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On the Configuration-LP of the Restricted Assignment Problem [article]

Klaus Jansen, Lars Rohwedder
2017 arXiv   pre-print
The configuration-LP is a linear programming relaxation for the Restricted Assignment problem.  ...  As a direct consequence this provides a polynomial (2 - 1/6 + ϵ)-estimation algorithm for the Restricted Assignment problem by approximating the configuration-LP.  ...  An important instrument for the Restricted Assignment problem is a linear programming formulation called the configuration-LP.  ... 
arXiv:1611.01934v2 fatcat:7vukmyovbvc7ponlkk2r4ocpby

On the Configuration-LP for Scheduling on Unrelated Machines [article]

José Verschae, Andreas Wiese
2010 arXiv   pre-print
One of the most important open problems in machine scheduling is the problem of scheduling a set of jobs on unrelated machines to minimize the makespan.  ...  Very recently Svensson studied the restricted assignment case, where each job can only be assigned to a given set of machines on which it has the same processing time.  ...  For this case, Svennson [22] proves even an upper bound of 5/3 + ε for the integrality gap of the configuration-LP for the restricted assignment problem.  ... 
arXiv:1011.4957v1 fatcat:wjpe666rdrb7jnbi3c7ugtzvbe

Strong LP Formulations for Scheduling Splittable Jobs on Unrelated Machines [chapter]

José R. Correa, Alberto Marchetti-Spaccamela, Jannik Matuschke, Leen Stougie, Ola Svensson, Víctor Verdugo, José Verschae
2014 Lecture Notes in Computer Science  
A natural extension of the makespan minimization problem on unrelated machines is to allow jobs to be partially processed by different machines while incurring an arbitrary setup time.  ...  Acknowledgments We would like to thank two anonymous referees for their insightful remarks, which helped improving the presentation of Sects. 4 and 6.  ...  This work was partially supported by Nucleo Milenio Información y Coordinación en Redes ICM/FIC P10-024F, by EU-IRSES Grant EUSACOU, by the DFG  ... 
doi:10.1007/978-3-319-07557-0_21 fatcat:nl3vt4s4rzhxpmldmpa6fbm3t4

Strong LP formulations for scheduling splittable jobs on unrelated machines

José Correa, Alberto Marchetti-Spaccamela, Jannik Matuschke, Leen Stougie, Ola Svensson, Víctor Verdugo, José Verschae
2014 Mathematical programming  
A natural extension of the makespan minimization problem on unrelated machines is to allow jobs to be partially processed by different machines while incurring an arbitrary setup time.  ...  Acknowledgments We would like to thank two anonymous referees for their insightful remarks, which helped improving the presentation of Sects. 4 and 6.  ...  This work was partially supported by Nucleo Milenio Información y Coordinación en Redes ICM/FIC P10-024F, by EU-IRSES Grant EUSACOU, by the DFG  ... 
doi:10.1007/s10107-014-0831-8 fatcat:egk7a32dzbd5niv5hfe7ipmtey

On the configuration-LP for scheduling on unrelated machines

José Verschae, Andreas Wiese
2013 Journal of Scheduling  
One of the most important open problems in machine scheduling is the problem of scheduling a set of jobs on unrelated machines to minimize the makespan.  ...  Very recently Svensson [22] studied the restricted assignment case, where each job can only be assigned to a given set of machines on which it has the same processing time.  ...  Our construction works on the very restricted setting of the unrelated graph balancing problem, where each job can only be assigned to two different machines.  ... 
doi:10.1007/s10951-013-0359-4 fatcat:ay2cjm4hcrceha7jya4cjunlmm

On the Configuration-LP for Scheduling on Unrelated Machines [chapter]

José Verschae, Andreas Wiese
2011 Lecture Notes in Computer Science  
One of the most important open problems in machine scheduling is the problem of scheduling a set of jobs on unrelated machines to minimize the makespan.  ...  Very recently Svensson [22] studied the restricted assignment case, where each job can only be assigned to a given set of machines on which it has the same processing time.  ...  Our construction works on the very restricted setting of the unrelated graph balancing problem, where each job can only be assigned to two different machines.  ... 
doi:10.1007/978-3-642-23719-5_45 fatcat:ztxpac35nfc6hldpmnhi6s5ub4

On the Configuration LP for Maximum Budgeted Allocation [article]

Christos Kalaitzis, Aleksander Ma̧dry, Alantha Newman, Lukáš Poláček, Ola Svensson
2014 arXiv   pre-print
In this direction, we prove that the integrality gap of the configuration LP is strictly better than 3/4, and provide corresponding polynomial time roundings, in the following restrictions of the problem  ...  Since the natural assignment LP is known to have an integrality gap of 3/4, which matches the best known approximation algorithms, our main focus is to improve our understanding of the stronger configuration  ...  The constraints of the configuration LP require that each player is assigned at most one configuration and each item is assigned to at most one player.  ... 
arXiv:1403.7519v1 fatcat:otjy5vftzvabvd7j4uogaaoslu

A polynomial time 12-approximation algorithm for restricted Santa Claus problem [article]

S Anil Kumar, N S Narayanaswamy
2020 arXiv   pre-print
To find this solution, we formulate a problem called the Extended Assignment Problem, and formulate it as an LP.  ...  In this paper, we consider the restricted case of the problem and improve the current best approximation ratio by presenting a polynomial time 12-approximation algorithm using linear programming and semi-definite  ...  We use two linear programs namely Assignment LP and the Configuration LP [1] to solve the restricted Santa Claus problem.  ... 
arXiv:2007.09849v2 fatcat:2iei7dt6zbc7xfs5rufzlfiwwe

Santa claus meets hypergraph matchings

Arash Asadpour, Uriel Feige, Amin Saberi
2012 ACM Transactions on Algorithms  
We consider the restricted assignment version of the problem of max-min fair allocation of indivisible goods, also known as the Santa Claus problem. There are m items and n players.  ...  As a result, we prove that the integrality gap of the configuration LP is no worse than 1 4 .  ...  Acknowledgements Part of this work was performed at Microsoft Research, Redmond, Washington.  ... 
doi:10.1145/2229163.2229168 fatcat:juenfplt6nahljvxesvpsairja

Estimating the Makespan of the Two-Valued Restricted Assignment Problem

Klaus Jansen, Kati Land, Marten Maack
2017 Algorithmica  
We consider a special case of the scheduling problem on unrelated machines, namely the Restricted Assignment Problem with two different processing times.  ...  We show that the configuration LP has an integrality gap of at most 5 3 ≈ 1.667 for this problem.  ...  Svensson [9] proved that the integrality gap of the configuration LP is at most 33/17 ≈ 1.941 for the Restricted Assignment Problem.  ... 
doi:10.1007/s00453-017-0314-4 fatcat:lwhqntzqgnfubdunpervocsbz4

An Improved Approximation Guarantee for the Maximum Budgeted Allocation Problem [article]

Christos Kalaitzis
2015 arXiv   pre-print
This algorithm works by rounding solutions to an LP called the Configuration-LP, therefore also showing that the Configuration-LP is strictly stronger than the Assignment-LP (for which we know that the  ...  We study the Maximum Budgeted Allocation problem, which is the problem of assigning indivisible items to players with budget constraints.  ...  The use of the Configuration-LP for the MBA problem was first proposed by Chakrabarty and Goel [5] . The worst known upper bound on the integrality gap of the Configuration-LP is 2( √ 2 − 1) [9] .  ... 
arXiv:1511.09293v1 fatcat:sq2vx2xc65f7ral25dxyvw4khm

Quasi-Polynomial Local Search for Restricted Max-Min Fair Allocation [article]

Lukas Polacek, Ola Svensson
2014 arXiv   pre-print
The restricted max-min fair allocation problem (also known as the restricted Santa Claus problem) is one of few problems that enjoys the intriguing status of having a better estimation algorithm than approximation  ...  Our techniques also have the interesting property that although we use the rather complex configuration LP in the analysis, we never actually solve it and therefore the resulting algorithm is purely combinatorial  ...  One of them is the restricted assignment problem 3 , for which the second author in [14] developed the techniques from [1] to show that the configuration LP can be used to approximate the optimal makespan  ... 
arXiv:1205.1373v2 fatcat:ske4ykzfrnhonkjaqpo45ycyzq

Quasi-Polynomial Local Search for Restricted Max-Min Fair Allocation

Lukáš Poláček, Ola Svensson
2015 ACM Transactions on Algorithms  
The restricted max-min fair allocation problem (also known as the restricted Santa Claus problem) is one of few problems that enjoys the intriguing status of having a better estimation algorithm than approximation  ...  Our techniques also have the interesting property that although we use the rather complex configuration LP in the analysis, we never actually solve it and therefore the resulting algorithm is purely combinatorial  ...  One of them is the restricted assignment problem 3 , for which the second author in [14] developed the techniques from [1] to show that the configuration LP can be used to approximate the optimal makespan  ... 
doi:10.1145/2818695 fatcat:5tnd4rqunfhkdn7fci6e2dfmyy

Quasi-polynomial Local Search for Restricted Max-Min Fair Allocation [chapter]

Lukas Polacek, Ola Svensson
2012 Lecture Notes in Computer Science  
The restricted max-min fair allocation problem (also known as the restricted Santa Claus problem) is one of few problems that enjoys the intriguing status of having a better estimation algorithm than approximation  ...  Our techniques also have the interesting property that although we use the rather complex configuration LP in the analysis, we never actually solve it and therefore the resulting algorithm is purely combinatorial  ...  One of them is the restricted assignment problem 3 , for which the second author in [14] developed the techniques from [1] to show that the configuration LP can be used to approximate the optimal makespan  ... 
doi:10.1007/978-3-642-31594-7_61 fatcat:rgeaa3asmje5zg4a6o2xorqqgy

On some special cases of the restricted assignment problem

Chao Wang, René Sitters
2016 Information Processing Letters  
We consider some special cases of the restricted assignment problem.  ...  In this scheduling problem on parallel machines, any job j can only be assigned to one of the machines in its given subset M j of machines.  ...  Here, each job j has a processing time p j and pro-A breakthrough was made by Svensson [2] , who showed that the integrality gap of the configuration LP for the restricted assignment problem is at most  ... 
doi:10.1016/j.ipl.2016.06.007 fatcat:lwg2fmewvnghdm2xzrv4ol53ja
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