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Approximation Schemes for Packing Splittable Items with Cardinality Constraints
2010
Algorithmica
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We continue the study of bin 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. ...
doi:10.1007/s00453-010-9445-6
fatcat:55sxum22u5hgzdvfzdyrm74gie
Approximation Schemes for Packing Splittable Items with Cardinality Constraints
[chapter]
2008
Lecture Notes in Computer Science
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We continue the study of bin 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. ...
doi:10.1007/978-3-540-77918-6_19
fatcat:scxnzgpojnc7rcdtka6b3shpvu
EPTAS for the dual of splittable bin packing with cardinality constraint
[article]
2022
arXiv
pre-print
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The problem considered is the 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. ...
arXiv:2204.04685v1
fatcat:7sbevw5qrvf7jj63nheyjgptby
On Packing Splittable Items with Cardinality Constraints
[chapter]
2010
IFIP Advances in Information and Communication Technology
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We show that NEXT FIT gives a ( 1 + 1 k ) -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. ...
doi:10.1007/978-3-642-15240-5_8
fatcat:cgtpx4zkdzagpbeokotzjrlauy
Approximation Algorithms for Scheduling with Class Constraints
[article]
2019
arXiv
pre-print
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Even though this problem is closely related to the Class 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. ...
arXiv:1909.11970v1
fatcat:emektwku75bpdl26swltkyr4gi
Approximation of the k-batch consolidation problem
2009
Theoretical Computer Science
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In particular, this implies an upper bound on the 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] . ...
doi:10.1016/j.tcs.2008.11.007
fatcat:3surhrh2urb6lawjw6qymdtdhu
Empowering the Configuration-IP - New PTAS Results for Scheduling with Setups Times
2018
Innovations in Theoretical Computer Science
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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 ...
doi:10.4230/lipics.itcs.2019.44
dblp:conf/innovations/JansenKMR19
fatcat:cj3bfgbtebg3lkjpvtfuazrmpi
Improved results for a memory allocation problem
[article]
2006
arXiv
pre-print
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We consider a memory allocation problem that can be modeled as a version of bin 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. ...
arXiv:cs/0612100v1
fatcat:xizieigwcbhcdk44wtbcmenuxa
Improved Results for a Memory Allocation Problem
2009
Theory of Computing Systems
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This problem can be modeled as a version of bin 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. ...
doi:10.1007/s00224-009-9226-2
fatcat:sxgfipsz3jdplhcbltt6i2js2i
Improved Results for a Memory Allocation Problem
[chapter]
2007
Lecture Notes in Computer Science
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This problem can be modeled as a version of bin 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. ...
doi:10.1007/978-3-540-73951-7_32
fatcat:kndslx6eijfzblqz5ulruyitxu
Empowering the Configuration-IP - New PTAS Results for Scheduling with Setups Times
[article]
2018
arXiv
pre-print
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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. ...
arXiv:1801.06460v2
fatcat:rgif5oa2jfa5bgrol4oh77ca3a
The Train Delivery Problem - Vehicle Routing Meets Bin Packing
[chapter]
2011
Lecture Notes in Computer Science
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Alternatively, we give a polynomial time 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. ...
doi:10.1007/978-3-642-18318-8_9
fatcat:sndm326fhbdhdm5umgnrgrc3d4
Heterogeneous Resource Allocation under Degree Constraints
2013
IEEE Transactions on Parallel and Distributed Systems
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In this paper, we consider the problem of assigning a set of clients 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. ...
doi:10.1109/tpds.2012.175
fatcat:rssr3bq6pjexda4vqt3bvf6mta
Reliable Service Allocation in Clouds with Memory and Capacity Constraints
[chapter]
2014
Lecture Notes in Computer Science
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In this context, the goal 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. ...
doi:10.1007/978-3-642-54420-0_68
fatcat:wrbzvfxrxndv5p7lzsegwl3mrm
The Vertex Coloring Problem and its generalizations
2008
4OR
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Jansen and Oehring [67] and Jansen [66] have shown that, 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 ...
doi:10.1007/s10288-008-0071-y
fatcat:73bododqzrcevonqizmugbzjhq
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