Parameterized Complexity of Candidate Control in Elections and Related Digraph Problems

Betzler, Nadja; Uhlmann, Johannes

doi:10.1007/978-3-540-85097-7_5

Cited by 26 publications

(45 citation statements)

References 9 publications

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“…Table 1 summarizes our results. We extend the previous results for MID [2] by showing that MID is W[2]-hard even when parameterized by s a whereas it turns fixed-parameter tractable for the combined parameter (k, s v ). Note that this also implies fixed-parameter tractability with respect to the combined parameter (k, s a ) since s a is a weaker parameter than s v in the sense that s v ≤ s a .…”

Section: Introductionsupporting

confidence: 77%

“…MID directly emerges from a problem concerning electoral control with respect to so-called "Llull voting" [2,9], one of the well-known voting systems based on pairwise comparision of candidates. Concerning MDD, in undirected social networks the degree of a vertex relates to its popularity or influence [18, pages 178-180].…”

Section: Introductionmentioning

confidence: 99%

“…Although both MID and MDD are simple and natural graph problems, we only know one previous publication concerning these problems. MID has been shown W [2]-complete for parameter solution size k even when restricted to tournament graphs and it is polynomial-time solvable on directed acyclic graphs [2].…”

Section: Introductionmentioning

confidence: 99%

“…In this sense, W [1]-hardness is the parameterized complexity analog of NP-hardness. The class W [2] means the next higher degree of parameterized intractability.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, all connected components induce trees. 2 Now, we take a look at an arbitrary solution set M of our MDD-instance. Since the final degree of w c is i, M must contain deg G (w c ) − i neighbors of w c .…”

mentioning

confidence: 99%

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On Making a Distinguished Vertex Minimum Degree by Vertex Deletion

Betzler

Bredereck

Niedermeier

et al. 2011

SOFSEM 2011: Theory and Practice of Computer Science

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Abstract. For directed and undirected graphs, we study the problem to make a distinguished vertex the unique minimum-(in)degree vertex through deletion of a minimum number of vertices. The corresponding NP-hard optimization problems are motivated by applications concerning control in elections and social network analysis. Continuing previous work for the directed case, we show that the problem is W[2]-hard when parameterized by the graph's feedback arc set number, whereas it becomes fixed-parameter tractable when combining the parameters "feedback vertex set number" and "number of vertices to delete". For the so far unstudied undirected case, we show that the problem is NP-hard and W[1]-hard when parameterized by the "number of vertices to delete". On the positive side, we show fixed-parameter tractability for several parameterizations measuring tree-likeness, including a vertex-linear problem kernel with respect to the parameter "feedback edge set number". On the contrary, we show a non-existence result concerning polynomial-size problem kernels for the combined parameter "vertex cover number and number of vertices to delete", implying corresponding nonexistence results when replacing vertex cover number by treewidth or feedback vertex set number.

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Section: Introductionsupporting

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In this sense, W [1]-hardness is the parameterized complexity analog of NP-hardness. The class W [2] means the next higher degree of parameterized intractability.…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

On Making a Distinguished Vertex Minimum Degree by Vertex Deletion

Betzler

Bredereck

Niedermeier

et al. 2011

SOFSEM 2011: Theory and Practice of Computer Science

Self Cite

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Sincere‐Strategy Preference‐Based Approval Voting Fully Resists Constructive Control and Broadly Resists Destructive Control

Erdélyi

Nowak

Rothe

2009

Mathematical Logic Qtrly

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We study sincere-strategy preference-based approval voting (SP-AV), a system proposed by Brams and Sanver [1] and here adjusted so as to coerce admissibility of the votes (rather than excluding inadmissible votes a priori), with respect to procedural control. In such control scenarios, an external agent seeks to change the outcome of an election via actions such as adding/deleting/partitioning either candidates or voters. SP-AV combines the voters' preference rankings with their approvals of candidates, where in elections with at least two candidates the voters' approval strategies are adjusted-if needed-to approve of their most-preferred candidate and to disapprove of their least-preferred candidate. This rule coerces admissibility of the votes even in the presence of control actions, and hybridizes, in effect, approval with pluralitiy voting.We prove that this system is computationally resistant (i.e., the corresponding control problems are NP-hard) to 19 out of 22 types of constructive and destructive control. Thus, SP-AV has more resistances to control than is currently known for any other natural voting system with a polynomial-time winner problem. In particular, SP-AV is (after Copeland voting, see Faliszewski et al. [2,3]) the second natural voting system with an easy winner-determination procedure that is known to have full resistance to constructive control, and unlike Copeland voting it in addition displays broad resistance to destructive control.

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

Kellerhals

Korenwein

Zschoche

et al. 2017

Lecture Notes in Computer Science

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Voter control problems model situations in which an external agent tries to affect 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 (constructive control) or lose (destructive control) the election. We study the constructive and destructive voter control problems when adding and deleting voters have a 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. ∀w : w ∈ κ(v) ⇔ v ∈ κ(w)), and if each voter has at most two voters associated with him, then destructive control is polynomialtime solvable while the constructive variant remains NP-hard. Even if the bundles are disjoint (i.e. ∀w : w ∈ κ(v) ⇔ 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. ⋆ PZ was supported by the Stiftung Begabtenförderung berufliche Bildung (SBB).

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Parameterized Complexity of Candidate Control in Elections and Related Digraph Problems

Cited by 26 publications

References 9 publications

On Making a Distinguished Vertex Minimum Degree by Vertex Deletion

On Making a Distinguished Vertex Minimum Degree by Vertex Deletion

Sincere‐Strategy Preference‐Based Approval Voting Fully Resists Constructive Control and Broadly Resists Destructive Control

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

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