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Quasi-PTAS for Scheduling with Precedences using LP Hierarchies [article]

Shashwat Garg
2017 arXiv   pre-print
We show that for fixed m and ϵ, ( n)^O(1) rounds of Sherali-Adams hierarchy applied to a natural LP of the problem provides a (1+ϵ)-approximation algorithm running in quasi-polynomial time.  ...  A central problem in scheduling is to schedule n unit size jobs with precedence constraints on m identical machines so as to minimize the makespan.  ...  Acknowledgements We would to like to thank Seeun William Umboh, Martin Böhm and Nikhil Bansal for helpful discussions throughout this work.  ... 
arXiv:1708.04369v1 fatcat:zvuphrbeenflbf53ia7ivhj2si

Quasi-PTAS for Scheduling with Precedences using LP Hierarchies

Shashwat Garg, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
We show that for fixed m and , polylog(n) rounds of Sherali-Adams hierarchy applied to a natural LP of the problem provides a (1+ )-approximation algorithm running in quasi-polynomial time.  ...  A central problem in scheduling is to schedule n unit size jobs with precedence constraints on m identical machines so as to minimize the makespan.  ...  Acknowledgements We would like to thank Seeun William Umboh, Martin Böhm and Nikhil Bansal for helpful discussions throughout this work.  ... 
doi:10.4230/lipics.icalp.2018.59 dblp:conf/icalp/Garg18 fatcat:7f2q4xdvgngwnarimvoxzecvda

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

Elaine Levey, Thomas Rothvoss
2018 arXiv   pre-print
We prove that for any fixed ε and m, an LP-hierarchy lift of the time-indexed LP with a slightly super poly-logarithmic number of r = ((n))^Θ( n) rounds provides a (1 + ε)-approximation.  ...  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.  ...  The main claim is that for any interval I * , LP-hierarchy solution x * and a set of jobs J * with x * j,I * = 1 we can schedule almost all jobs from J * within I * while respecting all precedence constraints  ... 
arXiv:1509.07808v2 fatcat:hkfsiy56evfqrgpivxk3v46gpi

Towards PTAS for Precedence Constrained Scheduling via Combinatorial Algorithms [article]

Shi Li
2020 arXiv   pre-print
For this problem, we show that the conditioning operations on the lifted LP solution can be replaced by making guesses about the optimum schedule.  ...  We study the classic problem of scheduling n precedence constrained unit-size jobs on m = O(1) machines so as to minimize the makespan.  ...  If we use the LP hierarchy framework, we need 1-level in the LP hierarchy for each guess, which corresponds to a multiplicative factor of poly(n) in the running time.  ... 
arXiv:2004.01231v2 fatcat:jr2ng534lvfolj2xdriy4i6bzu

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

Sami Davies, Janardhan Kulkarni, Thomas Rothvoss, Jakub Tarnawski, Yihao Zhang
2020 arXiv   pre-print
We consider the classic problem of scheduling jobs with precedence constraints on identical machines to minimize makespan, in the presence of communication delays.  ...  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  ...  Preliminaries The Sherali-Adams Hierarchy for LPs with Assignment Constraints In this section, we review the Sherali-Adams hierarchy which provides an automatic strengthening of linear relaxations for  ... 
arXiv:2004.09682v1 fatcat:yhympzbzqnbjxkezr5p7g4mary

8th International Colloquium on Automata, Languages and Programming (ICALP 81)

1981 IEEE Transactions on Software Engineering  
"Quasi-PTAS for Scheduling with Precedences using LP Hierarchies". Track B: Sarah Winter. "Uniformization problems for synchronizations of automatic relations on words".  ...  This year ICALP also solicitated brief announcements of work in progress with substantial interest for the community.  ... 
doi:10.1109/tse.1981.234528 fatcat:ob65j2ybgzbgba6y6ar7bczb6a

Strengths and Limitations of Linear Programming Relaxations

Abbas Bazzi
2017
Acknowledgements Acknowledgements Acknowledgements obtenons une NP-difficulté égale à 2 − ε pour le problème de "makespan minimization for scheduling with preemption on identical parallel machines" et  ...  une super constante d'inapproximabilité pour le problème de "scheduling on related parallel machines".  ...  Scheduling with Precedence Constraints.  ... 
doi:10.5075/epfl-thesis-7948 fatcat:yinseychxvcgrap7kdtkz6may4

Enclosing rail capacity/punctuality in accessibility measures: a two-step approach by using Data Envelopment Analysis and Analytic Hierarchy Process

Francesco Rotoli, Elena Navajas Cawood, Lorenzo Vannacci
2015 2015 International Conference on Industrial Engineering and Systems Management (IESM)  
, their schedules and the associated transportation itineraries for the forecast demand.  ...  We conclude with a number of challenging research directions.  ...  Analytical hierarchy process has been used to measure project complexity [4] .  ... 
doi:10.1109/iesm.2015.7380133 fatcat:hbiqir2zo5bejlasdudkjzom2e

Minimum color‐degree perfect b ‐matchings

Mariia Anapolska, Christina Büsing, Martin Comis, Tabea Krabs
2020 Networks  
The last speaker of the session will chair the session, with two exceptions for PhD-only sessions: Combinatorial Optimization (Mon 18, Room PP, 16-17) chaired by R.  ...  Schedule The seminar rooms are the Paul Painlevé (PP), the Robert Faure (Z) and the Jean-Baptiste Say (Y) amphitheatres, located in Access 1, lower ground floor.  ...  We use Ipopt [5] as local solver for both MWU and MS and Couenne [3] as global solver. For both the local solver and the global one we maintain the default settings.  ... 
doi:10.1002/net.21974 fatcat:4qgtutmxrrcy7anvxks4fivcii

Decomposition Methods for Nonlinear Optimization and Data Mining [article]

Brandon Dutra
2016 arXiv   pre-print
Finally, we end with an applied project using data science methods in medical research.  ...  Both polynomial decompositions have strengths and weaknesses, and we experiment with how to practically use them.  ...  Let us encode on which machine a job is scheduled by a binary variable: x ij :=      1 if job i is scheduled on machine j 0 else.  ... 
arXiv:1605.04983v1 fatcat:24io5ihhxvclbexqploxgji4m4

Complexity Theory, Game Theory, and Economics: The Barbados Lectures [article]

Tim Roughgarden
2019 arXiv   pre-print
be a PTAS for the problem.  ...  1,2 Three previous papers that used an ETH assumption (for NP) along with PCP machinery to prove quasi-polynomial-time lower bounds for NP problems are: 1. Aaronson et al.  ...  i ∈ [k], ì z −i denotes the (k − 1)-vector obtained by removing the ith component from ì z, and we identify (z i , ì z −i ) with ì z.  ... 
arXiv:1801.00734v2 fatcat:r6sz7jskqjbs7gxof52fbjikom

An investigation of the solution to the optimal power flow problem incorporating continuation methods

M. Huneault, F.D. Galiana
1990 IEEE Transactions on Power Systems  
Numerical simulations of the proposed optimal power flow algorithm using the minimum fuel cast task were performed 'on four test systems. with sizes •  ...  This constitutes an ex~mple of "incremental loadin& '. a technique already used for real power dispatch, but in this case a complete network model is used.  ...  W r pta. _ _ ..... ==a.. ... ____ y r ,... __ z r = _ o-D = bwA' ,.....  ... 
doi:10.1109/59.49093 fatcat:uhb5imvhirf67maap53wbuzysi

A Systems Thinking Approach to identify Leverage Points for Sustainability: A Case Study in the Cat Ba Biosphere Reserve, Vietnam

Nam C. Nguyen, Ockie J. H. Bosch
2012 Systems research and behavioral science  
For centuries humans have used top-down hierarchy systems in social institutions.  ...  This paper begins by defining lps and suggests criteria for determining what is and is not an lp.  ...  The schedule will provide ample time for relaxed social and professional interaction.  ... 
doi:10.1002/sres.2145 fatcat:2gofah363vaq3g43dbepghn4nu

Preventing blood-borne virus infection in people who inject drugs in the UK: systematic review, stakeholder interviews, psychosocial intervention development and feasibility randomised controlled trial

Gail Gilchrist, Davina Swan, April Shaw, Ada Keding, Sarah Towers, Noel Craine, Alison Munro, Elizabeth Hughes, Steve Parrott, Noreen Mdege, John Strang, Avril Taylor (+1 others)
2017 Health Technology Assessment  
A mean cost of £58.17 per participant was calculated for those attending one session, £148.54 for those attending two sessions and £270.67 for those attending all three sessions, compared with £0.86 in  ...  However, we have identified aspects where the service use questionnaire could be abbreviated given the low numbers reported in several care domains. No adverse events were reported.  ...  with the collection of outcome data for the feasibility trial (see Chapter 6) in London.  ... 
doi:10.3310/hta21720 pmid:29208190 fatcat:r4fmqbcwjnexvdorak2viwwxgi

Street Stops and Broken Windows: Terry, Race and Disorder in New York City

Jeffrey Fagan, Garth Davies
2001 Social Science Research Network  
enforcement. 74 However, the precinct commanders, who continued to meet with community groups, were now accountable to the NYPD's operational hierarchy for both their successes and their failures to produce  ...  The Street Crime Unit was disproportionately responsible for the use of stop and frisk actions to search for guns.  ...  society .... 177 Policing as a workplace is at once both regulated by the state but also subject to hierarchy, rules, coercion, formal sanctions, and restraint.  ... 
doi:10.2139/ssrn.257813 fatcat:y6thiccx4ve7tbwdywcet4kqwy
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