Facility location problems: A parameterized view

Fellows, Michael R.; Fernau, Henning

doi:10.1016/j.dam.2011.03.021

Cited by 21 publications

(4 citation statements)

References 22 publications

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“…An essential difference between this problem and the winner determination problem under the Chamberlin-Courant rule are the setup costs and the distance metric. The parameterized complexity of the Facility Location Problem was investigated by Fellows and Fernau [21]. The papers of Procaccia et al [48] and of Betzler et al [9] contain a brief discussion of the connection between the Facility Location Problem and the winner determination problem under the Chamberlin-Courant rule.…”

Section: Related Workmentioning

confidence: 99%

Achieving fully proportional representation: Approximability results

Skowron

Faliszewski

Slinko

2015

Artificial Intelligence

136

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We study the complexity of (approximate) winner determination under the Monroe and Chamberlin-Courant multiwinner voting rules, which determine the set of representatives by optimizing the total satisfaction or dissatisfaction of the voters with their representatives. The total (dis)satisfaction is calculated either as the sum of individual (dis)satisfactions in the utilitarian case or as the (dis)satisfaction of the worst off voter in the egalitarian case. We provide good approximation algorithms for the satisfaction-based utilitarian versions of the Monroe and Chamberlin-Courant rules, and inapproximability results for the dissatisfaction-based utilitarian versions of these rules and also for all egalitarian cases. Our algorithms are applicable and particularly appealing when voters submit truncated ballots. We provide experimental evaluation of the algorithms both on real-life preference-aggregation data and on synthetic preference data. These experiments show that our simple and fast algorithms can, in many cases, find near-perfect solutions.

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Section: Related Workmentioning

confidence: 99%

Achieving fully proportional representation: Approximability results

Skowron

Faliszewski

Slinko

2015

Artificial Intelligence

136

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“…The facility location problem (FLP), in its various forms including covering and median problems, is a well-known NP-hard combinatorial optimization problem that has attracted a lot of attention in literature [18][19][20]. In fact, many different models have been developed to deal with different real world applications with the choice of objective functions and constraints.…”

Section: A Linear Model For Facility Location Problemsmentioning

confidence: 99%

Modeling multiple unmanned aerial vehicles placement problem in ad hoc network via quadratic unconstrained binary optimization

Wang

Huang

et al. 2013

2013 International Conference on Unmanned Aircraft Systems (ICUAS)

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This paper addresses an important issue in ad hoc network connectivity using unmanned aerial vehicles (UAVs) as relay nodes and formulates the problem of locating UAVs in the network as a facility location problem. We propose a method to reformulate the facility location problem using quadratic unconstrained binary optimization (QUBO) and solve the QUBO model with off-shelf software. The analysis of the solutions produced by QUBO along with comparisons made with the linear model highlights both the attractiveness and robustness of the proposed approach.Haibo Wang is with Texas

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“…The only difference is the cost function: In addition to a term that resembles the misrepresentation for every voter (customer), every facility location comes with a certain cost that is required to install the facility. Similar to our study, Fellows and Fernau (2011) studied the parameter number k of winners/selected facilities locations and the total cost. For the parameter k, W[2]-hardness for CC-Multiwinner follows from the reduction given for the facility location problem.…”

Section: Relations To Facility Locationmentioning

confidence: 99%

“…Fellows and Fernau (2011) investigated the parameterized complexity of a variant of this problem that is closely related to CC-Multiwinner. Basically, the facility locations can be considered as the set of candidates, the customers as the multiset of voters and the goal is to find a set of facility locations to serve these customers.…”

Section: Relations To Facility Locationmentioning

confidence: 99%

On the Computation of Fully Proportional Representation

Betzler

Slinko

Uhlmann

2013

jair

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We investigate two systems of fully proportional representation suggested by Chamberlin & Courant and Monroe. Both systems assign a representative to each voter so that the "sum of misrepresentations" is minimized. The winner determination problem for both systems is known to be NP-hard, hence this work aims at investigating whether there are variants of the proposed rules and/or specific electorates for which these problems can be solved efficiently. As a variation of these rules, instead of minimizing the sum of misrepresentations, we considered minimizing the maximal misrepresentation introducing effectively two new rules. In the general case these "minimax" versions of classical rules appeared to be still NP-hard.We investigated the parameterized complexity of winner determination of the two classical and two new rules with respect to several parameters. Here we have a mixture of positive and negative results: e.g., we proved fixed-parameter tractability for the parameter the number of candidates but fixed-parameter intractability for the number of winners.For single-peaked electorates our results are overwhelmingly positive: we provide polynomial-time algorithms for most of the considered problems. The only rule that remains NP-hard for single-peaked electorates is the classical Monroe rule.

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Facility location problems: A parameterized view

Cited by 21 publications

References 22 publications

Achieving fully proportional representation: Approximability results

Achieving fully proportional representation: Approximability results

Modeling multiple unmanned aerial vehicles placement problem in ad hoc network via quadratic unconstrained binary optimization

On the Computation of Fully Proportional Representation

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