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Parameterized (in)approximability of subset problems

Édouard Bonnet, Vangelis Th. Paschos
2014 Operations Research Letters  
We discuss approximability and inapproximability in FPT-time for a large class of subset problems where a feasible solution S is a subset of the input data.  ...  Kratsch, Safe approximation and its relation to kernelization, IPEC 2011) and show strong parameterized inapproximability results for many of the subset problems handled.  ...  The very useful and pertinent comments and suggestions of an anonymous referee are gratefully acknowledged.  ... 
doi:10.1016/j.orl.2014.03.005 fatcat:dujrjhmp25hrhdh4dtldzpzzgm

Parameterized (in)approximability of subset problems [article]

Edouard Bonnet, Vangelis Th. Paschos
2013 arXiv   pre-print
The class handled encompasses many well-known graph, set, or satisfiability problems such as Dominating Set, Vertex Cover, Set Cover, Independent Set, Feedback Vertex Set, etc.  ...  We discuss approximability and inapproximability in FPT-time for a large class of subset problems where a feasible solution S is a subset of the input data and the value of S is |S|.  ...  The second claim is easy to be proved: m − k for D-min set cover is the standard parameter for min set cover and given a solution S 0 for the former problem, one can take S \ S 0 as solution for the latter  ... 
arXiv:1310.5576v1 fatcat:6kpsxqdu7ndp5cucqmzude4gei

Min-max formulation of the balance number in multiobjective global optimization

M. Ehrgott, E.A. Galperin
2002 Computers and Mathematics with Applications  
., [l-3], do not cover the entire Pareto set.  ...  The notion of the balance number introduced by Galperin through a certain set contraction procedure for nonscalarized multiobjective global optimization is represented via a min-max operation on the data  ...  The range p E (1, oo) with limits at the left and right of the interval covers only a portion xi E [50,175/3] of the Pareto set (31). is clear that the whole Pareto set (31) for xi E [50,75] is covered  ... 
doi:10.1016/s0898-1221(02)00202-x fatcat:2t3cwzl7gjfrzif3lfnnhhdcim

Differential Ratio Approximation [chapter]

Giorgio Ausiello, Vangelis Th. Paschos
2007 Handbook of Approximation Algorithms and Metaheuristics  
Proposition 3. ([11]) min independent dominating set ∈ 0-DAPX.  ...  The underlying idea for Π G Π in definition 3 is, starting from an instance of Π, to construct instances for Π that have only two distinct feasible values and to prove that any differential δ-approximation  ...  The worst solution for an instance of min vertex cover or of min coloring is the whole vertex-set of the input-graph, while for an instance of max independent set the worst solution is the empty set.  ... 
doi:10.1201/9781420010749.ch16 fatcat:vfrwaousvffgzb5wjb6jaqlgza

Efficient approximation of min set cover by moderately exponential algorithms

N. Bourgeois, B. Escoffier, V.Th. Paschos
2009 Theoretical Computer Science  
We study the approximation of min set cover combining ideas and results from polynomial approximation and from exact computation (with non-trivial worst case complexity upper bounds) for NP-hard problems  ...  We design approximation algorithms for min set cover achieving ratios that cannot be achieved in polynomial time (unless problems in NP could be solved by slightly super-polynomial algorithms) with worst-case  ...  Acknowledgment The very useful comments and suggestions of an anonymous referee are gratefully acknowledged.  ... 
doi:10.1016/j.tcs.2009.02.007 fatcat:bnmvbntpdjaink4ibtqwkkrkkq

An overview on polynomial approximation of NP-hard problems

Vangelis Paschos
2009 Yugoslav Journal of Operations Research  
In other words, heuristic computation consists of trying to find not the best solution but one solution which is "close to" the optimal one in reasonable time.  ...  Among the classes of heuristic methods for NP-hard problems, the polynomial approximation algorithms aim at solving a given NP-hard problem in polynomial time by computing feasible solutions that are,  ...  The very useful comments and suggestions of an anonymous referee are gratefully acknowledged.  ... 
doi:10.2298/yjor0901003p fatcat:ktg6znutsnaxlfvu5nywicj5qa

A hybrid Lagrangean heuristic with GRASP and path-relinking for set k-covering

Luciana S. Pessoa, Mauricio G.C. Resende, Celso C. Ribeiro
2013 Computers & Operations Research  
The set multicovering or set k-covering problem is an extension of the classical set covering problem, in which each object is required to be covered at least k times.  ...  We describe a GRASP with pathrelinking heuristic for the set k-covering problem, as well as the template of a family of Lagrangean heuristics.  ...  Beasley [3, 5] described a Lagrangean heuristic for set covering which can be extended to the set kcovering problem.  ... 
doi:10.1016/j.cor.2011.11.018 fatcat:jbaldo3aajes3c63t7ry4e2mre

The interval greedy algorithm for discrete optimization problems with interval objective function [article]

Alexander Prolubnikov
2020 arXiv   pre-print
Using the algorithm, we obtain the set of all possible greedy solutions and the set of all possible values of the objective function for the solutions.  ...  We consider a wide class of the discrete optimization problems with interval objective function. We give a generalization of the greedy algorithm for the problems.  ...  The united solution set is a set of all weak solutions. Using the concept of the united solution set, we may state the discrete optimization problem of the following form. Optimization problem (III).  ... 
arXiv:2003.01937v3 fatcat:fwr4qqlvvvhaxjdnsrmb5k4vka

On the Use of Equivalence Classes for Optimal and Suboptimal Bin Packing and Bin Covering

Sabino Roselli, Fredrik Hagebring, Sarmad Riazi, Martin Fabian, Knut Akesson
2020 IEEE Transactions on Automation Science and Engineering  
The optimization problem concerns minimizing, for bin packing, or maximizing, for bin covering, the number of bins.  ...  The problem concerns a set of items, each with its own value, that are to be sorted into bins in such a way that the total value of each bin, as measured by the sum of its item values, is not above (for  ...  His research interests include formal methods for automation systems in a broad sense, merging the fields of Control Engineering and Computer Science.  ... 
doi:10.1109/tase.2020.3022986 fatcat:oeevrcolazamfcttncn6qg6xqi

Approximating Edge Dominating Set in Dense Graphs [chapter]

Richard Schmied, Claus Viehmann
2011 Lecture Notes in Computer Science  
ratios of min{2, 3/(1 + 2ϵ)} and of min{2, 3/(3 − 2 √ 1 −ε)}, respectively.  ...  More precisely, we consider the computational complexity of approximating a generalization of the Minimum Edge Dominating Set problem, the so called Minimum Subset Edge Dominating Set problem.  ...  The second author's work was partially supported by Hausdorff Center for Mathematics, Bonn.  ... 
doi:10.1007/978-3-642-20877-5_5 fatcat:5gwr7ux4ubeaffrn2jmtkykqcu

Approximating edge dominating set in dense graphs

Richard Schmied, Claus Viehmann
2012 Theoretical Computer Science  
ratios of min{2, 3/(1 + 2ϵ)} and of min{2, 3/(3 − 2 √ 1 −ε)}, respectively.  ...  More precisely, we consider the computational complexity of approximating a generalization of the Minimum Edge Dominating Set problem, the so called Minimum Subset Edge Dominating Set problem.  ...  The second author's work was partially supported by Hausdorff Center for Mathematics, Bonn.  ... 
doi:10.1016/j.tcs.2011.10.001 fatcat:l4d2gn4i3rg3zdsi7grwblhpj4

On the differential approximation of MIN SET COVER

Cristina Bazgan, Jérôme Monnot, Vangelis Th. Paschos, Fabrice Serrière
2005 Theoretical Computer Science  
Next, we study another approximation algorithm for MIN SET COVER that computes 2-optimal solutions, i.e., solutions that cannot be improved by removing two sets belonging to them and adding another set  ...  We present in this paper differential approximation results for MIN SET COVER and MIN WEIGHTED SET COVER.  ...  Acknowledgements The pertinent remarks and suggestions of two anonymous referees are gratefully acknowledged.  ... 
doi:10.1016/j.tcs.2004.12.022 fatcat:2nf2yjjtu5gx5ccikp23vctvcy

Gradient-Based Multiobjective Optimization with Uncertainties [chapter]

Sebastian Peitz, Michael Dellnitz
2017 Studies in Computational Intelligence  
In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties.  ...  solutions to multiobjective optimization problems.  ...  Acknowledgement: This work is supported by the Priority Programme SPP 1962 "Non-smooth and Complementarity-based Distributed Parameter Systems" of the German Research Foundation (DFG).  ... 
doi:10.1007/978-3-319-64063-1_7 fatcat:7mvwk4vts5bifa7qfxpjknwfve

Instance Specific Approximations for Submodular Maximization [article]

Eric Balkanski, Sharon Qian, Yaron Singer
2021 arXiv   pre-print
The main challenge is that an optimal solution cannot be efficiently computed for intractable problems, and we therefore often do not know how far a solution is from being optimal.  ...  For the canonical problem of submodular maximization under a cardinality constraint, it is intractable to compute a solution that is better than a 1-1/e ≈ 0.63 fraction of the optimum.  ...  We show that a lower bound on this minimum cover problem implies an upper bound on the optimal value OPT for the max-coverage problem.  ... 
arXiv:2102.11911v1 fatcat:kbk6h66wjvblxie42obqaswgqe

Branch-and-Bound Method for Just-in-Time Optimization of Radar Search Patterns [chapter]

Yann Briheche, Frederic Barbaresco, Fouad Bennis, Damien Chablat
2020 Modeling and Processing for Next-Generation Big-Data Technologies  
Radar search pattern optimization can be approximated as a set cover problem and solved using integer programming, while accounting for localized clutter and terrain masks in detection constraints.  ...  We present a set cover problem approximation for time-budget minimization of radar search patterns, under constraints of range, detection probability and direction-specific scan update rates.  ...  The optimization formulation of this set cover problem can be written as: min C∈S T C s.t.  ... 
doi:10.1007/978-3-030-26458-1_25 fatcat:sobegs2m4zerrpqnueclmrem3y
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