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Parallel Approximation of Min-Max Problems

Gus Gutoski, Xiaodi Wu
2013 Computational Complexity  
This paper presents an efficient parallel approximation scheme for a new class of min-max problems.  ...  A special case of our result is a parallel approximation scheme for a specific class of semidefinite programs whose feasible region consists of lists of semidefinite matrices that satisfy a transcript-like  ...  Particularly, the alternative formulation of the strategies by density operators and measurements is inspired during the discussion with John Watrous. XW also wants to thank  ... 
doi:10.1007/s00037-013-0065-9 fatcat:y2mdtakesbhtjfl7ujuj5xr4cu

Parallel Approximation of Min-max Problems with Applications to Classical and Quantum Zero-Sum Games

Gus Gutoski, Xiaodi Wu
2012 2012 IEEE 27th Conference on Computational Complexity  
We also describe parallel implementations of this oracle for certain sets P, yielding an unconditionally efficient parallel approximation algorithm for the min-max problem (2) for those choices of P.  ...  This paper presents an efficient parallel algorithm for a new class of min-max problems based on the matrix multiplicative weights update method.  ...  GG's research is supported by the Government of Canada through Industry Canada, the Province of Ontario through the Ministry of Research and Innovation, NSERC, DTO-ARO, CIFAR, and QuantumWorks.  ... 
doi:10.1109/ccc.2012.12 dblp:conf/coco/GutoskiW12 fatcat:cnomniipjffrjatt32qllqvm6a

Parallel solution in time of ODEs: some achievements and perspectives

Pierluigi Amodio, Luigi Brugnano
2009 Applied Numerical Mathematics  
of the problem to be solved.  ...  The parallel solution of initial value problems for ordinary differential equations (ODE-IVPs) has received much interest from many researchers in the past years.  ...  iterations for the approximate solution of the reduced system; • (2) min - (2) max , i.e. the minimum and maximum number of conjugate gradient iterations required for solving the problems (28).  ... 
doi:10.1016/j.apnum.2008.03.024 fatcat:keveuug525gkjba72shiuv2dlm

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

Cuixia Miao, Juan Zou
2015 Mathematical Problems in Engineering  
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.  ...  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  ...  This work was supported by The National Natural Science Foundation of China (11201259), the Doctoral Fund of the Ministry of Education (20123705120001, 20123705110003), Domestic Visiting Scholar Program  ... 
doi:10.1155/2015/956158 fatcat:2flpozsvbfgwvpq47biqyskjjy

Page 3320 of Mathematical Reviews Vol. , Issue 2004d [page]

2004 Mathematical Reviews  
The max-min tiling problem is known to be NP-hard; here, we present first nontrivial approximation algorithms for solving it.”  ...  Given a weight bound W the goal of our max- min tiling problem is to find a tiling of A such that: (1) each tile is of weight at least W (the min condition), and (2) the number of tiles is maximized (the  ... 

Parallel Double Greedy Submodular Maximization

Xinghao Pan, Stefanie Jegelka, Joseph E. Gonzalez, Joseph K. Bradley, Michael I. Jordan
2014 Neural Information Processing Systems  
Many machine learning problems can be reduced to the maximization of submodular functions.  ...  The second, concurrency control approach guarantees a tight 1/2-approximation, at the quantifiable cost of additional coordination and reduced parallelism.  ...  This research was in part funded by the Office of Naval Research under contract/grant number N00014-11-1-0688. X. Pan's work is also supported by a DSO National Laboratories Postgraduate Scholarship.  ... 
dblp:conf/nips/PanJGBJ14 fatcat:2wc3canz4je3li26vigmycsrmy

Fully polynomial-time approximation schemes for time–cost tradeoff problems in series–parallel project networks

Nir Halman, Chung-Lun Li, David Simchi-Levi
2009 Operations Research Letters  
We consider the deadline problem and budget problem of the nonlinear time-cost tradeoff project scheduling model in a series-parallel activity network.  ...  We develop fully polynomial time approximation schemes for both problems using K-approximation sets and functions, together with series and parallel reductions.  ...  Acknowledgment This research was supported in part by the Research Grants Council of Hong Kong under grant PolyU5228/08E. Research is also supported by NSF Contract CMMI-0758069.  ... 
doi:10.1016/j.orl.2009.03.002 fatcat:rs4eweffkbbxpjryx76tsypzpe

A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties

Wencheng Wang, Xiaofei Liu
2021 Mathematics  
This problem generalizes a multiprocessor scheduling problem with rejection, the parallel-machine scheduling with submodular penalties, and the single machine scheduling problem with release dates and  ...  In this paper, we consider parallel-machine scheduling with release times and submodular penalties (P|rj,reject|Cmax+π(R)), in which each job can be accepted and processed on one of m identical parallel  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/math10010061 fatcat:hd25g46kd5et5os27m2i5yzjea

Page 4323 of Mathematical Reviews Vol. , Issue 94h [page]

1994 Mathematical Reviews  
of min-cut and max-cut problem.  ...  The existence of this bound is important because it implies that any feasible solution is a near-optimal approximation to such versions of the k-max-cut and k-min-cut problems.”  ... 

Approximation of the parallel machine scheduling problem with additional unit resources

Emmanuel Hebrard, Marie-José Huguet, Nicolas Jozefowiez, Adrien Maillard, Cédric Pralet, Gérard Verfaillie
2016 Discrete Applied Mathematics  
Moreover, the particular case of 2 parallel machines is also NP-hard since the problem P 2||C max is NP-hard, though pseudopolynomial.  ...  We show that the greedy heuristic MAXLOAD is a (2 − 2 m+1 )-approximation algorithm for the parallel machine scheduling problem with additional unit resources.  ...  Conclusion We have introduced a heuristic insertion algorithm for parallel machine scheduling problems with additional unit resources which is a (2 − 2 m+1 )-approximation.  ... 
doi:10.1016/j.dam.2016.07.003 fatcat:fn6xztz3tzbgfmpremwsgc2bni

Minimizing maximum fiber requirement in optical networks

Matthew Andrews, Lisa Zhang
2006 Journal of computer and system sciences (Print)  
On the positive side, we present algorithms with approximation ratios O(log m + log ), O(log D max + log ) and O(D max ) respectively, where D max is the length of the longest path.  ...  Our analysis is based on the hardness of approximating the chromatic numbers.  ...  Conclusions In this paper we have presented positive and negative results for approximating the MIN-FIBER problem.  ... 
doi:10.1016/j.jcss.2005.08.001 fatcat:gnjcffs55zbdhie36ffb2ijvca

Scheduling Simple Linear Deteriorating Jobs with Rejection

Juan Zou, Yuzhong Zhang
2014 Mathematical Problems in Engineering  
We consider the problems of scheduling deteriorating jobs with release dates on a single machine (parallel machines) and jobs can be rejected by paying penalties.  ...  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.  ...  ., max = max{ : ∈ }) plus the total penalty of the rejected jobs. In parallel-machine model, assume min{ | = 1, . . . , } = 0 > 0.  ... 
doi:10.1155/2014/170475 fatcat:xtp6535nvjgirdxnqsrwufkzpm

On the Bicriterion Maximum Flow Network Interdiction Problem [article]

Luca E. Schäfer, Stefan Ruzika, Sven O. Krumke, Carlos M. Fonseca
2020 arXiv   pre-print
We propose a pseudopolynomial time algorithm in the case of two-terminal series-parallel graphs and positive integer-valued interdiction costs.  ...  We extend this algorithm to a fully polynomial-time approximation scheme for the case of unit interdiction costs by appropriately partitioning the objective space.  ...  scheme and thus, addressing the gap of approximation schemes in network interdiction problems.  ... 
arXiv:2010.02730v2 fatcat:mmg3yzxw5fc2rmjxe4mypmeicu

Parallel Batch Scheduling of Deteriorating Jobs with Release Dates and Rejection

Juan Zou, Cuixia Miao
2014 The Scientific World Journal  
Then, we present two pseudopolynomial time algorithms and a fully polynomial-time approximation scheme to solve this problem.  ...  The objective is to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs. First, we show that the problem is NP-hard in the ordinary sense.  ...  [6, 7] presented new complexity results and approximation algorithms for the parallel batch scheduling problem subject to release dates.  ... 
doi:10.1155/2014/270942 pmid:25143969 pmcid:PMC4131089 fatcat:t7iuqe26fzdotem3e3p6fd5aba

Energy Efficiency in MIMO Interference Channels: Social Optimality and Max-Min Fairness

Yanq Yanql, Marius Pesavento
2018 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
To solve this multi-objective optimization problem, we consider both socially optimal solutions and max-min fairness solutions.  ...  iteration, and 2) efficient implementation as each approximate problem is natural for parallel computation and/or its solution has a closed-form expression.  ...  It consists of solving a sequence of successively refined approximate problems: in iteration t, the approximate problem defined around the point Q t consists of maximizing an approximate function, denoted  ... 
doi:10.1109/icassp.2018.8461910 dblp:conf/icassp/YanqlP18 fatcat:b4thgt6o3bfxflynpa67ousjua
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