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A Lasserre Lower Bound for the Min-Sum Single Machine Scheduling Problem [article]

Adam Kurpisz, Samuli Leppänen, Monaldo Mastrolilli
<span title="2015-11-27">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The Min-sum single machine scheduling problem (denoted 1||sum f_j) generalizes a large number of sequencing problems.  ...  In this paper we study the complexity of the Min-sum single machine scheduling problem under algorithms from the Lasserre hierarchy.  ...  Introduction The Min-sum single machine scheduling problem (often denoted 1|| f j ) is defined by a set of n jobs to be scheduled on a single machine.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1511.08644v1">arXiv:1511.08644v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/eg564pec2rfahmcux4gao5k4rq">fatcat:eg564pec2rfahmcux4gao5k4rq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200825165528/https://arxiv.org/pdf/1511.08644v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ce/45/ce45e8030ef9c13bf800ad567f3df12b9bbdb6c3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1511.08644v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Page 8088 of Mathematical Reviews Vol. , Issue 99k [page]

<span title="">1999</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The problem is to find a bound for the distance to one of the K centers which is valid for all time parameters f¢.  ...  At first, basic concepts and results are surveyed for GERT net- works and for single-machine and parallel-machine scheduling with GERT network precedence constraints.  ... 
<span class="external-identifiers"> </span>
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The Lasserre Hierarchy in Almost Diagonal Form [article]

Monaldo Mastrolilli
<span title="2014-04-02">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For the min-sum of tardy jobs scheduling problem, we show that the integrality gap is unbounded at level Ω(√(n)) (even when the objective function is integrated as a constraint).  ...  Using this, we prove strong lower bounds on integrality gaps of Lasserre hierarchy for two basic capacitated covering problems.  ...  I'm grateful to Joseph Cheriyan and Zhihan Gao for pointing out a mistake in an early version of the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1312.6493v4">arXiv:1312.6493v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xdqrlpgdirbf5gqtxzj6tgwo4m">fatcat:xdqrlpgdirbf5gqtxzj6tgwo4m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200901015511/https://arxiv.org/pdf/1312.6493v4.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/04/2f/042fb214ab0b6d978e291eed968be26898fb267f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1312.6493v4" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Scheduling (Dagstuhl Seminar 16081)

Nikhil Bansal, Nicole Megow, Clifford Stein, Marc Herbstritt
<span title="2016-08-17">2016</span> <i title="Schloss Dagstuhl Leibniz-Zentrum für Informatik GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/u2phfyhrhje7xnnubtp3vfklcu" style="color: black;">Dagstuhl Reports</a> </i> &nbsp;
The seminar was centered around recent new developments, discussion of open problems and exploring future research directions within the broader scheduling community.  ...  This report documents the program and the outcomes of Dagstuhl Seminar 16081 "Scheduling".  ...  We present a method to obtain asymptotic fully polynomial approximation schemes (AFPTAS) for the problems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/dagrep.6.2.97">doi:10.4230/dagrep.6.2.97</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/journals/dagstuhl-reports/BansalMS16.html">dblp:journals/dagstuhl-reports/BansalMS16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7yjnnvu26vcjfa3r6nknvrpkk4">fatcat:7yjnnvu26vcjfa3r6nknvrpkk4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210805105027/https://drops.dagstuhl.de/opus/volltexte/2016/5890/pdf/dagrep_v006_i002_p097_s16081.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/56/59/5659461111f36a311649a62ee11f33bed4505901.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/dagrep.6.2.97"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

On the Hardest Problem Formulations for the 0/1 Lasserre Hierarchy [article]

Adam Kurpisz, Samuli Leppänen, Monaldo Mastrolilli
<span title="2015-10-07">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The Lasserre/Sum-of-Squares (SoS) hierarchy is a systematic procedure for constructing a sequence of increasingly tight semidefinite relaxations.  ...  These problems are the hardest for the Lasserre hierarchy in this sense.  ...  Research supported by the Swiss National Science Foundation project 200020 144491/1 "Approximation Algorithms for Machine Scheduling Through Theory and Experiments".  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1510.01891v1">arXiv:1510.01891v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6rxxi3mh2rev3hjimbmaa5lb4y">fatcat:6rxxi3mh2rev3hjimbmaa5lb4y</a> </span>
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Semidefinite Programming in Timetabling and Mutual-Exclusion Scheduling [article]

Jakub Marecek, Andrew J. Parkes
<span title="2019-04-06">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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  ...  In theory, this provides the strongest known bounds for these problems that are computable to any precision in time polynomial in the dimensions.  ...  Clearly, the work on graph colouring provides a test of infeasibility for timetabling and scheduling problems incorporating the mutual exclusion problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1904.03539v1">arXiv:1904.03539v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/csewztv5draqhp7zdx5foqtsbq">fatcat:csewztv5draqhp7zdx5foqtsbq</a> </span>
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An improved model and a heuristic for capacitated lot sizing and scheduling in job shop problems

O. Poursabzi, M. Mohammadi, B. Naderi
<span title="2017-12-26">2017</span> <i title="SciTech Solutions"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ae72n2d2dzg5vk7hgkdy7z36mq" style="color: black;">Scientia Iranica. International Journal of Science and Technology</a> </i> &nbsp;
No lower bound and heuristic are developed for the problem. Therefore, we rst develop a linear model for the problem in hand.  ...  This paper studies the problem of capacitated lot-sizing and scheduling in job shops with a carryover set-up and a general product structure.  ...  Lasserre [19] and Dauzere-Peres and Lasserre [20] presented integrated models of multi-product, multiperiod job shop lot-sizing and scheduling problems considering set-up scheduling for the job shop  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.24200/sci.2017.20016">doi:10.24200/sci.2017.20016</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rce6dtypgzgs7hhnsoh2ud6b3e">fatcat:rce6dtypgzgs7hhnsoh2ud6b3e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190428220418/http://scientiairanica.sharif.edu/article_20016_3f8a13b45b090b67b63de7334efb606a.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/85/fd/85fd4551fde3f6996d3966661a495cc0aba8d072.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.24200/sci.2017.20016"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

A (1+epsilon)-Approximation for Makespan Scheduling with Precedence Constraints using LP Hierarchies [article]

Elaine Levey, Thomas Rothvoss
<span title="2018-02-16">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In a classical problem in scheduling, one has n unit size jobs with a precedence order and the goal is to find a schedule of those jobs on m identical machines as to minimize the makespan.  ...  It is one of the remaining four open problems from the book of Garey & Johnson whether or not this problem is NP-hard for m=3.  ...  In a typical scheduling application, the number of jobs might be huge compared to the number of machines, which does justify to ask for the complexity status of such problems if the number m of machines  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1509.07808v2">arXiv:1509.07808v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hkfsiy56evfqrgpivxk3v46gpi">fatcat:hkfsiy56evfqrgpivxk3v46gpi</a> </span>
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Minimising the weighted number of tardy jobs in a hybrid flow shop with genetic algorithm

C. Desprez, F. Chu, C. Chu
<span title="">2009</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3akwjclty5a4fo53lfbeklzp7m" style="color: black;">International journal of computer integrated manufacturing (Print)</a> </i> &nbsp;
The results show that the proposed GA performs well on the scheduling part for a given resource allocation, but it still requires an effective resource allocation procedure.  ...  This paper considers a real-world industrial problem in order to minimize the (weighted) number of tardy jobs.  ...  For example, if a lower bound exists, the stopping criterion can be the gap between the best solution found and the lower bound. The GA then stops when it reaches a solution that is within this gap.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/09511920902810938">doi:10.1080/09511920902810938</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jxvzsg74pjg7vkuoymjydyyeuu">fatcat:jxvzsg74pjg7vkuoymjydyyeuu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190228215114/http://pdfs.semanticscholar.org/91fe/8beabb05fe66ec4176441170770a5a629c23.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/91/fe/91fe8beabb05fe66ec4176441170770a5a629c23.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/09511920902810938"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> tandfonline.com </button> </a>

Scheduling with Communication Delays via LP Hierarchies and Clustering [article]

Sami Davies, Janardhan Kulkarni, Thomas Rothvoss, Jakub Tarnawski, Yihao Zhang
<span title="2020-04-21">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this work we give a polynomial-time O(log c ·log m)-approximation algorithm for this problem, where m is the number of machines and c is the communication delay.  ...  Even for a special case where an unlimited number of machines is available, the best known approximation ratio is 2/3 · (c+1), whereas Graham's greedy list scheduling algorithm already gives a (c+1)-approximation  ...  Our Techniques As we alluded earlier, there is a lack of combinatorial lower bounds for scheduling with communication delays.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2004.09682v1">arXiv:2004.09682v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yhympzbzqnbjxkezr5p7g4mary">fatcat:yhympzbzqnbjxkezr5p7g4mary</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200501020229/https://arxiv.org/pdf/2004.09682v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2004.09682v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Lift-and-Round to Improve Weighted Completion Time on Unrelated Machines [article]

Nikhil Bansal, Aravind Srinivasan, Ola Svensson
<span title="2015-12-01">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We consider the problem of scheduling jobs on unrelated machines so as to minimize the sum of weighted completion times.  ...  Our main result is a (3/2-c)-approximation algorithm for some fixed c>0, improving upon the long-standing bound of 3/2 (independently due to Skutella, Journal of the ACM, 2001, and Sethuraman & Squillante  ...  Aravind Srinivasan thanks Amit Chavan for his help with L A T E Xpackages.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1511.07826v2">arXiv:1511.07826v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2qsw2asj7zdxjpuh2a6oiw6o54">fatcat:2qsw2asj7zdxjpuh2a6oiw6o54</a> </span>
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Lift-and-round to improve weighted completion time on unrelated machines

Nikhil Bansal, Aravind Srinivasan, Ola Svensson
<span title="">2016</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jlc5kugafjg4dl7ozagimqfcbm" style="color: black;">Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2016</a> </i> &nbsp;
We consider the problem of scheduling jobs on unrelated machines so as to minimize the sum of weighted completion times.  ...  Our main result is a (3/2 − c)-approximation algorithm for some fixed c > 0, improving upon the long-standing bound of 3/2 (independently due to Skutella, Journal of the ACM, 2001, and Sethuraman & Squillante  ...  Aravind Srinivasan thanks Amit Chavan for his help with L A T E Xpackages.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2897518.2897572">doi:10.1145/2897518.2897572</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/stoc/BansalSS16.html">dblp:conf/stoc/BansalSS16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/anurs75s6ra2ve5bmr3mzyt6sm">fatcat:anurs75s6ra2ve5bmr3mzyt6sm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180719231842/https://pure.tue.nl/ws/files/91284149/1511.07826.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/97/78/97786eea3bb990f1d69670e6dd0824fcccba6da4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2897518.2897572"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Modeling industrial lot sizing problems: a review

Raf Jans, Zeger Degraeve
<span title="2008-03-15">2008</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/sowvaovjz5h3hpgfua7tikprd4" style="color: black;">International Journal of Production Research</a> </i> &nbsp;
In this paper we give an overview of recent developments in the field of modeling single-level dynamic lot sizing problems.  ...  Abstract In this paper we give an overview of recent developments in the field of modeling single-level dynamic lot sizing problems.  ...  Jordan and Drexl (1998) showed the equivalence between DLSP for a single machine and the batch sequencing problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/00207540600902262">doi:10.1080/00207540600902262</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5hocpks4mvcrtluhnm6dcedtmi">fatcat:5hocpks4mvcrtluhnm6dcedtmi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170817160702/https://repub.eur.nl/pub/6912/ERS%202005%20049%20LIS.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/98/11/9811fbb728fc9221966bd9f244705fbf317eb4a4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/00207540600902262"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> tandfonline.com </button> </a>

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

Victor Verdugo and José Verschae and Andreas Wiese
<span title="2020-05-16">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For many other problems, however, ad-hoc techniques give better approximation ratios than in the worst case, as shown by corresponding lower bound instances.  ...  In this paper, we study this for the case of the minimum makespan problem on identical machines.  ...  For estimation and detection problems, lower bounds have been shown for the planted clique problem, k-densest subgraph and tensor PCA, among others [21, 6] . Invariant Sum of Squares.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1811.08539v3">arXiv:1811.08539v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gctu2ebycjfutgo6es55vrde3q">fatcat:gctu2ebycjfutgo6es55vrde3q</a> </span>
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A polyhedral approach to single-machine scheduling problems

J.M. van den Akker, C.P.M. van Hoesel, M.W.P. Savelsbergh
<span title="">1999</span> <i title="Springer Nature America, Inc"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/o653fqsowvcyrhw6p4gdmpdkwm" style="color: black;">Mathematical programming</a> </i> &nbsp;
We report new results for a time-indexed formulation of nonpreemptive single-machine scheduling problems.  ...  We evaluate its performance on the strongly N P-hard single machine scheduling problem of minimizing the weighted sum of the job completion times subject to release dates.  ...  The authors wish to thank Cor Hurkens for his useful remarks and suggestions and for his help with the computational experiments and an anonymous referee for his comments on an earlier draft of the paper  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s101070050071">doi:10.1007/s101070050071</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/x4zpha7ocves7puxz742ebeoqy">fatcat:x4zpha7ocves7puxz742ebeoqy</a> </span>
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