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50
Towards a dichotomy of finding possible winners in elections based on scoring rules
 In Proc. 34th MFCS, volume 5734 of LNCS
, 2009
"... Abstract. To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings, the voters may often only provide partial orders. ..."
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Abstract. To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings, the voters may often only provide partial orders. This directly leads to the POSSIBLE WINNER problem that asks, given a set of partial votes, if a distinguished candidate can still become a winner. In this work, we consider the computational complexity of POSSIBLE WINNER for the broad class of voting protocols defined by scoring rules. A scoring rule provides a score value for every position which a candidate can have in a linear order. Prominent examples include plurality, kapproval, and Borda. Generalizing previous NPhardness results for some special cases and providing new manyone reductions, we settle the computational complexity for all but one scoring rule. More precisely, for an unbounded number of candidates and unweighted voters, we show that POSSIBLE WINNER is NPcomplete for all pure scoring rules except plurality, veto, and the scoring rule defined by the scoring vector (2,1,..., 1, 0), while it is solvable in polynomial time for plurality and veto. 1
E.Elkind. Campaign management under approvaldriven voting rules
 In Proc.AAAI11,pages 726–731, Aug.2011
"... Approvallike voting rules, such as sincerestrategy preferencebased approval voting (SPAV), the Bucklin rule, and the Fallback rule have many desirable properties: they are easy to understand, and encourage the candidates to choose electoral platforms that have a broad appeal. In this paper, we ..."
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Cited by 12 (7 self)
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Approvallike voting rules, such as sincerestrategy preferencebased approval voting (SPAV), the Bucklin rule, and the Fallback rule have many desirable properties: they are easy to understand, and encourage the candidates to choose electoral platforms that have a broad appeal. In this paper, we investigate both classic and parameterized computational complexity of electoral campaign management under such rules. We focus on two methods that can be used to promote a given candidate: asking voters to move this candidate upwards in their preference order or asking them to change the number of candidates they approve of. We show that finding an optimal campaign management strategy of the first type is easy for both Bucklin and Fallback. In contrast, the second method is computationally hard to implement, even if natural parameters of the problem are small. However, we identify a broad special class of campaign management scenarios that admit a fixedparameter tractable algorithm.
Parameterized Complexity of Eulerian Deletion Problems
 ALGORITHMICA
"... We study a family of problems where the goal is to make a graph Eulerian, i.e., connected and with all the vertices having even degrees, by a minimum number of deletions. We completely classify the parameterized complexity of various versions: undirected or directed graphs, vertex or edge deletions ..."
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We study a family of problems where the goal is to make a graph Eulerian, i.e., connected and with all the vertices having even degrees, by a minimum number of deletions. We completely classify the parameterized complexity of various versions: undirected or directed graphs, vertex or edge deletions, with or without the requirement of connectivity, etc. The collection of results shows an interesting contrast: while the nodedeletion variants remain intractable, i.e., W[1]hard for all the studied cases, edgedeletion problems are either fixedparameter tractable or polynomialtime solvable. Of particular interest is a randomized FPT algorithm for making an undirected graph Eulerian by deleting the minimum number of edges, based on a novel application of the colour coding technique. For versions that remain NPcomplete but fixedparameter tractable we consider also possibilities of polynomial kernelization; unfortunately, we prove that this is not possible unless NP ⊆ coNP/poly.
S.: Editing graphs to satisfy degree constraints: A parameterized approach
 J. Comput. Syst. Sci
, 2012
"... Abstract We study a wide class of graph editing problems that ask whether a given graph can be modified to satisfy certain degree constraints, using a limited number of vertex deletions, edge deletions, or edge additions. The problems generalize several wellstudied problems such as the General Fac ..."
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Abstract We study a wide class of graph editing problems that ask whether a given graph can be modified to satisfy certain degree constraints, using a limited number of vertex deletions, edge deletions, or edge additions. The problems generalize several wellstudied problems such as the General Factor Problem and the Regular Subgraph Problem. We classify the parameterized complexity of the considered problems taking upper bounds on the number of editing steps and the maximum degree of the resulting graph as parameters.
Constant thresholds can make target set selection tractable
 In MedAlg
"... Abstract. Target Set Selection, which is a prominent NPhard problem occurring in social network analysis and distributed computing, is notoriously hard both in terms of achieving useful approximation as well as fixedparameter algorithms. The task is to select a minimum number of vertices into a “t ..."
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Cited by 9 (3 self)
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Abstract. Target Set Selection, which is a prominent NPhard problem occurring in social network analysis and distributed computing, is notoriously hard both in terms of achieving useful approximation as well as fixedparameter algorithms. The task is to select a minimum number of vertices into a “target set ” such that all other vertices will become active in course of a dynamic process (which may go through several activation rounds). A vertex, which is equipped with a threshold value t, becomes active once at least t of its neighbors are active; initially, only the target set vertices are active. We contribute further insights into islands of tractability for Target Set Selection by spotting new parameterizations characterizing some sparse graphs as well as some “cliquish ” graphs and developing corresponding fixedparameter tractability and (parameterized) hardness results. In particular, we demonstrate that upperbounding the thresholds by a constant may significantly alleviate the search for efficiently solvable, but still meaningful special cases of Target Set Selection. 1
ENUMERATING HOMOMORPHISMS
, 2009
"... The homomorphism problem for relational structures is an abstract way of formulating constraint satisfaction problems (CSP) and various problems in database theory. The decision version of the homomorphism problem received a lot of attention in literature; in particular, the way the graphtheoretic ..."
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Cited by 8 (1 self)
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The homomorphism problem for relational structures is an abstract way of formulating constraint satisfaction problems (CSP) and various problems in database theory. The decision version of the homomorphism problem received a lot of attention in literature; in particular, the way the graphtheoretical structure of the variables and constraints influences the complexity of the problem is intensively studied. Here we study the problem of enumerating all the solutions with polynomial delay from a similar point of view. It turns out that the enumeration problem behaves very differently from the decision version. We give evidence that it is unlikely that a characterization result similar to the decision version can be obtained. Nevertheless, we show nontrivial cases where enumeration can be done with polynomial delay.
Completely inapproximable monotone and antimonotone parameterized problems
"... We prove that weighted monotone/antimonotone circuit satisfiability has no fixedparameter tractable approximation algorithm with any approximation ratio function ρ, unless FPT 6 = W [1]. In particular, not having such an fptapproximation algorithm implies that these problems have no polynomialti ..."
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We prove that weighted monotone/antimonotone circuit satisfiability has no fixedparameter tractable approximation algorithm with any approximation ratio function ρ, unless FPT 6 = W [1]. In particular, not having such an fptapproximation algorithm implies that these problems have no polynomialtime approximation algorithms with ratio ρ(OPT) for any nontrivial function ρ.
Parameterized Complexity of Stabbing Rectangles and Squares in the Plane
, 2009
"... The NPcomplete geometric covering problem Rectangle Stabbing is defined as follows: Given a set of horizontal and vertical lines in the plane, a set of rectangles in the plane, and a positive integer k, select at most k of the lines such that every rectangle is intersected by at least one of the ..."
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The NPcomplete geometric covering problem Rectangle Stabbing is defined as follows: Given a set of horizontal and vertical lines in the plane, a set of rectangles in the plane, and a positive integer k, select at most k of the lines such that every rectangle is intersected by at least one of the selected lines. While it is known that the problem can be approximated in polynomial time with a factor of two, its parameterized complexity with respect to the parameter k was open so far—only its generalization to three or more dimensions was known to be W[1]hard. Giving two fixedparameter reductions, one from the W[1]complete problem Multicolored Clique and one to the W[1]complete problem Short Turing Machine Acceptance, we prove that Rectangle Stabbing is W[1]complete with respect to the parameter k, which in particular means that there is no hope for fixedparameter tractability with respect to the parameter k. Our reductions show also the W[1]completeness of the more general problem Set Cover on instances that “almost have the consecutiveones property”, that is, on instances whose matrix representation has at most two blocks of 1s per row. For the special case of Rectangle Stabbing where all rectangles are squares of the same size we can also show W[1]hardness, while the parameterized complexity of the special case where the input consists of rectangles that do not overlap is open. By giving an algorithm running in (4k + 1) k · n O(1) time, we show that Rectangle Stabbing is fixedparameter tractable in the still NPhard case where both these restrictions apply.
The parameterized complexity of abduction
 Proceedings of the TwentySixth AAAI Conference on Artificial Intelligence
"... Abduction belongs to the most fundamental reasoning methods. It is a method for reverse inference, this means one is interested in explaining observed behavior by finding appropriate causes. We study logicbased abduction, where knowledge is represented by propositional formulas. The computational ..."
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Abduction belongs to the most fundamental reasoning methods. It is a method for reverse inference, this means one is interested in explaining observed behavior by finding appropriate causes. We study logicbased abduction, where knowledge is represented by propositional formulas. The computational complexity of this problem is highly intractable in many interesting settings. In this work we therefore present an extensive parameterized complexity analysis of abduction within various fragments of propositional logic together with (combinations of) natural parameters.