arXiv subjects

Jiehua Chen

Publications and source records attributed to Jiehua Chen.

50 records · Page 3Linked to original sources

arXiv2018

How hard is it to satisfy (almost) all roommates?

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 γ, 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 β of blocking pairs. Our main result is that Egal Stable Roommates parameterized by γ is fixed-parameter tractable, while Min-Block-Pair Stable Roommates parameterized by β is W[1]-hard, even if the length of each preference list is at most five.

cs.CC↗

arXiv2018

On the Number of Single-Peaked Narcissistic or Single-Crossing Narcissistic Preference Profiles

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 $2^{\binom{n-1}{2}}$.

math.CO↗

arXiv2018

Stable Marriage with Multi-Modal Preferences

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.

cs.MA↗

arXiv2017

Elections with Few Voters: Candidate Control Can Be Easy

We study the computational complexity of candidate control in elections with few voters, that is, we consider the parameterized complexity of candidate control in elections with respect to the number of voters as a parameter. We consider both the standard scenario of adding and deleting candidates, where one asks whether a given candidate can become a winner (or, in the destructive case, can be precluded from winning) by adding or deleting few candidates, as well as a combinatorial scenario where adding/deleting a candidate automatically means adding or deleting a whole group of candidates. Considering several fundamental voting rules, our results show that the parameterized complexity of candidate control, with the number of voters as the parameter, is much more varied than in the setting with many voters.

cs.AI↗

arXiv2017

On the Computational Complexity of Variants of Combinatorial Voter Control in Elections

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~$κ(v) $ of voters that are associated with~$v$. While the bundle~$κ(v)$ 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 κ(v) \Leftrightarrow v \in κ(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 κ(v) \Leftrightarrow κ(v) = κ(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.

cs.MA↗

arXiv2016

Prices Matter for the Parameterized Complexity of Shift Bribery

In the Shift Bribery problem, we are given an election (based on preference orders), a preferred candidate $p$, and a budget. The goal is to ensure that $p$ wins by shifting $p$ higher in some voters' preference orders. However, each such shift request comes at a price (depending on the voter and on the extent of the shift) and we must not exceed the given budget. We study the parameterized computational complexity of Shift Bribery with respect to a number of parameters (pertaining to the nature of the solution sought and the size of the election) and several classes of price functions. When we parameterize Shift Bribery by the number of affected voters, then for each of our voting rules (Borda, Maximin, Copeland) the problem is W[2]-hard. If, instead, we parameterize by the number of positions by which $p$ is shifted in total,then the problem is fixed-parameter tractable for Borda and Maximin,and is W[1]-hard for Copeland. If we parameterize by the budget, then the results depend on the price function class. We also show that Shift Bribery tends to be tractable when parameterized by the number of voters, but that the results for the number of candidates are more enigmatic.

cs.MA↗

arXiv2016

Teams in Online Scheduling Polls: Game-Theoretic Aspects

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.

cs.GT↗

arXiv2016

Partitioning Perfect Graphs into Stars

The partition of graphs into "nice" subgraphs is a central algorithmic problem with strong ties to matching theory. We study the partitioning of undirected graphs into same-size stars, a problem known to be NP-complete even for the case of stars on three vertices. We perform a thorough computational complexity study of the problem on subclasses of perfect graphs and identify several polynomial-time solvable cases, for example, on interval graphs and bipartite permutation graphs, and also NP-complete cases, for example, on grid graphs and chordal graphs.

cs.DM↗

arXiv2015

Are there any nicely structured preference~profiles~nearby?

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.

cs.GT↗

arXiv2015

Parliamentary Voting Procedures: Agenda Control, Manipulation, and Uncertainty

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.

cs.GT↗

arXiv2015

The one-dimensional Euclidean domain: Finitely many obstructions are not enough

We show that one-dimensional Euclidean preference profiles can not be characterized in terms of finitely many forbidden substructures. This result is in strong contrast to the case of single-peaked and single-crossing preference profiles, for which such finite characterizations have been derived in the literature.

cs.GT↗

arXiv2015

Network-Based Vertex Dissolution

We introduce a graph-theoretic vertex dissolution model that applies to a number of redistribution scenarios such as gerrymandering in political districting or work balancing in an online situation. The central aspect of our model is the deletion of certain vertices and the redistribution of their load to neighboring vertices in a completely balanced way. We investigate how the underlying graph structure, the knowledge of which vertices should be deleted, and the relation between old and new vertex loads influence the computational complexity of the underlying graph problems. Our results establish a clear borderline between tractable and intractable cases.

cs.DM↗

arXiv2014

Parameterized Algorithmics for Computational Social Choice: Nine Research Challenges

Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problem-specific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context.

cs.MA↗

arXiv2014

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 $κ(v)$ 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.

cs.MA↗