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Sofia Simola

Publications and source records attributed to Sofia Simola.

12 recordsLinked to original sources
arXiv2026

Control in Hedonic Games

We initiate the study of control in hedonic games, where an external actor influences coalition formation by adding or deleting agents. We consider three basic control goals (1) enforcing that an agent is not alone (NA); (2) enforcing that a pair of agents is in the same coalition (PA); (3) enforcing that all agents are in the same grand coalition (GR), combined with two control actions: adding agents (AddAg) or deleting agents (DelAg). We analyze these problems for friend-oriented and additive preferences under individual rationality, individual stability, Nash stability, and core stability. We provide a complete computational complexity classification for control in hedonic games.

cs.GT↗
arXiv2025

Partitioned Combinatorial Optimization Games

We propose a class of cooperative games, called d Partitioned Compbinatorial Optimization Games (PCOGs). The input of PCOG consists of a set of agents and a combinatorial structure (typically a graph) with a fixed optimization goal on this structure (e.g., finding a minimum dominating set on a graph) such that the structure is divided among the agents. The value of each coalition of agents is derived from the optimal solution for the part of the structure possessed by the coalition. We study two fundamental questions related to the core: Core Stability Verification and Core Stability Existence. We analyze the algorithmic complexity of both questions for four classic graph optimization tasks: minimum vertex cover, minimum dominating set, minimum spanning tree, and maximum matching.

cs.GT↗
arXiv2025

FPT-Approximability of Stable Matching Problems

We study parameterized approximability of three optimization problems related to stable matching: (1) Min-BP-SMI: Given a stable marriage instance and a number k, find a size-at-least-k matching that minimizes the number $\beta$ of blocking pairs; (2) Min-BP-SRI: Given a stable roommates instance, find a matching that minimizes the number $\beta$ of blocking pairs; (3) Max-SMTI: Given a stable marriage instance with preferences containing ties, find a maximum-size stable matching. The first two problems are known to be NP-hard to approximate to any constant factor and W[1]-hard with respect to $\beta$, making the existence of an EPTAS or FPT-algorithms unlikely. We show that they are W[1]-hard with respect to $\beta$ to approximate to any function of $\beta$. This means that unless FPT=W[1], there is no FPT-approximation scheme for the parameter $\beta$. The last problem (Max-SMTI) is known to be NP-hard to approximate to factor-29/33 and W[1]-hard with respect to the number of ties. We complement this and present an FPT-approximation scheme for the parameter "number of agents with ties".

cs.GT↗
arXiv2025

Parameterized Complexity of Hedonic Games with Enemy-Oriented Preferences

Hedonic games model settings in which a set of agents have to be partitioned into groups which we call coalitions. In the enemy aversion model, each agent has friends and enemies, and an agent prefers to be in a coalition with as few enemies as possible and, subject to that, as many friends as possible. A partition should be stable, i.e., no subset of agents prefer to be together rather than being in their assigned coalition under the partition. We look at two stability concepts: core stability and strict core stability. This yields several algorithmic problems: determining whether a (strictly) core stable partition exists, finding such a partition, and checking whether a given partition is (strictly) core stable. Several of these problems have been shown to be NP-complete, or even beyond NP. This motivates the study of parameterized complexity. We conduct a thorough computational study using several parameters: treewidth, number of friends, number of enemies, partition size, and coalition size. We give polynomial algorithms for restricted graph classes as well as FPT algorithms with respect to the number of friends an agent may have and the treewidth of the graph representing the friendship or enemy relations. We show W[1]-hardness or para-NP-hardness with respect to the other parameters. We conclude this paper with results in the setting in which agents can have neutral relations with each other, including hardness-results for very restricted cases.

cs.GT↗
arXiv2024

Parameterized Algorithms for Optimal Refugee Resettlement

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.

cs.GT↗
arXiv2023

Efficient Algorithms for Monroe and CC Rules in Multi-Winner Elections with (Nearly) Structured Preferences

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].

cs.MA↗
arXiv2023

Coalition Formation with Bounded Coalition Size

In many situations when people are assigned to coalitions, the utility of each person depends on the friends in her coalition. Additionally, in many situations, the size of each coalition should be bounded. This paper studies such coalition formation scenarios in both weighted and unweighted settings. Since finding a partition that maximizes the utilitarian social welfare is computationally hard, we provide a polynomial-time approximation algorithm. We also investigate the existence and the complexity of finding stable partitions. Namely, we show that the Contractual Strict Core (CSC) is never empty, but the Strict Core (SC) of some games is empty. Finding partitions that are in the CSC is computationally easy, but even deciding whether an SC of a given game exists is NP-hard. The analysis of the core is more involved. In the unweighted setting, we show that when the coalition size is bounded by 3 the core is never empty, and we present a polynomial time algorithm for finding a member of the core. However, for the weighted setting, the core may be empty, and we prove that deciding whether there exists a core is NP-hard.

cs.GT↗
arXiv2023

Hedonic Games With Friends, Enemies, and Neutrals: Resolving Open Questions and Fine-Grained Complexity

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.

cs.GT↗
arXiv2022

Game Implementation: What Are the Obstructions?

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.

cs.GT↗
arXiv2022

Multidimensional Manhattan Preferences

A preference profile (i.e., a collection of linear preference orders of the voters over a set of alternatives) with $m$ alternatives and $n$ voters is $d$-Manhattan (resp. $d$-Euclidean) if both the alternatives and the voters can be placed into a $d$-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. We study how $d$-Manhattan preference profiles depend on the values $m$ and $n$. First, we provide explicit constructions to show that each preference profile with $m$ alternatives and $n$ voters is $d$-Manhattan whenever $d \ge \min(n, m - 1)$. We further extend this positive result for other $p$-norms with $p \in R_{\ge 1} \cup \{\infty\}$. Second, for $d = 2$, we develop forbidden substructures-preference patterns among small sets of voters that constrain any 2-Manhattan embedding -- and use them to show that the smallest non-2-Manhattan preference profile has either 3 voters and 6 alternatives, or 4 voters and 5 alternatives, or 5 voters and 4 alternatives. This is more complex than the case with $d$-Euclidean preferences (see (Bogomolnaia and Laslier, 2007) and (Bulteau and Chen, 2022)). We also show that $d$-Manhattan preferences imply $(2d-1)$-dimensional single-peakedness, while 2-Manhattanness is incomparable with single-peakedness and single-crossingness.

cs.MA↗
arXiv2021

Profile-based optimal stable matchings in the Roommates problem

The stable roommates problem can admit multiple different stable matchings. We have different criteria for deciding which one is optimal, but computing those is often NP-hard. We show that the problem of finding generous or rank-maximal stable matchings in an instance of the roommates problem with incomplete lists is NP-hard even when the preference lists are at most length 3. We show that just maximising the number of first choices or minimising the number of last choices is NP-hard with the short preference lists. We show that the number of $R^{th}$ choices, where $R$ is the minimum-regret of a given instance of SRI, is 2-approximable among all the stable matchings. Additionally, we show that the problem of finding a stable matching that maximises the number of first choices does not admit a constant time approximation algorithm and is W[1]-hard with respect to the number of first choices. We implement integer programming and constraint programming formulations for the optimality criteria of SRI. We find that constraint programming outperforms integer programming and an earlier answer set programming approach by Erdam et. al. (2020) for most optimality criteria. Integer programming outperforms constraint programming and answer set programming on the almost stable roommates problem.

cs.DS↗