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Approximation schemes for the Min-Max Starting Time Problem

Leah Epstein, Tamir Tassa
2004 Acta Informatica  
Our main result is a polynomial time approximation scheme for this problem in the case where m is considered as part of the input.  ...  We consider the off-line scheduling problem of minimizing the maximal starting time.  ...  The authors would like to thank Yossi Azar from Tel-Aviv University for his helpful suggestions.  ... 
doi:10.1007/s00236-004-0145-z fatcat:jxlq552tjzd7xjwpcj2jknsvva

Approximation Schemes for the Min-Max Starting Time Problem [chapter]

Leah Epstein, Tamir Tassa
2003 Lecture Notes in Computer Science  
Our main result is a polynomial time approximation scheme for this problem in the case where m is considered as part of the input.  ...  We consider the off-line scheduling problem of minimizing the maximal starting time.  ...  The authors would like to thank Yossi Azar from Tel-Aviv University for his helpful suggestions.  ... 
doi:10.1007/978-3-540-45138-9_35 fatcat:ughad4mb4vf2xpfvu6de4n3qmm

Bounded single-machine parallel-batch scheduling with release dates and rejection

Lingfa Lu, T.C.E. Cheng, Jinjiang Yuan, Liqi Zhang
2009 Computers & Operations Research  
For the general problem, we provide a 2-approximation algorithm and a polynomial-time approximation scheme.  ...  We consider the bounded single-machine parallel-batch scheduling problem with release dates and rejection.  ...  Acknowledgments This research was supported in part by the Research Grants Council of Hong Kong under grant number N-PolyU502/07.  ... 
doi:10.1016/j.cor.2008.12.003 fatcat:ju3y4aakebdcbo34n3fx3v3oky

Parallel-Machine Scheduling with Time-Dependent and Machine Availability Constraints

Cuixia Miao, Juan Zou
2015 Mathematical Problems in Engineering  
For the total completion time minimization problem, we analyze the strong NP-hardness, and we present a dynamic programming algorithm and a fully polynomial time approximation scheme for the two-machine  ...  We consider the parallel-machine scheduling problem in which the machines have availability constraints and the processing time of each job is simple linear increasing function of its starting times.  ...  Acknowledgments The authors thank the editor and the anonymous reviewers for their helpful and detailed comments on an earlier version of their paper.  ... 
doi:10.1155/2015/956158 fatcat:2flpozsvbfgwvpq47biqyskjjy

Scheduling Simple Linear Deteriorating Jobs with Rejection

Juan Zou, Yuzhong Zhang
2014 Mathematical Problems in Engineering  
We show that the problem is NP-hard in the strong sense and presents a fully polynomial time approximation scheme to solve it when all jobs have agreeable release dates and due dates.  ...  When the jobs have identical release dates, we first propose a fully polynomial time approximation scheme to solve it.  ...  The problem 1 | , = , | max ( ) + ∑ ∈ is strongly NP-hard, so it has no fully polynomial time approximation scheme unless = . 3. 2. An FPTAS for One Special Case.  ... 
doi:10.1155/2014/170475 fatcat:xtp6535nvjgirdxnqsrwufkzpm

Approximating Min-Max (Regret) Versions of Some Polynomial Problems [chapter]

Hassene Aissi, Cristina Bazgan, Daniel Vanderpooten
2006 Lecture Notes in Computer Science  
For a bounded number of scenarios, we establish a general approximation scheme which can be used for min-max and min-max regret versions of some polynomial problems.  ...  While the complexity of min-max and min-max regret versions of most classical combinatorial optimization problems has been thoroughly investigated, there are very few studies about their approximation.  ...  on the running time of the approximation scheme for the multi-objective version.  ... 
doi:10.1007/11809678_45 fatcat:xhxydjkcibdajbl2z6tnzdptle

A Note on a Fully Polynomial-Time Approximation Scheme for Minimizing Makespan of Deteriorating Jobs

Long Wan
2013 Mathematical Problems in Engineering  
So the fully polynomial-time approximation scheme is also invalid.  ...  In (1998), Kovalyov and Kubiak studied the problem of scheduling n deteriorating jobs on a single machine to minimize makespan.  ...  A family of (1 + )approximation algorithm { } defines a fully polynomialtime approximation scheme (FPTAS for short), if for any > 0, runs in time bounded by a polynomial of , , and 1/ , where = log max  ... 
doi:10.1155/2013/957494 fatcat:x2xwtwal4baszjcjadtbqdrfea

Minimizing the makespan on a single parallel batching machine

Shenpeng Lu, Haodi Feng, Xiuqian Li
2010 Theoretical Computer Science  
First, we give a polynomial time approximation scheme (PTAS) for the case where jobs can be split. Then, we propose a 2-approximation algorithm for the special case with identical release dates.  ...  Finally, we present an approximation algorithm for the general problem with worst-case ratio 2 + , where > 0 is an arbitrarily small constant.  ...  For the problem 1|p-batch, B < n, r j |C max + W , Lu et al. [14] proved that it is unary NP-hard, then gave a 2-approximation algorithm and a polynomial time approximation scheme.  ... 
doi:10.1016/j.tcs.2009.12.008 fatcat:6ogkhsl4ubgu3mhj6zdi6wcqne

Penalty Methods for the Solution of Discrete HJB Equations—Continuous Control and Obstacle Problems

J. H. Witte, C. Reisinger
2012 SIAM Journal on Numerical Analysis  
In this paper, we present a novel penalty approach for the numerical solution of continuously controlled HJB equations and HJB obstacle problems.  ...  Our results include estimates of the penalisation error for a class of penalty terms, and we show that variations of Newton's method can be used to obtain globally convergent iterative solvers for the  ...  We thank Guy Barles, Laboratoire de Mathématiques et Physique Théorique, Tours, for many helpful comments.  ... 
doi:10.1137/110835840 fatcat:rpv4ywuo6ff67f3oxb3u5fqg3q

UAV Trajectory and Communication Co-design: Flexible Path Discretization and Path Compression [article]

Yijun Guo, Changsheng You, Changchuan Yin, Rui Zhang
2020 arXiv   pre-print
To tackle the challenge of infinite design variables arising from the continuous-time UAV trajectory optimization, a commonly adopted approach is by approximating the UAV trajectory with piecewise-linear  ...  non-designable waypoints are used in calculating the approximated communication utility along the UAV trajectory for ensuring high trajectory discretization accuracy.  ...  travel nearby each SN (resembling the traveling-salesman-problem (TSP) solution [1] In Figs. 8(a) and 8(b), we compare the max-min rate and algorithm running time of the proposed FPD-PC scheme based  ... 
arXiv:2010.07068v1 fatcat:2zk2kgs2jnfcllp4hloxreox3m

Optimum Broadcasting in Complete Weighted-Vertex Graphs [chapter]

Hovhannes Harutyunyan, Shahin Kamali
2010 Lecture Notes in Computer Science  
+ guess value for broadcast time br Output: A broadcast scheme (tree) completes in time br OR BadGuess Let α be the soonest time to inform an uninformed node If α + ω(min)+ 1+ω(max) ≤ br Stick min to  ...  Conference 13 2nd Canadian Discrete and Algorithmic Mathematics Conference 14 α + ω(min)+ 1+ω(max) = Existing Results NP-hardness Linear algorithm for trees (represent schemes with trees) Approximation  ... 
doi:10.1007/978-3-642-11266-9_41 fatcat:pfyccmelijcr3ibqwarxy2snhe

An FPTAS for scheduling jobs with piecewise linear decreasing processing times to minimize makespan

Min Ji, T.C.E. Cheng
2007 Information Processing Letters  
The objective is to minimize makespan. We first give a fully polynomialtime approximation scheme (FPTAS) for the case with a single machine.  ...  start time.  ...  In Section 2 we propose a fully polynomialtime approximation scheme for the problem 1|p j = a j −b j min{s j , D}|C max , and prove its correctness and establish its time complexity.  ... 
doi:10.1016/j.ipl.2006.11.014 fatcat:mncsyrom25enlbduy7mgmrtuka

Min-Max quickest path problems

Stefan Ruzika, Markus Thiemann
2012 Networks  
In this article, min-max versions of robust quickest path problems are investigated and, depending on their complexity status, exact algorithms or fully polynomial-time approximation schemes are proposed  ...  In a dynamic network, the quickest path problem asks for a path such that a given amount of flow can be sent from source to sink via this path in minimal time.  ...  Further research should also concentrate on robust versions of other (dynamic) network flow problems, including maximum (dynamic) flows, quickest flows, and minimum cost flows.  ... 
doi:10.1002/net.21473 fatcat:ceep2f4rrjfunjsnlaqjr7c5qe

On scenario aggregation to approximate robust combinatorial optimization problems

André Chassein, Marc Goerigk
2017 Optimization Letters  
As most robust combinatorial min-max and min-max regret problems with discrete uncertainty sets are NP-hard, research in approximation algorithm and approximability bounds has been a fruitful area of recent  ...  Our method can be applied to minmax as well as min-max regret problems.  ...  We show that if the min-max problem for a constant number of scenarios is sufficiently approximable, then there is a polynomial-time εK-approximation for any constant ε > 0.  ... 
doi:10.1007/s11590-017-1206-x fatcat:z3lcaafo7ffunjmgc6ymq4b7dy

Parallel-Batch Scheduling with Two Models of Deterioration to Minimize the Makespan

Cuixia Miao
2014 Abstract and Applied Analysis  
And we propose fully polynomial time approximation schemes to solve the identical-parallel-machine problem and uniform-parallel-machine problem, respectively.  ...  The objective is to minimize the makespan. We presentO(n log n)time algorithms for the single-machine problems, respectively.  ...  Acknowledgments The author thanks the anonymous reviewers for their helpful and detailed comments on an earlier version of our paper. This work was supported by the National Natural  ... 
doi:10.1155/2014/495187 fatcat:j6sfmkrfrvaxpoziarmlqup2fq
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