scholarly journals An Optimal Approximation for Submodular Maximization Under a Matroid Constraint in the Adaptive Complexity Model

2021 ◽  
Author(s):  
Eric Balkanski ◽  
Aviad Rubinstein ◽  
Yaron Singer
Keyword(s):  
Greedy Algorithm ◽  
Fundamental Problem ◽  
Constant Factor ◽  
Optimal Approximation ◽  
Approximation Guarantee ◽  
Adaptive Complexity ◽  
Submodular Maximization ◽  
The Greedy Algorithm ◽  
Novel Algorithm

An Exponentially Faster Algorithm for Submodular Maximization Under a Matroid Constraint This paper studies the problem of submodular maximization under a matroid constraint. It is known since the 1970s that the greedy algorithm obtains a constant-factor approximation guarantee for this problem. Twelve years ago, a breakthrough result by Vondrák obtained the optimal 1 − 1/e approximation. Previous algorithms for this fundamental problem all have linear parallel runtime, which was considered impossible to accelerate until recently. The main contribution of this paper is a novel algorithm that provides an exponential speedup in the parallel runtime of submodular maximization under a matroid constraint, without loss in the approximation guarantee.

Precautionary rumor containment via trustworthy people in social networks

2016 ◽  
Vol 08 (01) ◽  
pp. 1650004 ◽  
Author(s):  
Lidan Fan ◽  
Weili Wu ◽  
Kai Xing ◽  
Wonjun Lee
Keyword(s):  
Greedy Algorithm ◽  
Constant Factor ◽  
Propagation Model ◽  
Information Propagation ◽  
Precautionary Measure ◽  
Real World Data ◽  
Rumor Propagation ◽  
Entire Network ◽  
Np Hardness ◽  
The Greedy Algorithm

In a social network, rumor containment is vital, as the diffusion of a rumor will bring terrible results. Precautionary measure can be used to control rumor propagation: Anticipating the spread of a rumor, one can (1) select a set of trustworthy people (TP) in the network, (2) alert the TP about the rumor, and (3) ask the TP to protect their neighbors by sending out alerts. In this paper, we study the problem of how to select the least number of TP, satisfying the requirement that the entire network is protected by the alerts that the TP send. We propose an asymmetric trust (AT) information propagation model. Under this model, we study the Least Number TP Selection (LNTS) problem, establish its NP-hardness and reformulate it as a minimum submodular cover problem. As a result, the Greedy Algorithm is a constant-factor approximation algorithm. Using real-world data, we evaluate the performance of the Greedy Algorithm, and compare it with other algorithms. Experimental results indicate that the Greedy Algorithm performs the best among its competitors.

scholarly journals Fast Pareto Optimization for Subset Selection with Dynamic Cost Constraints

2021 ◽  
Author(s):  
Chao Bian ◽  
Chao Qian ◽  
Frank Neumann ◽  
Yang Yu
Keyword(s):  
Objective Function ◽  
Greedy Algorithm ◽  
Real World ◽  
Fundamental Problem ◽  
Subset Selection ◽  
Selection Strategy ◽  
Cost Constraints ◽  
Approximation Guarantee ◽  
Changes Over Time ◽  
Over Time

Subset selection with cost constraints is a fundamental problem with various applications such as influence maximization and sensor placement. The goal is to select a subset from a ground set to maximize a monotone objective function such that a monotone cost function is upper bounded by a budget. Previous algorithms with bounded approximation guarantees include the generalized greedy algorithm, POMC and EAMC, all of which can achieve the best known approximation guarantee. In real-world scenarios, the resources often vary, i.e., the budget often changes over time, requiring the algorithms to adapt the solutions quickly. However, when the budget changes dynamically, all these three algorithms either achieve arbitrarily bad approximation guarantees, or require a long running time. In this paper, we propose a new algorithm FPOMC by combining the merits of the generalized greedy algorithm and POMC. That is, FPOMC introduces a greedy selection strategy into POMC. We prove that FPOMC can maintain the best known approximation guarantee efficiently.

Implementasi Algoritma Dijkstra Pada Game Pacman

CCIT Journal ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 170-176
Author(s):  
Anggit Dwi Hartanto ◽  
Aji Surya Mandala ◽  
Dimas Rio P.L. ◽  
Sidiq Aminudin ◽  
Andika Yudirianto
Keyword(s):  
Artificial Intelligence ◽  
Greedy Algorithm ◽  
Dijkstra Algorithm ◽  
Testing Phase ◽  
A Value ◽  
Route Problem ◽  
Starting Point ◽  
The Greedy Algorithm

Pacman is one of the labyrinth-shaped games where this game has used artificial intelligence, artificial intelligence is composed of several algorithms that are inserted in the program and Implementation of the dijkstra algorithm as a method of solving problems that is a minimum route problem on ghost pacman, where ghost plays a role chase player. The dijkstra algorithm uses a principle similar to the greedy algorithm where it starts from the first point and the next point is connected to get to the destination, how to compare numbers starting from the starting point and then see the next node if connected then matches one path with the path). From the results of the testing phase, it was found that the dijkstra algorithm is quite good at solving the minimum route solution to pursue the player, namely by getting a value of 13 according to manual calculations

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 An Optimized Algorithm and Test Bed for Improvement of Efficiency of ESS and Energy Use

Electronics ◽  
2018 ◽  
Vol 7 (12) ◽  
pp. 388 ◽  
Author(s):  
Seung-Mo Je ◽  
Jun-Ho Huh
Keyword(s):  
Greedy Algorithm ◽  
Energy Use ◽  
Storage System ◽  
Lithium Ion ◽  
Energy Storage System ◽  
Test Bed ◽  
C Language ◽  
Improvement Plan ◽  
The Republic ◽  
The Greedy Algorithm

The Republic of Korea (ROK) has four distinct seasons. Such an environment provides many benefits, but also brings some major problems when using new and renewable energies. The rainy season or typhoons in summer become the main causes of inconsistent production rates of these energies, and this would become a fatal weakness in supplying stable power to the industries running continuously, such as the aquaculture industry. This study proposed an improvement plan for the efficiency of Energy Storage System (ESS) and energy use. Use of sodium-ion batteries is suggested to overcome the disadvantages of lithium-ion batteries, which are dominant in the current market; a greedy algorithm and the Floyd–Warshall algorithm were also proposed as a method of scheduling energy use considering the elements that could affect communication output and energy use. Some significant correlations between communication output and energy efficiency have been identified through the OPNET-based simulations. The simulation results showed that the greedy algorithm was more efficient. This algorithm was then implemented with C-language to apply it to the Test Bed developed in the previous study. The results of the Test Bed experiment supported the proposals.

scholarly journals Enhanced Particle Swarm Optimization for Effective Relay Nodes Deployment in Wireless Sensor Networks

2021 ◽  
Vol 13 (1) ◽  
pp. 53-73
Author(s):  
Bader Alshaqqawi ◽  
Sardar Anisul Haque ◽  
Mohammed Alreshoodi ◽  
Ibrahim Alsukayti
Keyword(s):  
Wireless Sensor Networks ◽  
Particle Swarm Optimization ◽  
Sensor Networks ◽  
Greedy Algorithm ◽  
Pso Algorithm ◽  
Optimization Process ◽  
Wireless Sensor ◽  
Optimization Approach ◽  
Swarm Optimization ◽  
The Greedy Algorithm

One of the critical design problems in Wireless Sensor Networks (WSNs) is the Relay Node Placement (RNP) problem. Inefficient deployment of RNs would have adverse effects on the overall performance and energy efficiency of WSNs. The RNP problem is a typical example of an NP-hard optimization problem which can be addressed using metaheuristics with multi-objective formulation. In this paper, we aimed to provide an efficient optimization approach considering the unconstrained deployment of energy-harvesting RNs into a pre-established stationary WSN. The optimization was carried out for three different objectives: energy consumption, network coverage, and deployment cost. This was approached using a novel optimization approach based on the integration of the Particle Swarm Optimization (PSO) algorithm and a greedy technique. In the optimization process, the greedy algorithm is an essential component to provide effective guidance during PSO convergence. It supports the PSO algorithm with the required information to efficiently alleviate the complexity of the PSO search space and locate RNs in the spots of critical significance. The evaluation of the proposed greedy-based PSO algorithm was carried out with different WSN scenarios of varying complexity levels. A comparison was established with two PSO variants: the classical PSO and a PSO hybridized with the pattern search optimizer. The experimental results demonstrated the significance of the greedy algorithm in enhancing the optimization process for all the considered PSO variants. The results also showed how the solution quality and time efficiency were considerably improved by the proposed optimization approach. Such improvements were achieved using a simple integration technique without adding to the complexity of the system and introducing additional optimization stages. This was more evident in the RNP scenarios of considerably large search spaces, even with highly complex and challenging setups.

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