{"type":"ScholarlyArticle","title":"The Complexity Landscape of Resource-Constrained Scheduling","authors":[{"name":"Robert Ganian","slug":"robert-ganian","given":"Robert","family":"Ganian","affiliation":"Vienna University of Technology"},{"name":"Thekla Hamm","slug":"thekla-hamm","given":"Thekla","family":"Hamm","affiliation":"Vienna University of Technology"},{"name":"Guillaume Mescoff","slug":"guillaume-mescoff","given":"Guillaume","family":"Mescoff","affiliation":"Rennes University"}],"abstract":"The Resource-Constrained Project Scheduling Problem (RCPSP) and its extension via activity modes (MRCPSP) are well-established scheduling frameworks that have found numerous applications in a broad range of settings related to artificial intelligence. Unsurprisingly, the problem of finding a suitable schedule in these frameworks is known to be NP-complete; however, aside from a few results for special cases, we have lacked an in-depth and comprehensive understanding of the complexity of the problems from the viewpoint of natural restrictions of the considered instances.\r\n\r\nIn the first part of our paper, we develop new algorithms and give hardness-proofs in order to obtain a detailed complexity map of (M)RCPSP that settles the complexity of all 1024 considered variants of the problem defined in terms of explicit restrictions of natural parameters of instances. In the second part, we turn to implicit structural restrictions defined in terms of the complexity of interactions between individual activities. In particular, we show that if the treewidth of a graph which captures such interactions is bounded by a constant, then we can solve MRCPSP in polynomial time.","doi":"10.24963/ijcai.2020/241","url":"https://ijcai.org/proceedings/2020/241","pdf":"https://ijcai.org/proceedings/2020/0241.pdf","markdown":"https://ijcai.org/proceedings/2020/241.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/241","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":241,"pages":{"first":1741,"last":1747},"keywords":["Knowledge Representation and Reasoning: Computational Complexity of Reasoning","Planning and Scheduling: Scheduling","Planning and Scheduling: Theoretical Foundations of Planning"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/24845/file_24845.m3u8","length_sec":298,"provider":"hls"}],"references":[{"position":1,"raw":"[Arnborg et al., 1987] Stefan Arnborg, Derek G. Corneil, and Andrzej Proskurowski. Complexity of finding embed- dings in a k-tree. SIAM J. Algebraic Discrete Methods, 8(2):277-284, 1987.","title":"Complexity of finding embeddings in a k-tree","authors":"Stefan Arnborg, Derek G Corneil, Andrzej Proskurowski","year":"1987","venue":"SIAM J. Algebraic Discrete Methods","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Artigues et al., 2008] Christian Artigues, Sophie Demassey, and Emmanuel Neron. Resource-Constrained Project Scheduling: Models, Algorithms, Extensions and Appli- cations. ISTE/Wiley, 2008.","title":"Christian Artigues, Sophie Demassey, and Emmanuel Neron","authors":"Artigues","year":"2008","venue":"Resource-Constrained Project Scheduling: Models, Algorithms, Extensions and Applications","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Barrios et al., 2011] Agustín Barrios, Francisco Ballestín, and Vicente Valls. A double genetic algorithm for the mr- cpsp/max. Computers & OR, 38(1):33-43, 2011.","title":"Agustín Barrios, Francisco Ballestín, and Vicente Valls. A double genetic algorithm for the mrcpsp/max","authors":"Barrios","year":"2011","venue":"Computers & OR","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Blazewicz et al., 1983] Jacek Blazewicz, Jan Karel Lenstra, and A. H. G. Rinnooy Kan. Scheduling subject to resource constraints: classification and complexity. Discrete Ap- plied Mathematics, 5(1):11-24, 1983.","title":"Scheduling subject to resource constraints: classification and complexity","authors":"Jacek Blazewicz, Jan Karel Lenstra, A H G Rinnooy Kan","year":"1983","venue":"Discrete Applied Mathematics","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Bodlaender et al., 2016] Hans L. Bodlaender, Pål Grønås Drange, Markus S. Dregi, Fedor V. Fomin, Daniel Lok- shtanov, and Michal Pilipczuk. A c k n 5-approximation algorithm for treewidth. SIAM J. Comput., 45(2):317-378, 2016.","title":"A c k n 5-approximation algorithm for treewidth","authors":"L Hans, Pål Bodlaender, Markus S Grønås Drange, Dregi, V Fedor, Daniel Fomin, Michal Lokshtanov, Pilipczuk","year":"2016","venue":"SIAM J. Comput","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bofill et al., 2017] Miquel Bofill, Jordi Coll, Josep Suy, and Mateu Villaret. An efficient SMT approach to solve mr- cpsp/max instances with tight constraints on resources. In CP 2017, pages 71-79, 2017.","title":"An efficient SMT approach to solve mrcpsp/max instances with tight constraints on resources","authors":"Miquel Bofill, Jordi Coll, Josep Suy, Mateu Villaret","year":"2017","venue":"CP 2017","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Cohen et al., 2015] David A. Cohen, Martin C. Cooper, Pe- ter G. Jeavons, and Stanislav Zivny. Tractable classes of binary csps defined by excluded topological minors. In IJCAI 2015, pages 1945-1951, 2015.","title":"Tractable classes of binary csps defined by excluded topological minors","authors":"David A Cohen, Martin C Cooper, Peter G Jeavons, Stanislav Zivny","year":"2015","venue":"IJCAI 2015","doi":null,"url":null,"internal_url":"/proceedings/2015/276"},{"position":8,"raw":"[Cygan et al., 2015] Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. Parame- terized Algorithms. Springer, 2015.","title":"Parameterized Algorithms","authors":"Marek Cygan, V Fedor, Lukasz Fomin, Daniel Kowalik, Dániel Lokshtanov, Marcin Marx, Michal Pilipczuk, Saket Pilipczuk, Saurabh","year":"2015","venue":null,"doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Damay et al., 2007] Jean Damay, Alain Quilliot, and Eric Sanlaville. Linear programming based algorithms for pre- emptive and non-preemptive RCPSP. European J. of Op- erational Research, 182(3):1012-1022, 2007.","title":"Linear programming based algorithms for preemptive and non-preemptive RCPSP","authors":"Damay","year":"2007","venue":"European J. of Operational Research","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Downey and Fellows, 2013] Rodney G. Downey and Michael R. Fellows. Fundamentals of Parameterized Complexity. Texts in Computer Science. Springer, 2013.","title":"Fundamentals of Parameterized Complexity","authors":"Rodney G Downey, Michael R Fellows","year":"2013","venue":"Texts in Computer Science","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Du and Leung, 1989] Jianzhong Du and Joseph Y.-T. Le- ung. Complexity of scheduling parallel task systems. SIAM J. Discrete Math., 2(4):473-487, 1989.","title":"Complexity of scheduling parallel task systems","authors":"Jianzhong Du, Joseph Y.-T Leung","year":"1989","venue":"SIAM J. Discrete Math","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Fu et al., 2010] Na Fu, Pradeep Varakantham, and Hoong Chuin Lau. Towards finding robust execu- tion strategies for rcpsp/max with durational uncertainty. In ICAPS 2010, pages 73-80, 2010.","title":"Towards finding robust execution strategies for rcpsp/max with durational uncertainty","authors":"Na Fu, Pradeep Varakantham, Hoong Chuin Lau","year":"2010","venue":"ICAPS 2010","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Fu et al., 2016] Na Fu, Pradeep Varakantham, and Hoong Chuin Lau. Robust partial order schedules for rcpsp/max with durational uncertainty. In ICAPS 2016, pages 124-130, 2016.","title":"Robust partial order schedules for rcpsp/max with durational uncertainty","authors":"Na Fu, Pradeep Varakantham, Hoong Chuin Lau","year":"2016","venue":"ICAPS 2016","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Ganian and Ordyniak, 2018] Robert Ganian and Sebastian Ordyniak. The complexity landscape of decompositional parameters for ILP. Artif. Intell., 257:61-71, 2018.","title":"The complexity landscape of decompositional parameters for ILP","authors":"Robert Ganian, Sebastian Ordyniak","year":"2018","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Garey and Johnson, 1975] M. R. Garey and David S. John- son. Complexity results for multiprocessor scheduling un- der resource constraints. SIAM J. Comput., 4(4):397-411, 1975.","title":"Complexity results for multiprocessor scheduling under resource constraints","authors":"M R Garey, David S Johnson","year":"1975","venue":"SIAM J. Comput","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Garey and Johnson, 1979] M. R. Garey and David S. John- son. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979. [","title":"Computers and Intractability: A Guide to the Theory of NP-Completeness","authors":"M R Garey, David S Johnson","year":"1979","venue":null,"doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Gehrke et al., 2018] Jan Clemens Gehrke, Klaus Jansen, Stefan E. J. Kraft, and Jakob Schikowski. A PTAS for scheduling unrelated machines of few different types. Int. J. Found. Comput. Sci., 29(4):591-621, 2018.","title":"A PTAS for scheduling unrelated machines of few different types","authors":"Gehrke","year":"2018","venue":"Int. J. Found. Comput. Sci","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Gottlob et al., 2002] Georg Gottlob, Francesco Scarcello, and Martha Sideri. Fixed-parameter complexity in AI and nonmonotonic reasoning. Artif. Intell., 138(1-2):55-86, 2002.","title":"Fixed-parameter complexity in AI and nonmonotonic reasoning","authors":"Gottlob","year":"2002","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Kloks, 1994] Ton Kloks. Treewidth, Computations and Ap- proximations, volume 842 of LNCS. Springer, 1994.","title":"Computations and Approximations","authors":"Ton Kloks, Treewidth","year":"1994","venue":null,"doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Kolisch and Padman, 2001] R. Kolisch and R. Padman. An integrated survey of deterministic project scheduling. Omega, 29(3):249-272, 2001.","title":"An integrated survey of deterministic project scheduling","authors":"R Kolisch, R Padman","year":"2001","venue":"Omega","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Kuster et al., 2007] Jürgen Kuster, Dietmar Jannach, and Gerhard Friedrich. Handling alternative activities in resource-constrained project scheduling problems. In IJ- CAI 2007, pages 1960-1965, 2007.","title":"Handling alternative activities in resource-constrained project scheduling problems","authors":"Jürgen Kuster, Dietmar Jannach, Gerhard Friedrich","year":"2007","venue":"IJ-CAI 2007","doi":null,"url":null,"internal_url":"/proceedings/2007/316"},{"position":22,"raw":"[Poppenborg and Knust, 2016] Jens Poppenborg and Sigrid Knust. Modeling and optimizing the evacuation of hospi- tals based on the MRCPSP with resource transfers. EURO J. Computational Optimization, 4(3-4):349-380, 2016.","title":"Modeling and optimizing the evacuation of hospitals based on the MRCPSP with resource transfers","authors":"Knust Poppenborg, Jens Poppenborg, Sigrid Knust","year":"2016","venue":"EURO J. Computational Optimization","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Schwindt and Zimmermann, 2015] Christoph Schwindt and Jürgen Zimmermann. Handbook on Project Management and Scheduling Vol.1. Springer, 2015.","title":"Handbook on Project Management and Scheduling","authors":"Zimmermann Schwindt","year":"2015","venue":null,"doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Smith and Pyle, 2004] Tristan B. Smith and John M. Pyle. An effective algorithm for project scheduling with arbi- trary temporal constraints. In AAAI 2004, pages 544-549, 2004.","title":"An effective algorithm for project scheduling with arbitrary temporal constraints","authors":"Tristan B Smith, John M Pyle","year":"2004","venue":"AAAI 2004","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Song, 2017] Wen Song. Project scheduling in complex busi- ness environments. In AAAI 2017, pages 5052-5053, 2017.","title":"Project scheduling in complex business environments","authors":"Wen Song","year":"2017","venue":"AAAI 2017","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Thorup, 1998] Mikkel Thorup. All structured programs have small tree-width and good register allocation. Inf. Comput., 142(2):159-181, 1998.","title":"All structured programs have small tree-width and good register allocation","authors":"Mikkel Thorup, Thorup","year":"1998","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Uetz, 2011] Marc Uetz. Algorithms for Deterministic and Stochastic Scheduling. PhD thesis, 2011.","title":"Algorithms for Deterministic and Stochastic Scheduling","authors":"Marc Uetz","year":"2011","venue":null,"doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[van Bevern et al., 2016] René van Bevern, Robert Bred- ereck, Laurent Bulteau, Christian Komusiewicz, Nim- rod Talmon, and Gerhard J. Woeginger. Precedence- constrained scheduling problems parameterized by partial order width. In DOOR 2016, pages 105-120, 2016.","title":"Precedenceconstrained scheduling problems parameterized by partial order width","authors":"Van Bevern","year":"2016","venue":"DOOR 2016","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Varakantham et al., 2016] Pradeep Varakantham, Na Fu, and Hoong Chuin Lau. A proactive sampling approach to project scheduling under uncertainty. In AAAI 2016, pages 3195-3201, 2016.","title":"A proactive sampling approach to project scheduling under uncertainty","authors":"Pradeep Varakantham, Na Fu, Hoong Chuin Lau","year":"2016","venue":"AAAI 2016","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}