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Quasi-PTAS for Scheduling with Precedences using LP Hierarchies
[article]
2017
arXiv
pre-print
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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
2018
International Colloquium on Automata, Languages and Programming
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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]
2018
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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
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"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
2017
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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
2015
2015 International Conference on Industrial Engineering and Systems Management (IESM)
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, 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
2020
Networks
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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]
2016
arXiv
pre-print
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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]
2019
arXiv
pre-print
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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
1990
IEEE Transactions on Power Systems
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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
2012
Systems research and behavioral science
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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
2017
Health Technology Assessment
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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
2001
Social Science Research Network
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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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