Approximation Algorithms for Product-Form Networks

2003 ◽  
pp. 379-420
Keyword(s):  
Approximation Algorithms ◽  
Product Form

A preliminary semantic differential study on users' product form perception

2003 ◽  
Author(s):  
Shi-Jian Luo ◽  
Ming-Xi Tang ◽  
Shang-Shang Zhu ◽  
John Hamilton Frazer ◽  
Shou-Qian Sun ◽  
...  
Keyword(s):  
Semantic Differential ◽  
Product Form ◽  
Form Perception

Ceramic-ware along the Ancient Silk Trade Route—A Short Study of Cross-Cultural Influences on Product Form

2016 ◽  
Vol 4 (2) ◽  
pp. 84-97
Author(s):  
Ravi Mokashi Punekar ◽  
◽  
Shiva Ji ◽  
Keyword(s):  
Material Culture ◽  
Cultural Influences ◽  
Cross Cultural ◽  
Product Form ◽  
Ceramic Ware ◽  
Ancient Times ◽  
Silk Route ◽  
Trade Route ◽  
Multiple Domains ◽  
Trading Routes

The exchange of goods and materials by way of trading and exchanges were common in ancient times between India and China via silk route and other trading routes. The movement of people from one place to another brought exchange of not only materials but also techniques and processes and helped to establish their own manufacturing facilities and craftsmanship. This has resulted into a cross-cultural influence over the craft forms as reflected in many resemblances of material culture, annotations and apologies seen in various forms and shapes in multiple domains such as ceramic pottery, glazed pottery, metalware, ship buildings, printing, silk and other fabrics, patterns and motifs etc. Observations of ancient remains from Belitung and artifacts from Indian cities along secondary and tertiary Silk routes, show significant influence in the similarities in techniques, materials, surface treatments, kiln processes, colors, motifs , etc. This paper examines a cross-cultural resemblance of product form factor between Changsha pottery and pots to ceramic ware from eastern parts and metalware from western regions of India like Gujarat and Rajasthan. The spread of Buddhism from India to China and other eastern and south eastern countries during this period must also form a strong reason for this cultural exchange.

State-dependent signalling in queueing networks

1994 ◽  
Vol 26 (02) ◽  
pp. 436-455 ◽  
Author(s):  
W. Henderson ◽  
B. S. Northcote ◽  
P. G. Taylor
Keyword(s):  
Queueing Networks ◽  
State Dependence ◽  
Product Form ◽  
Batch Size ◽  
Single Server ◽  
Negative Customers ◽  
Affect Control ◽  
State Dependent ◽  
Special Cases ◽  
Equilibrium Distributions

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network. This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

Approximation Algorithms for Submodular Data Summarization with a Knapsack Constraint

2021 ◽  
Vol 5 (1) ◽  
pp. 1-31
Author(s):  
Kai Han ◽  
Shuang Cui ◽  
Tianshuai Zhu ◽  
Enpei Zhang ◽  
Benwei Wu ◽  
...  
Keyword(s):  
Approximation Algorithms ◽  
Fundamental Problem ◽  
Randomized Algorithm ◽  
Deterministic Algorithm ◽  
Submodular Function ◽  
Approximation Ratio ◽  
Performance Bounds ◽  
Data Summarization ◽  
Submodular Optimization ◽  
Knapsack Constraint

Data summarization, i.e., selecting representative subsets of manageable size out of massive data, is often modeled as a submodular optimization problem. Although there exist extensive algorithms for submodular optimization, many of them incur large computational overheads and hence are not suitable for mining big data. In this work, we consider the fundamental problem of (non-monotone) submodular function maximization with a knapsack constraint, and propose simple yet effective and efficient algorithms for it. Specifically, we propose a deterministic algorithm with approximation ratio 6 and a randomized algorithm with approximation ratio 4, and show that both of them can be accelerated to achieve nearly linear running time at the cost of weakening the approximation ratio by an additive factor of ε. We then consider a more restrictive setting without full access to the whole dataset, and propose streaming algorithms with approximation ratios of 8+ε and 6+ε that make one pass and two passes over the data stream, respectively. As a by-product, we also propose a two-pass streaming algorithm with an approximation ratio of 2+ε when the considered submodular function is monotone. To the best of our knowledge, our algorithms achieve the best performance bounds compared to the state-of-the-art approximation algorithms with efficient implementation for the same problem. Finally, we evaluate our algorithms in two concrete submodular data summarization applications for revenue maximization in social networks and image summarization, and the empirical results show that our algorithms outperform the existing ones in terms of both effectiveness and efficiency.

scholarly journals Approximation Algorithms for Maximin Fair Division

2020 ◽  
Vol 8 (1) ◽  
pp. 1-28
Author(s):  
Siddharth Barman ◽  
Sanath Kumar Krishnamurthy
Keyword(s):  
Approximation Algorithms ◽  
Fair Division

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.

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