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Approximation Schemes for Packing Splittable Items with Cardinality Constraints

2010
*
Algorithmica
*

We continue the study of bin

doi:10.1007/s00453-010-9445-6
fatcat:55sxum22u5hgzdvfzdyrm74gie
*packing**with**splittable**items*and*cardinality**constraints*. In this problem, a set of*items*must be*packed*into as few bins as possible. ... We first present a*scheme**for*the case k = 2 and then*for*the general case of constant k. Additionally, we present dual*approximation**schemes**for*k = 2 and constant k. ... Conclusions In this paper, we provided*approximation**schemes**for*bin*packing*of*splittable**items**with**cardinality**constraints**for*all values of k. We also provided dual*approximation**schemes*. ...##
###
Approximation Schemes for Packing Splittable Items with Cardinality Constraints
[chapter]

2008
*
Lecture Notes in Computer Science
*

We continue the study of bin

doi:10.1007/978-3-540-77918-6_19
fatcat:scxnzgpojnc7rcdtka6b3shpvu
*packing**with**splittable**items*and*cardinality**constraints*. In this problem, a set of*items*must be*packed*into as few bins as possible. ... We first present a*scheme**for*the case k = 2 and then*for*the general case of constant k. Additionally, we present dual*approximation**schemes**for*k = 2 and constant k. ... Conclusions In this paper, we provided*approximation**schemes**for*bin*packing*of*splittable**items**with**cardinality**constraints**for*all values of k. We also provided dual*approximation**schemes*. ...##
###
EPTAS for the dual of splittable bin packing with cardinality constraint
[article]

2022
*
arXiv
*
pre-print

The problem considered is the

arXiv:2204.04685v1
fatcat:7sbevw5qrvf7jj63nheyjgptby
*splittable*bin*packing**with**cardinality**constraint*. ... Two versions of the*splittable*bin*packing**with**cardinality**constraint*have been studied in the literature. ... Many variations of the*splittable*bin*packing**with**cardinality**constraint*have been studied. ...##
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On Packing Splittable Items with Cardinality Constraints
[chapter]

2010
*
IFIP Advances in Information and Communication Technology
*

We show that NEXT FIT gives a ( 1 + 1 k ) -

doi:10.1007/978-3-642-15240-5_8
fatcat:cgtpx4zkdzagpbeokotzjrlauy
*approximation*asymptotically,*for*k ≥ 2. ... This problem can be modeled as a variation of bin*packing*where each*item*corresponds to a different type and the normalized weight of each*item*can be greater than 1, which is the size of a bin. ...*Packing*splittale*items**with*a*cardinality**constraint*of k parts of*items*per bin is NP-hard in the strong sense*for*any fixed k ≥ 3. Proof. ...##
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Approximation Algorithms for Scheduling with Class Constraints
[article]

2019
*
arXiv
*
pre-print

Even though this problem is closely related to the Class

arXiv:1909.11970v1
fatcat:emektwku75bpdl26swltkyr4gi
*Constraint*Bin*Packing*, the Class*Constraint*Knapsack and the*Cardinality**Constraint*variants, CCS lacks results regarding*approximation*algorithms ... Further we developed the first simple*approximation*algorithms*with*a constant*approximation*ratio running in strongly polynomial time. ...*For*CCS*approximation**schemes*are known*for*two special cases. ...##
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Approximation of the k-batch consolidation problem

2009
*
Theoretical Computer Science
*

In particular, this implies an upper bound on the

doi:10.1016/j.tcs.2008.11.007
fatcat:3surhrh2urb6lawjw6qymdtdhu
*approximation*factor, 2H k − 1, where H k = 1 + 1 2 + · · · + 1 k . ... We will show that the k-batch consolidation problem admits an*approximation*whose factor is twice that of the k-set cover problem. ... Another related model is*packing**splittable**items**with**cardinality**constraints*, or PSIC [5] . ...##
###
Empowering the Configuration-IP - New PTAS Results for Scheduling with Setups Times

2018
*
Innovations in Theoretical Computer Science
*

*For*both of the variants that jobs can be executed in parallel or not, we obtain an efficient polynomial time

*approximation*

*scheme*(EPTAS) of running time f (1/ε) × poly(|I|)

*with*a single exponential ... Integer linear programs of configurations, or configuration IPs, are a classical tool in the design of algorithms

*for*scheduling and

*packing*problems, where a set of

*items*has to be placed in multiple ... Acknowledgements We thank Syamantak Das

*for*helpful discussions on the problem. 1 German Research Foundation (DFG) project JA 612/20-1 ...

##
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Improved results for a memory allocation problem
[article]

2006
*
arXiv
*
pre-print

We consider a memory allocation problem that can be modeled as a version of bin

arXiv:cs/0612100v1
fatcat:xizieigwcbhcdk44wtbcmenuxa
*packing*where*items*may be split, but each bin may contain at most two (parts of)*items*. ... A 3/2-*approximation*algorithm and an NP-hardness proof*for*this problem was given by Chung et al. We give a simpler 3/2-*approximation*algorithm*for*it which is in fact an online algorithm. ... Given such an instance of the 3-Partition problem we define an instance of the*splittable**item**packing**with**cardinality**constraints*as follows. ...##
###
Improved Results for a Memory Allocation Problem

2009
*
Theory of Computing Systems
*

This problem can be modeled as a version of bin

doi:10.1007/s00224-009-9226-2
fatcat:sxgfipsz3jdplhcbltt6i2js2i
*packing*where*items*may be split, but each bin may contain at most two (parts of)*items*. This problem was recently introduced by Chung et al. [3] . ... Additionally, we design an efficient*approximation*algorithm,*for*which the*approximation*ratio can be made arbitrarily close to 7 5 . ... NP-hardness of the problem (in the strong sense) Theorem 1*Packing**splittable**items**with*a*cardinality**constraint*of k parts of*items*per bin is NP-hard in the strong sense*for*any fixed k ≥ 3. ...##
###
Improved Results for a Memory Allocation Problem
[chapter]

2007
*
Lecture Notes in Computer Science
*

This problem can be modeled as a version of bin

doi:10.1007/978-3-540-73951-7_32
fatcat:kndslx6eijfzblqz5ulruyitxu
*packing*where*items*may be split, but each bin may contain at most two (parts of)*items*. This problem was recently introduced by Chung et al. [3] . ... Additionally, we design an efficient*approximation*algorithm,*for*which the*approximation*ratio can be made arbitrarily close to 7 5 . ... NP-hardness of the problem (in the strong sense) Theorem 1*Packing**splittable**items**with*a*cardinality**constraint*of k parts of*items*per bin is NP-hard in the strong sense*for*any fixed k ≥ 3. ...##
###
Empowering the Configuration-IP - New PTAS Results for Scheduling with Setups Times
[article]

2018
*
arXiv
*
pre-print

*For*both of the variants that jobs can be executed in parallel or not, we obtain an efficient polynomial time

*approximation*

*scheme*(EPTAS) of running time f(1/ε)×poly(|I|)

*with*a single exponential term ... Integer linear programs of configurations, or configuration IPs, are a classical tool in the design of algorithms

*for*scheduling and

*packing*problems, where a set of

*items*has to be placed in multiple ...

*schemes*

*for*scheduling problems

*with*setup times. ...

##
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The Train Delivery Problem - Vehicle Routing Meets Bin Packing
[chapter]

2011
*
Lecture Notes in Computer Science
*

Alternatively, we give a polynomial time

doi:10.1007/978-3-642-18318-8_9
fatcat:sndm326fhbdhdm5umgnrgrc3d4
*approximation**scheme**for*the case where W , an input parameter that corresponds to the bin size or the vehicle capacity, is polynomial in the number of*items*or ... The train delivery problem is strongly NP-Hard and does not admit an*approximation*ratio better than 3/2. We design the first*approximation**schemes**for*the problem. ... Such algorithms are called asymptotic polynomial time*approximation**schemes*(APTAS). Our Results. We give the first*approximation**schemes**for*the train delivery problem. ...##
###
Heterogeneous Resource Allocation under Degree Constraints

2013
*
IEEE Transactions on Parallel and Distributed Systems
*

In this paper, we consider the problem of assigning a set of clients

doi:10.1109/tpds.2012.175
fatcat:rssr3bq6pjexda4vqt3bvf6mta
*with*demands to a set of servers*with*capacities and degree*constraints*. ... We first show that the degree*constraint*on the maximal number of clients that a server can handle is realistic in many contexts. ... Related Works A closely related problem is Bin*Packing**with**Splittable**Items*and*Cardinality**Constraints*, where the goal is to*pack*a given set of*items*in as few bins as possible. ...##
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Reliable Service Allocation in Clouds with Memory and Capacity Constraints
[chapter]

2014
*
Lecture Notes in Computer Science
*

In this context, the goal

doi:10.1007/978-3-642-54420-0_68
fatcat:wrbzvfxrxndv5p7lzsegwl3mrm
*for*the Cloud provider is to find an allocation of VMs onto PMs so as to satisfy, at minimal cost, both capacity and reliability*constraints**for*each service. ... In this paper, we propose a simple model*for*reliability*constraints*and we prove that it is possible to derive efficient heuristics. ... Under this assumption, the*packing*problem was equivalent to a mono-dimensional*splittable**item*bin*packing*problem, that can be solved in polynomial time without*cardinality**constraints*. ...##
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The Vertex Coloring Problem and its generalizations

2008
*
4OR
*

Jansen and Oehring [67] and Jansen [66] have shown that,

doi:10.1007/s10288-008-0071-y
fatcat:73bododqzrcevonqizmugbzjhq
*for*general graph, no polynomial time*approximation**schemes*can be derived, while they derive polynomial time*approximation**schemes**for*special ... The corresponding problem is known as Bounded Vertex Coloring Problem (BVCP) or Bin*Packing*Problem*with*Conflicts (where the Bin*Packing*Problem requires to assign a set of*items*, each one*with*a positive ... The problem of routing packets through the network should consider both the efficiency of the routing and its fairness, i.e. the contribution that each node gives to the network*with*respect to the benefit ...
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