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Parameterized (in)approximability of subset problems

2014
*
Operations Research Letters
*

We discuss approximability and inapproximability in FPT-time

doi:10.1016/j.orl.2014.03.005
fatcat:dujrjhmp25hrhdh4dtldzpzzgm
*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. ...##
###
Parameterized (in)approximability of subset problems
[article]

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 ...

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

2002
*
Computers and Mathematics with Applications
*

., [l-

doi:10.1016/s0898-1221(02)00202-x
fatcat:2t3cwzl7gjfrzif3lfnnhhdcim
*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*...##
###
Differential Ratio Approximation
[chapter]

2007
*
Handbook of Approximation Algorithms and Metaheuristics
*

Proposition

doi:10.1201/9781420010749.ch16
fatcat:vfrwaousvffgzb5wjb6jaqlgza
*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*. ...##
###
Efficient approximation of min set cover by moderately exponential algorithms

2009
*
Theoretical Computer Science
*

We study

doi:10.1016/j.tcs.2009.02.007
fatcat:bnmvbntpdjaink4ibtqwkkrkkq
*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. ...##
###
An overview on polynomial approximation of NP-hard problems

2009
*
Yugoslav Journal of Operations Research
*

In other words, heuristic

doi:10.2298/yjor0901003p
fatcat:ktg6znutsnaxlfvu5nywicj5qa
*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. ...##
###
A hybrid Lagrangean heuristic with GRASP and path-relinking for set k-covering

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*. ...

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

2020
*
arXiv
*
pre-print

Using

arXiv:2003.01937v3
fatcat:fwr4qqlvvvhaxjdnsrmb5k4vka
*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). ...##
###
On the Use of Equivalence Classes for Optimal and Suboptimal Bin Packing and Bin Covering

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. ...

##
###
Approximating Edge Dominating Set in Dense Graphs
[chapter]

2011
*
Lecture Notes in Computer Science
*

ratios of

doi:10.1007/978-3-642-20877-5_5
fatcat:5gwr7ux4ubeaffrn2jmtkykqcu
*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. ...##
###
Approximating edge dominating set in dense graphs

2012
*
Theoretical Computer Science
*

ratios of

doi:10.1016/j.tcs.2011.10.001
fatcat:l4d2gn4i3rg3zdsi7grwblhpj4
*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. ...##
###
On the differential approximation of MIN SET COVER

2005
*
Theoretical Computer Science
*

Next, we study another approximation algorithm

doi:10.1016/j.tcs.2004.12.022
fatcat:2nf2yjjtu5gx5ccikp23vctvcy
*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. ...##
###
Gradient-Based Multiobjective Optimization with Uncertainties
[chapter]

2017
*
Studies in Computational Intelligence
*

In this article we develop a gradient-based algorithm

doi:10.1007/978-3-319-64063-1_7
fatcat:7mvwk4vts5bifa7qfxpjknwfve
*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). ...##
###
Instance Specific Approximations for Submodular Maximization
[article]

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*. ...

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

2020
*
Modeling and Processing for Next-Generation Big-Data Technologies
*

Radar search pattern

doi:10.1007/978-3-030-26458-1_25
fatcat:sobegs2m4zerrpqnueclmrem3y
*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. ...
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