Submodular Maximization with Bounded Marginal Values

2021 ◽  
pp. 353-361
Author(s):  
Ruiqi Yang ◽  
Suixiang Gao ◽  
Changjun Wang ◽  
Dongmei Zhang
Keyword(s):  
Marginal Values ◽  
Submodular Maximization

COMMUNICATION OF COMMON AND MARGINAL CHARACTERISTICS OF CONDITIONS IN A TWO-CHANNEL SYSTEM WITH SIMPLE STREAMLINES OF APPLICATIONS

2017 ◽  
pp. 7-19 ◽  
Author(s):  
Georgiy Aleksandrovich Popov
Keyword(s):  
Operating Systems ◽  
Queue Length ◽  
Recurrence Relations ◽  
Queuing Systems ◽  
Channel System ◽  
Current Period ◽  
Multichannel Systems ◽  
Incoming Call ◽  
Marginal Values ◽  
Time Required

The article deals with a two-channel queuing system with a Poisson incoming call flow, in which the application processing time on each of the devices is different. Such models are used, in particular, when describing the operation of the system for selecting service requests in a number of operating systems. A complex system characteristic was introduced at the time of service endings on at least one of the devices, including the queue length, the remaining service time on the occupied device, and the time since the beginning of the current period of employment. This characteristic determines the state of the system at any time. Recurrence relations are obtained that connect this characteristic with its marginal values when there is no queue in the system. The method of introducing additional events was chosen as one of the main methods for analyzing the model. The relationships presented in this article can be used for analysis of the average characteristics of this system, as well as in the process of its simulation. Summarizing the results of work on multichannel systems with an arbitrary number of servicing devices will significantly reduce the time required for simulating complex systems described by sets of multichannel queuing systems.

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 A study on ground water quality of industrial area at Gajraula (U.P.), India

2009 ◽  
Vol 1 (2) ◽  
pp. 275-279 ◽  
Author(s):  
D. S. Malik ◽  
Pawan Kumar ◽  
Umesh Bharti
Keyword(s):  
Water Quality ◽  
Ground Water ◽  
Water Samples ◽  
Water Quality Index ◽  
Quality Index ◽  
Analytical Techniques ◽  
Industrial Area ◽  
Quality Standard ◽  
Quality Parameters ◽  
Marginal Values

The present study aims to identify the ground water contamination problem in villages located in the close vicinity of Gajraula industrial area at Gajraula (U.P.), India. Ground water samples were collected from different villages at the depth of 40 and 120 feet from earth’s surface layer. Analytical techniques as described in the standard methods for examination of water and waste water were adopted for physico-chemical analysis of ground water samples and the results compared with the standards given by WHO and BIS guidelines for drinking water. Water quality index was calculated for quality standard of ground water for drinking purposes. The present investigation revealed that the water quality is moderately degraded due to high range of seven water quality parameters such as Temperature (18.33-32.36 0C), conductivity (925.45-1399.59 μmho/cm), TDS (610.80-923.73 mgL-1), Alkalinity (260.17- 339.83 mgL-1), Ca-Hardness (129.68-181.17 mgL-1), Mg-Hardness (94.07-113.50 mgLÉ1) and COD (13.99-25.62 mgL-1). The water quality index (WQI) also indicated the all the water quality rating comes under the standard marginal values (45-64) i.e. water quality is frequently threatened or impaired and conditions usually depart from natural or desirable levels.

scholarly journals Deterministic Algorithms for Submodular Maximization Problems

2018 ◽  
Vol 14 (3) ◽  
pp. 1-20 ◽  
Author(s):  
Niv Buchbinder ◽  
Moran Feldman
Keyword(s):  
Deterministic Algorithms ◽  
Submodular Maximization

Two-stage submodular maximization problem beyond nonnegative and monotone

2021 ◽  
pp. 1-16
Author(s):  
Zhicheng Liu ◽  
Hong Chang ◽  
Ran Ma ◽  
Donglei Du ◽  
Xiaoyan Zhang
Keyword(s):  
Approximation Algorithms ◽  
Approximation Algorithm ◽  
Objective Function ◽  
Modular Function ◽  
Submodular Function ◽  
Maximization Problem ◽  
Cardinality Constraint ◽  
Two Stage ◽  
Time Efficiency ◽  
Submodular Maximization

Abstract We consider a two-stage submodular maximization problem subject to a cardinality constraint and k matroid constraints, where the objective function is the expected difference of a nonnegative monotone submodular function and a nonnegative monotone modular function. We give two bi-factor approximation algorithms for this problem. The first is a deterministic $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}}}} \right),1} \right)$ -approximation algorithm, and the second is a randomized $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}}}} \right) - \varepsilon ,1} \right)$ -approximation algorithm with improved time efficiency.

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