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Jiehua Chen

Publications and source records attributed to Jiehua Chen.

At least 19 recordsLinked to original sources
arXiv2026

Control and Bribery in Stable Marriage and Stable Roommates: A Complete Complexity Landscape

We study control and bribery problems for stable matchings: A central authority (the controller, resp. briber) may add agents, delete agents, delete acceptable pairs, swap two adjacent agents in some agent's preference list, or arbitrarily reorder some agent's preference list, in an instance of Stable Marriage or Stable Roommates. We extend previous work on control and bribery in stable matchings by Boehmer et al. [8]. We consider goals capturing individual and pair inclusion, stability, and uniqueness requirements: Matching a designated agent (MA), matching a designated pair (MP), realizing a stable matching consistent with a given matching (MS), making a given matching the unique stable matching (USM), or guaranteeing that a stable (resp. perfect and stable) matching exists ($\exists$SM/$\exists$PSM). We provide a unified complexity map for all non-trivial action-goal combinations in both settings, consolidating known results and extending the study to the roommates model, where stable matchings need not exist.

cs.GT↗
arXiv2026

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↗
arXiv2026

Multi-Winner Voting Games in TU and NTU: When is the Core Always Non-Empty?

Multi-winner approval voting selects a size-$k$ committee that aggregates voters' approval preferences over a set of alternatives. A central question is coalitional stability: No coalition should be able to pick a committee -- of size at most its proportional share -- under which every coalition member has strictly more approved alternatives. This notion, introduced by Aziz et al. (2017) as core-stable committees, is naturally interpreted as a core notion with non-transferable utility. We introduce multi-winner voting games, a cooperative-game framework that unifies prior work and supports a systematic study of two utility-transfer models across different voting rules. Players are voters. Each coalition has a proportional seat cap and may only propose admissible committees up to that size. Fixing a multi-winner rule, each admissible committee induces a utility vector for the members of the coalition. In the transferable utility (TU) model, a coalition may redistribute the total utility of an admissible committee among its members. In the non-transferable utility (NTU) model, a coalition may only use utility vectors that are realized directly by some admissible committee. The core consists of utility vectors feasible for the grand coalition that are not blocked by any coalition. A coalition is blocking if it can propose an admissible committee that makes all its members strictly better off, directly in NTU and after redistribution in TU. When instantiated with the standard PAV/approval utility, the NTU-core is equivalent to the core-stable committee concept studied in prior work. To our knowledge, the TU-core for multi-winner voting has not been previously studied. We analyze core existence and computation for four prominent rules: Approval Voting (AV), Satisfaction Approval Voting (SAV), Chamberlin--Courant (CC), Proportional Approval Voting (PAV).

cs.GT↗
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

MP-Aggregation MP(R,2-WO) is Polynomial-Time Solvable When the Output Should Be Dichotomous Weak Preference Order

We consider the median procedure (Barthelemy and Monjardet, 1981) that aggregates a sequence n of binary relations from some input class into a single binary relation from some (possibly different) output class, minimizing the number of disagreed order pairs. We show that if the output class should be a dichotomous weak order (2-WO), then the problem is polynomial-time solvable.

cs.CC↗
arXiv2025

How Hard is it to Explain Preferences Using Few Boolean Attributes?

We study the computational complexity of explaining preference data through Boolean attribute models (BAMs), motivated by extensive research involving attribute models and their promise in understanding preference structure and enabling more efficient decision-making processes. In a BAM, each alternative has a subset of Boolean attributes, each voter cares about a subset of attributes, and voters prefer alternatives with more of their desired attributes. In the BAM problem, we are given a preference profile and a number k, and want to know whether there is a Boolean k-attribute model explaining the profile. We establish a complexity dichotomy for the number of attributes k: BAM is linear-time solvable for $k \le 2$ but NP-complete for $k \ge 3$. The problem remains hard even when preference orders have length two. On the positive side, BAM becomes fixed-parameter tractable when parameterized by the number of alternatives m. For the special case of two voters, we provide a linear-time algorithm. We also analyze variants where partial information is given: When voter preferences over attributes are known (BAM WITH CARES) or when alternative attributes are specified (BAM WITH HAS), we show that for most parameters BAM WITH CARES is more difficult whereas BAM WITH HAS is more tractable except for being NP-hard even for one voter.

cs.MA↗
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 $β$ of blocking pairs; (2) Min-BP-SRI: Given a stable roommates instance, find a matching that minimizes the number $β$ 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 $β$, making the existence of an EPTAS or FPT-algorithms unlikely. We show that they are W[1]-hard with respect to $β$ to approximate to any function of $β$. This means that unless FPT=W[1], there is no FPT-approximation scheme for the parameter $β$. 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

Multi-Organizational Scheduling: Individual Rationality, Optimality, and Complexity

We investigate multi-organizational scheduling problems, building upon the framework introduced by Pascual et al.[2009]. In this setting, multiple organizations each own a set of identical machines and sequential jobs with distinct processing times. The challenge lies in optimally assigning jobs across organizations' machines to minimize the overall makespan while ensuring no organization's performance deteriorates. To formalize this fairness constraint, we introduce individual rationality, a game-theoretic concept that guarantees each organization benefits from participation. Our analysis reveals that finding an individually rational schedule with minimum makespan is $Θ_2^{\text{P}}$-hard, placing it in a complexity class strictly harder than both NP and coNP. We further extend the model by considering an alternative objective: minimizing the sum of job completion times, both within individual organizations and across the entire system. The corresponding decision variant proves to be NP-complete. Through comprehensive parameterized complexity analysis of both problems, we provide new insights into these computationally challenging multi-organizational scheduling scenarios.

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↗
arXiv2024

Optimal Capacity Modification for Many-To-One Matching Problems

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.

cs.GT↗
arXiv2024

Cutsets and EF1 Fair Division of Graphs

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.

cs.GT↗
arXiv2023

Algorithms and Complexity for Congested Assignments

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.

cs.GT↗
arXiv2023

A Note on Clustering Aggregation for Binary Clusterings

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 Ð 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.

cs.CC↗
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

Optimal Seat Arrangement: What Are the Hard and Easy Cases?

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.

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↗