate a parameterized and multivariate complexity analysis of Swap Bribery, focusing on the case of k-approval. We investigate how different cost functions affect the computational complexity of the problem. We identify a special case of k-approval for which the problem can be solved in polynomial time, whereas we prove NP-hardness for a slightly more general scenario. We obtain fixed-parameter tractability as well as W[1]-hardness results for certain natural parameters., Comment: 20 pages. Conference version published at IPEC 2010

To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings, the voters may often only provide partial orders. This directly leads to the Possible Winner problem that asks, given a set of partial votes, whether a distinguished candidate can still become a winner. In this work, we consider the computational complexity of Possible Winner for the broad class of voting protocols defined by scoring rules. A scoring rule provides a score value for every position which a candidate can have in a linear order. Prominent examples include plurality, k-approval, and Borda. Generalizing previous NP-hardness results for some special cases, we settle the computational complexity for all but one scoring rule. More precisely, for an unbounded number of candidates and unweighted voters, we show that Possible Winner is NP-complete for all pure scoring rules except plurality, veto, and the scoring rule defined by the scoring vector (2,1,...,1,0), while it is solvable in polynomial time for plurality and veto., Comment: minor changes and updates; accepted for publication in JCSS, online version available.