scholarly journals Branch and Bound Algorithm for Dependency Parsing with Non-local Features

2013 ◽  
Vol 1 ◽  
pp. 37-48 ◽  
Author(s):  
Xian Qian ◽  
Yang Liu
Keyword(s):  
Dynamic Programming ◽  
Computational Complexity ◽  
Branch And Bound ◽  
Graphical Models ◽  
Upper Bound ◽  
Local Features ◽  
Dependency Parsing ◽  
Non Local ◽  
Efficient Decoding ◽  
High Computational Complexity

Graph based dependency parsing is inefficient when handling non-local features due to high computational complexity of inference. In this paper, we proposed an exact and efficient decoding algorithm based on the Branch and Bound (B&B) framework where non-local features are bounded by a linear combination of local features. Dynamic programming is used to search the upper bound. Experiments are conducted on English PTB and Chinese CTB datasets. We achieved competitive Unlabeled Attachment Score (UAS) when no additional resources are available: 93.17% for English and 87.25% for Chinese. Parsing speed is 177 words per second for English and 97 words per second for Chinese. Our algorithm is general and can be adapted to non-projective dependency parsing or other graphical models.

scholarly journals Revisiting Modified Greedy Algorithm for Monotone Submodular Maximization with a Knapsack Constraint

2021 ◽  
Vol 5 (1) ◽  
pp. 1-22
Author(s):  
Jing Tang ◽  
Xueyan Tang ◽  
Andrew Lim ◽  
Kai Han ◽  
Chongshou Li ◽  
...  
Keyword(s):  
Approximation Algorithms ◽  
Greedy Algorithm ◽  
Branch And Bound ◽  
Upper Bound ◽  
Optimization Problem ◽  
Approximation Factor ◽  
Real World Application ◽  
Efficiency Of Algorithms ◽  
Knapsack Constraint ◽  
Submodular Maximization

Monotone submodular maximization with a knapsack constraint is NP-hard. Various approximation algorithms have been devised to address this optimization problem. In this paper, we revisit the widely known modified greedy algorithm. First, we show that this algorithm can achieve an approximation factor of 0.405, which significantly improves the known factors of 0.357 given by Wolsey and (1-1/e)/2\approx 0.316 given by Khuller et al. More importantly, our analysis closes a gap in Khuller et al.'s proof for the extensively mentioned approximation factor of (1-1/\sqrte )\approx 0.393 in the literature to clarify a long-standing misconception on this issue. Second, we enhance the modified greedy algorithm to derive a data-dependent upper bound on the optimum. We empirically demonstrate the tightness of our upper bound with a real-world application. The bound enables us to obtain a data-dependent ratio typically much higher than 0.405 between the solution value of the modified greedy algorithm and the optimum. It can also be used to significantly improve the efficiency of algorithms such as branch and bound.

scholarly journals Single-Manufacturer Multi-Retailer Supply Chain Models with Discrete Stochastic Demand

2021 ◽  
Vol 13 (15) ◽  
pp. 8271
Author(s):  
Yaqing Xu ◽  
Jiang Zhang ◽  
Zihao Chen ◽  
Yihua Wei
Keyword(s):  
Dynamic Programming ◽  
Supply Chain ◽  
Computational Complexity ◽  
Stackelberg Game ◽  
Programming Model ◽  
Dynamic Programming Method ◽  
Game Model ◽  
Chain Model ◽  
Stochastic Demands ◽  
Demand Models

Although there are highly discrete stochastic demands in practical supply chain problems, they are seldom considered in the research on supply chain systems, especially the single-manufacturer multi-retailer supply chain systems. There are no significant differences between continuous and discrete demand supply chain models, but the solutions for discrete random demand models are more challenging and difficult. This paper studies a supply chain system of a single manufacturer and multiple retailers with discrete stochastic demands. Each retailer faces a random discrete demand, and the manufacturer utilizes different wholesale prices to influence each retailer’s ordering decision. Both Make-To-Order and Make-To-Stock scenarios are considered. For each scenario, the corresponding Stackelberg game model is constructed respectively. By proving a series of theorems, we transfer the solution of the game model into non-linear integer programming model, which can be easily solved by a dynamic programming method. However, with the increase in the number of retailers and the production capacity of manufacturers, the computational complexity of dynamic programming drastically increases due to the Dimension Barrier. Therefore, the Fast Fourier Transform (FFT) approach is introduced, which significantly reduces the computational complexity of solving the supply chain model.

scholarly journals Research on Optimization Algorithm Design Techniques

2019 ◽  
Vol 8 (6S3) ◽  
pp. 1991-1992
Keyword(s):  
Dynamic Programming ◽  
State Space ◽  
Branch And Bound ◽  
Optimization Algorithm ◽  
Feasible Solution ◽  
Algorithm Design ◽  
Optimization Techniques ◽  
Greedy Method ◽  
Design Techniques

This paper discusses various optimization algorithm design techniques. So, optimization techniques which are discussed in this paper are greedy method, dynamic programming and branch and bound. Problem comes under optimization are used to find either maximum or minimum. All these techniques we have multiple inputs and some constraints and we have to find feasible solution using these inputs and constraints. In greedy method we follow some predefined method. Using that predefined method, we reach to the solution. On contrary to this in dynamic programming we take decision at every step and in the end we reach to the solution. In branch and bound we create state space tree and explore all possibilities of live node. Based on some constraint we start killing some alive nodes. Here, firstly I will discuss all the design techniques. Then types of problems that can be solved under each design techniques and their time complexities.

scholarly journals Branch and Bound Method to Solve Multi Objectives Function

2016 ◽  
Vol 12 (3) ◽  
pp. 5964-5974
Author(s):  
Tahani Jabbar Kahribt ◽  
Mohammed Kadhim Al- Zuwaini
Keyword(s):  
Lower Bounds ◽  
Branch And Bound ◽  
Single Machine ◽  
Upper Bound ◽  
Completion Time ◽  
Heuristic Method ◽  
Total Weighted Completion Time ◽  
Branch And Bound Method ◽  
Special Cases ◽  
Weighted Completion Time

This paper  presents  a  branch  and  bound  algorithm  for  sequencing  a  set  of  n independent  jobs  on  a single  machine  to  minimize sum of the discounted total weighted completion time and maximum lateness,  this problems is NP-hard. Two lower bounds were proposed and heuristic method to get an upper bound. Some special cases were  proved and some dominance rules were suggested and proved, the problem solved with up to 50 jobs.

Divide and recombine (D&R) data science projects for deep analysis of big data and high computational complexity

2018 ◽  
Vol 1 (1) ◽  
pp. 139-156 ◽  
Author(s):  
Wen-wen Tung ◽  
Ashrith Barthur ◽  
Matthew C. Bowers ◽  
Yuying Song ◽  
John Gerth ◽  
...  
Keyword(s):  
Big Data ◽  
Computational Complexity ◽  
Data Science ◽  
Science Projects ◽  
High Computational Complexity
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