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We study variants of the Optimal Refugee Resettlement problem where a set $F$ of refugee families need to be allocated to a set $L$ of possible places of resettlement in a feasible and optimal way. Feasibility issues emerge from the assumption that each family requires certain services (such as accommodation, school seats, or medical assistance), while there is an upper and, possibly, a lower quota on the number of service units provided at a given place. Besides studying the problem of finding a feasible assignment, we also investigate two natural optimization variants. In the first one, we allow families to express preferences over $P$, and we aim for a Pareto-optimal assignment. In a more general setting, families can attribute utilities to each place in $P$, and the task is to find a feasible assignment with maximum total utilities. We study the computational complexity of all three variants in a multivariate fashion using the framework of parameterized complexity. We provide fixed-parameter tractable algorithms for a handful of natural parameterizations, and complement these tractable cases with tight intractability results.

In fair division of a connected graph $G = (V, E)$, each of $n$ agents receives a share of $G$'s vertex set $V$. These shares partition $V$, with each share required to induce a connected subgraph. Agents use their own valuation functions to determine the non-negative numerical values of the shares, which determine whether the allocation is fair in some specified sense. We introduce forbidden substructures called graph cutsets, which block divisions that are fair in the EF1 (envy-free up to one item) sense by cutting the graph into "too many pieces". Two parameters - gap and valence - determine blocked values of $n$. If $G$ guarantees connected EF1 allocations for $n$ agents with valuations that are CA (common and additive), then $G$ contains no elementary cutset of gap $k \ge 2$ and valence in the interval $\[n - k + 1, n - 1\]$. If $G$ guarantees connected EF1 allocations for $n$ agents with valuations in the broader CM (common and monotone) class, then $G$ contains no cutset of gap $k \ge 2$ and valence in the interval $\[n - k + 1, n - 1\]$. These results rule out the existence of connected EF1 allocations in a variety of situations. For some graphs $G$ we can, with help from some new positive results, pin down $G$'s spectrum - the list of exactly which values of $n$ do/do not guarantee connected EF1 allocations. Examples suggest a conjectured common spectral pattern for all graphs. Further, we show that it is NP-hard to determine whether a graph admits a cutset. We also provide an example of a (non-traceable) graph on eight vertices that has no cutsets of gap $\ge 2$ at all, yet fails to guarantee connected EF1 allocations for three agents with CA preferences., Comment: Extended abstract accepted at AAMAS'24

We study the congested assignment problem as introduced by Bogomolnaia and Moulin (2023). We show that deciding whether a competitive assignment exists can be done in polynomial time, while deciding whether an envy-free assignment exists is NP-complete.

We investigate winner determination for two popular proportional representation systems: the Monroe and Chamberlin-Courant (abbrv. CC) systems. Our study focuses on (nearly) single-peaked resp. single-crossing preferences. We show that for single-crossing approval preferences, winner determination of the Monroe rule is polynomial, and for both rules, winner determination mostly admits FPT algorithms with respect to the number of voters to delete to obtain single-peaked or single-crossing preferences. Our results answer some complexity questions from the literature [18, 28, 21]., Comment: A conference version appeared in ECAI 2023

We study four NP-hard optimal seat arrangement problems [Bodlaender et al., 2020a], which each have as input a set of n agents, where each agent has cardinal preferences over other agents, and an n-vertex undirected graph (called seat graph). The task is to assign each agent to a distinct vertex in the seat graph such that either the sum of utilities or the minimum utility is maximized, or it is envy-free or exchange-stable. Aiming at identifying hard and easy cases, we extensively study the algorithmic complexity of the four problems by looking into natural graph classes for the seat graph (e.g., paths, cycles, stars, or matchings), problem-specific parameters (e.g., the number of non-isolated vertices in the seat graph or the maximum number of agents towards whom an agent has non-zero preferences), and preference structures (e.g., non-negative or symmetric preferences). For strict preferences and seat graphs with disjoint edges and isolated vertices, we correct an error by Bodlaender et al. [2020b] and show that finding an envy-free arrangement remains NP-hard in this case., Comment: A conference version of the paper appeared at IJCAI 2023

We consider many-to-one matching problems, where one side consists of students and the other side of schools with capacity constraints. We study how to optimally increase the capacities of the schools so as to obtain a stable and perfect matching (i.e., every student is matched) or a matching that is stable and Pareto-efficient for the students. We consider two common optimality criteria, one aiming to minimize the sum of capacity increases of all schools (abbrv. as MinSum) and the other aiming to minimize the maximum capacity increase of any school (abbrv. as MinMax). We obtain a complete picture in terms of computational complexity: Except for stable and perfect matchings using the MinMax criteria which is polynomial-time solvable, all three remaining problems are NP-hard. We further investigate the parameterized complexity and approximability and find that achieving stable and Pareto-efficient matchings via minimal capacity increases is much harder than achieving stable and perfect matchings., Comment: Extended abstract accepted at AAMAS 2023

In many applications, we want to influence the decisions of independent agents by designing incentives for their actions. We revisit a fundamental problem in this area, called GAME IMPLEMENTATION: Given a game in standard form and a set of desired strategies, can we design a set of payment promises such that if the players take the payment promises into account, then all undominated strategies are desired? Furthermore, we aim to minimize the cost, that is, the worst-case amount of payments. We study the tractability of computing such payment promises and determine more closely what obstructions we may have to overcome in doing so. We show that GAME IMPLEMENTATION is NP-hard even for two players, solving in particular a long open question (Eidenbenz et al. 2011) and suggesting more restrictions are necessary to obtain tractability results. We thus study the regime in which players have only a small constant number of strategies and obtain the following. First, this case remains NP-hard even if each player's utility depends only on three others. Second, we repair a flawed efficient algorithm for the case of both small number of strategies and small number of players. Among further results, we characterize sets of desired strategies that can be implemented at zero cost as a kind of stable core of the game.

A preference profile with m alternatives and n voters is 2-dimensional Euclidean if both the alternatives and the voters can be placed into a 2-dimensional space such that for each pair of alternatives, every voter prefers the one which has a shorter Euclidean distance to the voter. We study how 2-dimensional Euclidean preference profiles depend on the values m and n. We find that any profile with at most two voters or at most three alternatives is 2-dimensional Euclidean while for three voters, we can show this property for up to seven alternatives. The results are tight in terms of Bogomolnaia and Laslier [2, Proposition 15(1)].

We investigate verification and existence problems for prominent stability concepts in hedonic games with friends, enemies, and optionally with neutrals [8, 16]. We resolve several (long-standing) open questions [4, 16, 20, 23] and show that for friend-oriented preferences, under the friends and enemies model, it is coNP-complete to verify whether a given agent partition is (strictly) core stable, while under the friends, enemies, and neutrals model, it is NP-complete to determine whether an individual stable partition exists. We further look into natural restricted cases from the literature, such as when the friends and enemies relationships are symmetric, when the initial coalitions have bounded size, when the vertex degree in the friendship graph (resp. the union of friendship and enemy graph) is bounded, or when such graph is acyclic or close to being acyclic. We obtain a complete (parameterized) complexity picture regarding these cases., Comment: extended abstract appeared at AAMAS 2023

Answering an open question by Betzler et al. [Betzler et al., JAIR'13], we resolve the parameterized complexity of the multi-winner determination problem under two famous representation voting rules: the Chamberlin-Courant (in short CC) rule [Chamberlin and Courant, APSR'83] and the Monroe rule [Monroe, APSR'95]. We show that under both rules, the problem is W[1]-hard with respect to the sum $\beta$ of misrepresentations, thereby precluding the existence of any $f(\beta) \cdot |I|^{O(1)}$ -time algorithm, where $|I|$ denotes the size of the input instance.

A preference profile with $m$ alternatives and $n$ voters is $d$-Manhattan (resp. $d$-Euclidean) if both the alternatives and the voters can be placed into the $d$-dimensional space such that between each pair of alternatives, every voter prefers the one which has a shorter Manhattan (resp. Euclidean) distance to the voter. Following Bogomolnaia and Laslier [Journal of Mathematical Economics, 2007] and Chen and Grottke [Social Choice and Welfare, 2021] who look at $d$-Euclidean preference profiles, we study which preference profiles are $d$-Manhattan depending on the values $m$ and $n$. First, we show that each preference profile with $m$ alternatives and $n$ voters is $d$-Manhattan whenever $d$ $\geq$ min($n$, $m$-$1$). Second, for $d = 2$, we show that the smallest non $d$-Manhattan preference profile has either three voters and six alternatives, or four voters and five alternatives, or five voters and four alternatives. This is more complex than the case with $d$-Euclidean preferences (see [Bogomolnaia and Laslier, 2007] and [Bulteau and Chen, 2020].

We investigate the Euclidean $d$-Dimensional Stable Roommates problem, which asks whether a given set~$V$ of $d \cdot n$ points from the 2-dimensional Euclidean space can be partitioned into $n$ disjoint (unordered) subsets $\Pi=\{V_1,\ldots,V_{n}\}$ with $|V_i|=d$ for each $V_i\in \Pi$ such that $\Pi$ is stable. Here, stability means that no point subset $W\subseteq V$ is blocking $\Pi$ and $W$ is said to be blocking $\Pi$ if $|W|= d$ such that $\sum_{w'\in W}\delta(w,w') < \sum_{v\in \Pi(w)}\delta(w,v)$ holds for each point $w\in W$, where $\Pi(w)$ denotes the subset $V_i\in \Pi$ which contains $w$ and $\delta(a,b)$ denotes the Euclidean distance between points $a$ and $b$. Complementing the existing known polynomial-time result for $d=2$, we show that such polynomial-time algorithms cannot exist for any fixed number $d \ge 3$ unless P=NP. Our result for $d=3$ answers a decade-long open question in the theory of Stable Matching and Hedonic Games [17, 1, 9, 25, 20].

We study (coalitional) exchange stability, which Alcalde [Economic Design, 1995] introduced as an alternative solution concept for matching markets involving property rights, such as assigning persons to two-bed rooms. Here, a matching of a given Stable Marriage or Stable Roommates instance is called coalitional exchange-stable if it does not admit any exchange-blocking coalition, that is, a subset S of agents in which everyone prefers the partner of some other agent in S. The matching is exchange-stable if it does not admit any exchange-blocking pair, that is, an exchange-blocking coalition of size two. We investigate the computational and parameterized complexity of the Coalitional Exchange-Stable Marriage (resp. Coalitional Exchange Roommates) problem, which is to decide whether a Stable Marriage (resp. Stable Roommates) instance admits a coalitional exchange-stable matching. Our findings resolve an open question and confirm the conjecture of Cechl\'arov\'a and Manlove [Discrete Applied Mathematics, 2005] that Coalitional Exchange-Stable Marriage is NP-hard even for complete preferences without ties. We also study bounded-length preference lists and a local-search variant of deciding whether a given matching can reach an exchange-stable one after at most k swaps, where a swap is defined as exchanging the partners of the two agents in an exchange-blocking pair.

Participatory budgeting (PB) is a democratic process where citizens jointly decide on how to allocate public funds to indivisible projects. This paper focuses on PB processes where citizens may give additional money to projects they want to see funded. We introduce a formal framework for this kind of PB with donations. Our framework also allows for diversity constraints, meaning that each project belongs to one or more types, and there are lower and upper bounds on the number of projects of the same type that can be funded. We propose three general classes of methods for aggregating the citizens' preferences in the presence of donations and analyze their axiomatic properties. Furthermore, we investigate the computational complexity of determining the outcome of a PB process with donations and of finding a citizen's optimal donation strategy.

We thoroughly study a generalized version of the classic Stable Marriage and Stable Roommates problems where agents may share partners. We consider two prominent stability concepts: ordinal stability [Aharoni and Fleiner, Journal of Combinatorial Theory, 2003] and cardinal stability [Caragiannis et al., ACM EC 2019] and two optimality criteria: maximizing social welfare (i.e., the overall satisfaction of the agents) and maximizing the number of fully matched agents (i.e., agents whose shares sum up to one). After having observed that ordinal stability always exists and implies cardinal stability, and that the set of ordinally stable matchings in a restricted case admits a lattice structure, we obtain a complete picture regarding the computational complexity of finding an optimal ordinally stable or cardinally stable matching. In the process we answer an open question raised by Caragiannis et al. [AIJ 2020].

We present a data structure that in a dynamic graph of treedepth at most $d$, which is modified over time by edge insertions and deletions, maintains an optimum-height elimination forest. The data structure achieves worst-case update time $2^{{\cal O}(d^2)}$, which matches the best known parameter dependency in the running time of a static fpt algorithm for computing the treedepth of a graph. This improves a result of Dvo\v{r}\'ak et al. [ESA 2014], who for the same problem achieved update time $f(d)$ for some non-elementary (i.e. tower-exponential) function $f$. As a by-product, we improve known upper bounds on the sizes of minimal obstructions for having treedepth $d$ from doubly-exponential in $d$ to $d^{{\cal O}(d)}$. As applications, we design new fully dynamic parameterized data structures for detecting long paths and cycles in general graphs. More precisely, for a fixed parameter $k$ and a dynamic graph $G$, modified over time by edge insertions and deletions, our data structures maintain answers to the following queries: - Does $G$ contain a simple path on $k$ vertices? - Does $G$ contain a simple cycle on at least $k$ vertices? In the first case, the data structure achieves amortized update time $2^{{\cal O}(k^2)}$. In the second case, the amortized update time is $2^{{\cal O}(k^4)} + {\cal O}(k \log n)$. In both cases we assume access to a dictionary on the edges of $G$., Comment: 74 pages, 5 figures

We investigate the following many-to-one stable matching problem with diversity constraints (SMTI-Diverse): Given a set of students and a set of colleges which have preferences over each other, where the students have overlapping types, and the colleges each have a total capacity as well as quotas for individual types (the diversity constraints), is there a matching satisfying all diversity constraints such that no unmatched student-college pair has an incentive to deviate? SMTI-Diverse is known to be NP-hard. However, as opposed to the NP-membership claims in the literature [Aziz et al., AAMAS 2019; Huang, SODA 2010], we prove that it is beyond NP: it is complete for the complexity class $\Sigma^{\text{P}}_2$. In addition, we provide a comprehensive analysis of the problem's complexity from the viewpoint of natural restrictions to inputs and obtain new algorithms for the problem.

Adaptivity to changing environments and constraints is key to success in modern society. We address this by proposing "incrementalized versions" of Stable Marriage and Stable Roommates. That is, we try to answer the following question: for both problems, what is the computational cost of adapting an existing stable matching after some of the preferences of the agents have changed. While doing so, we also model the constraint that the new stable matching shall be not too different from the old one. After formalizing these incremental versions, we provide a fairly comprehensive picture of the computational complexity landscape of Incremental Stable Marriage and Incremental Stable Roommates. To this end, we exploit the parameters "degree of change" both in the input (difference between old and new preference profile) and in the output (difference between old and new stable matching). We obtain both hardness and tractability results, in particular showing a fixed-parameter tractability result with respect to the parameter "distance between old and new stable matching"., Comment: Accepted to AAAI 2020

We study the Reaching Stable Marriage via Divorces (DivorceSM) problem of deciding, given a Stable Marriage instance and an initial matching $M$ , whether there exists a stable matching which is reachable from $M$ by divorce operations as introduced by Knuth [12]. Towards answering an open question of Manlove [13] and Cechl\'arov\'a et al. [3], we show that for incomplete preferences without ties, DivorceSM is NP-hard. Our hardness reduction also implies that the problem remains parameterized intractable for the number $\kappa$ of allowed divorce operations. It remains NP-hard even if the maximum length $d$ of the preferences is a constant. For the combined parameter ($\kappa$, $d$), the problem is fixed-parameter tractable.

We study a simple exchange market, introduced by Gourv\'{e}s, Lesca and Wilczynski (IJCAI-17), where every agent initially holds a single object. The agents have preferences over the objects, and two agents may swap their objects if they both prefer the object of the other agent. The agents live in an underlying social network that governs the structure of the swaps: Two agents can only swap their objects if they are adjacent. We investigate the REACHABLE OBJECT problem, which asks whether a given starting situation can ever lead, by means of a sequence of swaps, to a situation where a given agent obtains a given object. Our results answer several central open questions on the complexity of REACHABLE OBJECT. First, the problem is polynomial-time solvable if the social network is a path. Second, the problem is NP-hard on cliques and generalized caterpillars. Finally, we establish a three-versus-four dichotomy result for preference lists of bounded length: The problem is easy if all preference lists have length at most three, and the problem becomes NP-hard even if all agents have preference lists of length at most four.

This paper gives an overview on and summarizes existing complexity and algorithmic results of some variants of the Stable Marriage and the Stable Roommates problems. The last section defines a list of stable matching problems mentioned in the paper. If you find any corrections, suggestions, new or missing results, please send them to jiehua.chen2@gmail.com.

The classical Stable Roommates problem is to decide whether there exists a matching of an even number of agents such that no two agents which are not matched to each other would prefer to be with each other rather than with their respectively assigned partners. We investigate Stable Roommates with complete (i.e., every agent can be matched with any other agent) or incomplete preferences, with ties (i.e., two agents are considered of equal value to some agent) or without ties. It is known that in general allowing ties makes the problem NP-complete. We provide algorithms for Stable Roommates that are, compared to those in the literature, more efficient when the input preferences are complete and have some structural property, such as being narcissistic, single-peaked, and single-crossing. However, when the preferences are incomplete and have ties, we show that being single-peaked and single-crossing does not reduce the computational complexity--Stable Roommates remains NP-complete.

We propose two solution concepts for matchings under preferences: robustness and near stability. The former strengthens while the latter relaxes the classic definition of stability by Gale and Shapley (1962). Informally speaking, robustness requires that a matching must be stable in the classic sense, even if the agents slightly change their preferences. Near stability, on the other hand, imposes that a matching must become stable (again, in the classic sense) provided the agents are willing to adjust their preferences a bit. Both of our concepts are quantitative; together they provide means for a fine-grained analysis of stability for matchings. Moreover, our concepts allow to explore the trade-offs between stability and other criteria of societal optimality, such as the egalitarian cost and the number of unmatched agents. We investigate the computational complexity of finding matchings that implement certain predefined trade-offs. We provide a polynomial-time algorithm that given agents' preferences returns a socially optimal robust matching, and we prove that finding a socially optimal and nearly stable matching is computationally hard., Comment: 47 pages. Accepted for presentation at the 20th ACM Conference on Economics and Computation (EC '19)

We characterize one-dimensional Euclidean preference profiles with a small number of alternatives and voters. In particular, we show the following. 1. Every preference profile with up to two voters is one-dimensional Euclidean if and only if it is single-peaked. 2. Every preference profile with up to five alternatives is one-dimensional Euclidean if and only if it is single-peaked and single-crossing. By [12], we thus obtain that the smallest single-peaked and single-crossing preference profiles that are not one-dimensional Euclidean consist of three voters and six alternatives.

We consider the clustering aggregation problem in which we are given a set of clusterings and want to find an aggregated clustering which minimizes the sum of mismatches to the input clusterings. In the binary case (each clustering is a bipartition) this problem was known to be NP-hard under Turing reductions. We strengthen this result by providing a polynomial-time many-one reduction. Our result also implies that no $2^{o(n)}\cdot |I'|^{O(1)}$-time algorithm exists that solves any given clustering instance $I'$ with $n$ elements, unless the \ETH{} fails. On the positive side, we show that the problem is fixed-parameter tractable with respect to the number of input clusterings and we give an integer linear programming formulation.

In this paper we consider the $p$-Norm Hamming Centroid problem which asks to determine whether some given binary strings have a centroid with a bound on the $p$-norm of its Hamming distances to the strings. Specifically, given a set of strings $S$ and a real $k$, we consider the problem of determining whether there exists a string $s^*$ with $\big(\sum_{s \in S}d^p(s^*,s)\big)^{1/p} \leq k$, where $d(,)$ denotes the Hamming distance metric. This problem has important applications in data clustering, and is a generalization of the well-known polynomial-time solvable \textsc{Consensus String} $(p=1)$ problem, as well as the NP-hard \textsc{Closest String} $(p=\infty)$ problem. Our main result shows that the problem is NP-hard for all fixed rational $p > 1$, closing the gap for all rational values of $p$ between $1$ and $\infty$. Under standard complexity assumptions the reduction also implies that the problem has no $2^{o(n+m)}$-time or $2^{o(k^{\frac{p}{(p+1)}})}$-time algorithm, where $m$ denotes the number of input strings and $n$ denotes the length of each string, for any fixed $p > 1$. Both running time lower bounds are tight. In particular, we provide a $2^{k^{\frac{p}{(p+1)}+\varepsilon}}$-time algorithm for each fixed $\varepsilon > 0$. In the last part of the paper, we complement our hardness result by presenting a fixed-parameter algorithm and a factor-$2$ approximation algorithm for the problem., Comment: To appear at ESA 2019

We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one "evaluation mode" (e.g., more than one criterion); thus, each agent is equipped with multiple preference lists, each ranking the counterparts in a possibly different way. We introduce and study three natural concepts of stability, investigate their mutual relations and focus on computational complexity aspects with respect to computing stable matchings in these new scenarios. Mostly encountering computational hardness (NP-hardness), we can also spot few islands of tractability and make a surprising connection to the \textsc{Graph Isomorphism} problem.

Motivated by the recent rapid growth of research for algorithms to cluster multi-layer and temporal graphs, we study extensions of the classical Cluster Editing problem. In Multi-Layer Cluster Editing we receive a set of graphs on the same vertex set, called layers and aim to transform all layers into cluster graphs (disjoint unions of cliques) that differ only slightly. More specifically, we want to mark at most $d$ vertices and to transform each layer into a cluster graph using at most $k$ edge additions or deletions per layer so that, if we remove the marked vertices, we obtain the same cluster graph in all layers. In Temporal Cluster Editing we receive a sequence of layers and we want to transform each layer into a cluster graph so that consecutive layers differ only slightly. That is, we want to transform each layer into a cluster graph with at most $k$ edge additions or deletions and to mark a distinct set of $d$ vertices in each layer so that each two consecutive layers are the same after removing the vertices marked in the first of the two layers. We study the combinatorial structure of the two problems via their parameterized complexity with respect to the parameters $d$ and $k$, among others. Despite the similar definition, the two problems behave quite differently: In particular, Multi-Layer Cluster Editing is fixed-parameter tractable with running time $k^{O(k+d)}\cdot s^{O(1)}$ for inputs of size $s$, whereas Temporal Cluster Editing is W[1]-hard with respect to $k$ even if $d = 3$.

The classic Stable Roommates problem (which is the non-bipartite generalization of the well-known Stable Marriage problem) asks whether there is a stable matching for a given set of agents, i.e. a partitioning of the agents into disjoint pairs such that no two agents induce a blocking pair. Herein, each agent has a preference list denoting who it prefers to have as a partner, and two agents are blocking if they prefer to be with each other rather than with their assigned partners. Since stable matchings may not be unique, we study an NP-hard optimization variant of Stable Roommates, called Egal Stable Roommates, which seeks to find a stable matching with a minimum egalitarian cost {\gamma}, i.e. the sum of the dissatisfaction of the agents is minimum. The dissatisfaction of an agent is the number of agents that this agent prefers over its partner if it is matched; otherwise it is the length of its preference list. We also study almost stable matchings, called Min-Block-Pair Stable Roommates, which seeks to find a matching with a minimum number {\beta} of blocking pairs. Our main result is that Egal Stable Roommates parameterized by {\gamma} is fixed-parameter tractable, while Min-Block-Pair Stable Roommates parameterized by {\beta} is W[1]-hard, even if the length of each preference list is at most five.

We investigate preference profiles for a set $\mathcal{V}$ of voters, where each voter $i$ has a preference order $\succ_i$ on a finite set $A$ of alternatives (that is, a linear order on $A$) such that for each two alternatives $a,b\in A$, voter $i$ prefers $a$ to $b$ if $a\succ_i b$. Such a profile is narcissistic if each alternative $a$ is preferred the most by at least one voter. It is single-peaked if there is a linear order $\triangleright^{\text{sp}}$ on the alternatives such that each voter's preferences on the alternatives along the order $\triangleright^{\text{sp}}$ are either strictly increasing, or strictly decreasing, or first strictly increasing and then strictly decreasing. It is single-crossing if there is a linear order $\triangleright^{\text{sc}}$ on the voters such that each pair of alternatives divides the order $\triangleright^{\text{sc}}$ into at most two suborders, where in each suborder, all voters have the same linear order on this pair. We show that for $n$ voters and $n$ alternatives,the number of single-peaked narcissistic profiles is $\prod_{i=2}^{n-1} \binom{n-1}{i-1}$ while the number of single-crossing narcissistic profiles is $2^{\binom{n-1}{2}}$., Comment: To appear in Discrete Mathematics

Voter control problems model situations in which an external agent tries toaffect the result of an election by adding or deleting the fewest number of voters. The goal of the agent is to make a specific candidate either win (\emph{constructive} control) or lose (\emph{destructive} control) the election. We study the constructive and destructive voter control problems whenadding and deleting voters have a \emph{combinatorial flavor}: If we add (resp.\ delete) a voter~$v$, we also add (resp.\ delete) a bundle~$\kappa(v) $ of voters that are associated with~$v$. While the bundle~$\kappa(v)$ may have more than one voter, a voter may also be associated with more than one voter. We analyze the computational complexity of the four voter control problems for the Plurality rule. We obtain that, in general, making a candidate lose is computationally easier than making her win. In particular, if the bundling relation is symmetric (i.e.\ $\forall w\colon w \in \kappa(v) \Leftrightarrow v \in \kappa(w) $), and if each voter has at most two voters associated with him, then destructive control is polynomial-time solvable while the constructive variant remains $\NP$-hard. Even if the bundles are disjoint (i.e.\ $\forall w\colon w \in \kappa(v) \Leftrightarrow \kappa(v) = \kappa(w) $), the constructive problem variants remain intractable. Finally, the minimization variant of constructive control by adding voters does not admit an efficient approximation algorithm, unless P=NP., Comment: Accepted for TAMC 2017

Consider an important meeting to be held in a team-based organization. Taking availability constraints into account, an online scheduling poll is being used in order to decide upon the exact time of the meeting. Decisions are to be taken during the meeting, therefore each team would like to maximize its relative attendance in the meeting (i.e., the proportional number of its participating team members). We introduce a corresponding game, where each team can declare (in the scheduling poll) a lower total availability, in order to improve its relative attendance---the pay-off. We are especially interested in situations where teams can form coalitions. We provide an efficient algorithm that, given a coalition, finds an optimal way for each team in a coalition to improve its pay-off. In contrast, we show that deciding whether such a coalition exists is NP-hard. We also study the existence of Nash equilibria: Finding Nash equilibria for various small sizes of teams and coalitions can be done in polynomial time while it is coNP-hard if the coalition size is unbounded.

We investigate the problem of deciding whether a given preference profile is close to having a certain nice structure, as for instance single-peaked, single-caved, single-crossing, value-restricted, best-restricted, worst-restricted, medium-restricted, or group-separable profiles. We measure this distance by the number of voters or alternatives that have to be deleted to make the profile a nicely structured one. Our results classify the problem variants with respect to their computational complexity, and draw a clear line between computationally tractable (polynomial-time solvable) and computationally intractable (NP-hard) questions.

We study computational problems for two popular parliamentary voting procedures: the amendment procedure and the successive procedure. While finding successful manipulations or agenda controls is tractable for both procedures, our real-world experimental results indicate that most elections cannot be manipulated by a few voters and agenda control is typically impossible. If the voter preferences are incomplete, then finding which alternatives can possibly win is NP-hard for both procedures. Whilst deciding if an alternative necessarily wins is coNP-hard for the amendment procedure, it is polynomial-time solvable for the successive one.