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

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*. ...

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

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*. ...

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

2014
*
Lecture Notes in Computer Science
*

A natural extension

doi:10.1007/978-3-319-07557-0_21
fatcat:nl3vt4s4rzhxpmldmpa6fbm3t4
*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 ...##
###
Strong LP formulations for scheduling splittable jobs on unrelated machines

2014
*
Mathematical programming
*

A natural extension

doi:10.1007/s10107-014-0831-8
fatcat:egk7a32dzbd5niv5hfe7ipmtey
*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 ...##
###
On the configuration-LP for scheduling on unrelated machines

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. ...

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

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. ...

##
###
On the Configuration LP for Maximum Budgeted Allocation
[article]

2014
*
arXiv
*
pre-print

In this direction, we prove that

arXiv:1403.7519v1
fatcat:otjy5vftzvabvd7j4uogaaoslu
*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. ...##
###
A polynomial time 12-approximation algorithm for restricted Santa Claus problem
[article]

2020
*
arXiv
*
pre-print

To find this solution, we formulate a

arXiv:2007.09849v2
fatcat:2iei7dt6zbc7xfs5rufzlfiwwe
*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*. ...##
###
Santa claus meets hypergraph matchings

2012
*
ACM Transactions on Algorithms
*

We consider

doi:10.1145/2229163.2229168
fatcat:juenfplt6nahljvxesvpsairja
*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. ...##
###
Estimating the Makespan of the Two-Valued Restricted Assignment Problem

2017
*
Algorithmica
*

We consider a special case

doi:10.1007/s00453-017-0314-4
fatcat:lwhqntzqgnfubdunpervocsbz4
*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*. ...##
###
An Improved Approximation Guarantee for the Maximum Budgeted Allocation Problem
[article]

2015
*
arXiv
*
pre-print

This algorithm works by rounding solutions to an

arXiv:1511.09293v1
fatcat:sq2vx2xc65f7ral25dxyvw4khm
*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] . ...##
###
Quasi-Polynomial Local Search for Restricted Max-Min Fair Allocation
[article]

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 ...

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

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 ...

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

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 ...

##
###
On some special cases of the restricted assignment problem

2016
*
Information Processing Letters
*

We consider some special cases

doi:10.1016/j.ipl.2016.06.007
fatcat:lwg2fmewvnghdm2xzrv4ol53ja
*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 ...
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