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Item type:Publication, Access status: with files , Voting and bribing in single-exponential time(Association for Computing Machinery (ACM), 2020-06-20); ; We introduce a general problem about bribery in voting systems. In theR-Multi-Briberyproblem,the goal is to bribe a set of voters at minimum cost such that a desired candidate wins the perturbedelection under the voting ruleR. Voters assign prices for withdrawing their vote, for swapping thepositions of two consecutive candidates in their preference order, and for perturbing their approval countto favour candidates.As our main result, we show thatR-Multi-Briberyis fixed-parameter tractable parameterized bythe number of candidates for many natural voting rulesR, including Kemeny rule, all scoring protocols,maximin rule, Bucklin rule, fallback rule, SP-AV, and any C1 rule. In particular, our result resolves theparameterized complexity ofR-Swap Briberyfor all those voting rules, thereby solving a long-standingopen problem and “Challenge #2” of the “Nine Research Challenges in Computational Social Choice”by Bredereck et al.Further, our algorithm runs in single-exponential time for arbitrary cost; it thus improves the earlierdouble-exponential time algorithm by Dorn and Schlotter that is restricted to the uniform-cost case forall scoring protocols, the maximin rule, and Bucklin rule.Publicationtype: Journal Article195 16 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Multitype integer monoid optimization and applications(2019-09-16); ; ; ; Configuration integer programs (IP) have been key in the design of algorithms for NP-hard high-multiplicity problems since the pioneering work of Gilmore and Gomory [Oper. Res., 1961]. Configuration IPs have one variable for each possible configuration, which describes a placement of items into a location, and whose value corresponds to the number of locations with that placement. In high multiplicity problems items come in types, and are represented succinctly by a vector of multiplicities; solving the configuration IP then amounts to deciding whether the input vector of multiplicities of items of each type can be decomposed into a given number of configurations. We make this typically implicit notion explicit by observing that the set of all input vectors which can be decomposed into configurations forms a monoid of configurations, and the problem corresponding to solving the configuration IP is the Monoid Decomposition problem. Then, motivated by applications, we enrich this problem in two ways. First, in certain problems each configuration additionally has an objective value, and the problem becomes an optimization problem of finding a “best” decomposition under the given objective. Second, there are often different types of configurations derived from different types of locations. The resulting problem is then to optimize over decompositions of the input multiplicity vector into configurations of several types, and we call it Multitype Integer Monoid Optimization, or simply MIMO. We develop fast exact (exponential-time) algorithms for various MIMO with few or many location types and with various objectives. Our algorithms build on a novel proximity theorem which connects the solutions of a certain configuration IP to those of its continuous relaxation. We then cast several fundamental scheduling and bin packing problems as MIMOs, and thereby obtain new or substantially faster algorithms for them. We complement our positive algorithmic results by hardness results which show that, under common complexity assumptions, the algorithms cannot be extended into more relaxed regimes.Publicationtype: Preprint217 86