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Breaking symmetries to rescue Sum of Squares in the case of makespan scheduling
[article]

2020
*
arXiv
*
pre-print

In this paper, we study this

arXiv:1811.08539v3
fatcat:gctu2ebycjfutgo6es55vrde3q
*for*the case of the minimum makespan problem on*identical**machines*. ... Then, we consider the weaker assignment*linear**program**and*add a well chosen set of symmetry breaking inequalities that removes a subset of the*machine*permutation symmetries. ... to yield a (1 + ε)*integrality**gap*(*and*hence also the weaker assignment*linear**program*below). ...##
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Convex programming for scheduling unrelated parallel machines

2005
*
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing - STOC '05
*

To the best of our knowledge, this is the first time that general convex

doi:10.1145/1060590.1060639
dblp:conf/stoc/AzarE05
fatcat:jksogjheznfvfgghnpvplmsviq
*programming*techniques (apart from SDPs*and*CQPs) are used in the area of*scheduling*. ... We consider the classical problem of*scheduling*parallel unrelated*machines*. Each job is to be processed by exactly one*machine*. Processing job j on*machine*i requires time pij . ... There are several applications of*linear**programming*relaxations*for**machine**scheduling*problems, see, e.g., [14, 16, 10, 4, 5] . ...##
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Convex quadratic and semidefinite programming relaxations in scheduling

2001
*
Journal of the ACM
*

Finally,

doi:10.1145/375827.375840
fatcat:5dbcodih3vdkdddei236hzi2l4
*for*the special case of two*machines*we introduce a more sophisticated*semidefinite**programming*relaxation*and*apply the random hyperplane technique introduced by Goemans*and*Williamson*for*the ... We also consider preemptive*scheduling*problems*and*derive approximation algorithms*and*results on the power of preemption which improve upon the best previously known results*for*these settings. ... The author is grateful to Michel Goemans, Andreas Schulz,*and*an anonymous referee*for*helpful comments. ...##
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Semidefinite Programming in Timetabling and Mutual-Exclusion Scheduling
[article]

2019
*
arXiv
*
pre-print

This corresponds to the vertex colouring problem in graph theory,

arXiv:1904.03539v1
fatcat:csewztv5draqhp7zdx5foqtsbq
*for*which there are well-known*semidefinite**programming*(SDP) relaxations. ... We present SDP relaxations*for*a variety of mutual-exclusion*scheduling**and*timetabling problems, starting from a bound on the number of tasks executed within each period, which corresponds to graph colouring ... Notation*and*Related Work*Semidefinite**Programming*Firstly, let us revisit the definition of*semidefinite**programming*, which is a popular extension of*linear**programming*. ...##
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A strong conic quadratic reformulation for machine-job assignment with controllable processing times

2009
*
Operations Research Letters
*

We describe a polynomial-size conic quadratic reformulation

doi:10.1016/j.orl.2008.12.009
fatcat:jyoj5nypyffnrkrahsunx4ym64
*for*a*machine*-job assignment problem with separable convex cost. ... Gürel was a visiting scholar at the University of California-Berkeley with support from the Scientific*and*Technological Research Council of Turkey under Grant 2214. A. ... In Table 1 we also observe that with tighter*machining*capacity, the*integrality**gap*is higher*for*all problems sizes. ...##
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Sum-of-squares hierarchy lower bounds for symmetric formulations
[article]

2016
*
arXiv
*
pre-print

We also show that the SoS hierarchy requires a non-constant number of rounds to improve the initial

arXiv:1407.1746v2
fatcat:wxu7jef6gvc2nk3iq4kh3pukhq
*integrality**gap*of 2*for*the Min-Knapsack*linear**program*strengthened with cover inequalities. ... We illustrate the technique on two problems, one unconstrained*and*the other with constraints. ... The authors would like to express their gratitude to Ola Svensson*for*helpful discussions*and*ideas regarding this paper. ...##
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Human-machine interaction for real-time linear optimization

2012
*
2012 IEEE International Conference on Systems, Man, and Cybernetics (SMC)
*

Mixed-Initiative-Systems (MIS) are hybrid decisionmaking systems in which human

doi:10.1109/icsmc.2012.6377804
dblp:conf/smc/HamelGQBM12
fatcat:arzkzixr6zcpbf4cnkytgiluwi
*and**machine*collaborate in order to produce a solution. ... However, this delay is unacceptable*for*iterative*and*interactive decision-making contexts where users need to provide their input. ... The two first constraints of this*linear**program*force the variable g to be at least as large as j j x x ′ − . The unknown of this problem are the vector α*and*the*gap*variable g. ...##
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Approximability of average completion time scheduling on unrelated machines

2016
*
Mathematical programming
*

This provides one of the last missing pieces in the complexity classification of

doi:10.1007/s10107-016-1004-8
fatcat:6u5cw6zic5awlfaaomymfwwiwy
*machine**scheduling*with (weighted) sum of completion times objective. ... The proof is based on a mixed integer*linear**program*. This means that verification of the reduction is partly done by an ILPsolver. This gives a concise proof which is easy to verify. ... reproduction in any medium, provided you give appropriate credit to the original author(s)*and*the source, provide a link to the Creative Commons license,*and*indicate if changes were made. ...##
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Lift-and-Round to Improve Weighted Completion Time on Unrelated Machines
[article]

2015
*
arXiv
*
pre-print

To do this, we first introduce a new lift-

arXiv:1511.07826v2
fatcat:2qsw2asj7zdxjpuh2a6oiw6o54
*and*-project based SDP relaxation*for*the problem. This is necessary as the previous convex*programming*relaxations have an*integrality**gap*of 3/2. ... We consider the problem of*scheduling*jobs on unrelated*machines*so as to minimize the sum of weighted completion times. ... We thank Nick Harvey*and*Bruce Shepherd*for*organizing the Bellairs Workshop on Combinatorial Optimization 2015, which was the starting point*for*this work. ...##
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Lift-and-round to improve weighted completion time on unrelated machines

2016
*
Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2016
*

To do this, we first introduce a new lift-andproject based SDP relaxation

doi:10.1145/2897518.2897572
dblp:conf/stoc/BansalSS16
fatcat:anurs75s6ra2ve5bmr3mzyt6sm
*for*the problem. This is necessary as the previous convex*programming*relaxations have an*integrality**gap*of 3/2. ... We consider the problem of*scheduling*jobs on unrelated*machines*so as to minimize the sum of weighted completion times. ... We thank Nick Harvey*and*Bruce Shepherd*for*organizing the Bellairs Workshop on Combinatorial Optimization 2015, which was the starting point*for*this work. ...##
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Unrelated Machine Scheduling of Jobs with Uniform Smith Ratios

2017
*
Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms
*

In this work, we take a different approach

doi:10.1137/1.9781611974782.175
dblp:conf/soda/KalaitzisST17
fatcat:234eas2xvjantfqay6hsopna3e
*and*propose to use the same elegant rounding scheme*for*the weighted completion time objective as devised by Shmoys*and*Tardos*for*optimizing a*linear*function ... We consider the classic problem of*scheduling*jobs on unrelated*machines*so as to minimize the weighted sum of completion times. ... The*integrality**gap*of the Configuration-LP*for*R|| p j C j is at least 1.08. ...##
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A branch-and-cut algorithm based on semidefinite programming for the minimum k-partition problem

2008
*
Annals of Operations Research
*

The main contribution of this paper is the design

doi:10.1007/s10479-008-0481-4
fatcat:vxq6dt22tfc4xikzxxqwhscxd4
*and*implementation of a branch-*and*-cut algorithm based on*semidefinite**programming*(SBC)*for*the MkP problem. ... The two key ingredients*for*this algorithm are: the combination of*semidefinite**programming*(SDP) with polyhedral results;*and*the iterative clustering heuristic (ICH) that finds feasible solutions*for*... Usually, (*linear**programming*) relaxations are used*and*strengthened during the run of the algorithm. ...##
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Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition

2000
*
INFORMS journal on computing
*

We show how these techniques are useful in important application areas such as network design

doi:10.1287/ijoc.12.1.2.11900
fatcat:zticaywmezc4rl7uji44l7u6tu
*and*crew*scheduling*. ... Finally, we discuss the relatively new research areas of parallel integer*programming**and*stochastic integer*programming*. ... Consider the*GAP*in which all*machines*are*identical*. ...##
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Fifty years of scheduling: a survey of milestones

2009
*
Journal of the Operational Research Society
*

A discussion of the main topics of

doi:10.1057/jors.2009.2
fatcat:trzjs3iaqbdara3waf7u2fagam
*scheduling*research*for*the past five decades is provided, highlighting the key contributions that helped shape the subject. ... The main topics covered in the respective decades are combinatorial analysis, branch*and*bound, computational complexity*and*classification, approximate solution algorithms,*and*enhanced*scheduling*models ... challenges remain*for*new*and*established researchers in this exciting*and*rewarding area. ...##
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Guaranteed Accuracy for Conic Programming Problems in Vector Lattices
[article]

2007
*
arXiv
*
pre-print

Numerical results, applications

arXiv:0707.4366v1
fatcat:wdcd5f2bvne47khgvntofwwvi4
*and*software*for**linear**and**semidefinite**programming*problems are described. ... In the case of*linear**programming*, second order cone*programming*,*and**semidefinite**programming*specialized formulas are deduced yielding guaranteed accuracy. ... A detailed description of this algorithm can be found in the case of*linear**programming*in [14] ,*for*smooth convex*programming*problems in [13] ,*and**for**semidefinite**programming*problems*and**linear*...
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