On an Optimal Deterministic Algorithm for SAT

1999 ◽  
pp. 179-187 ◽  
Author(s):  
Zenon Sadowski
Keyword(s):  
Deterministic Algorithm

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 Dynamic Markov Model: Password Guessing Using Probability Adjustment Method

2021 ◽  
Vol 11 (10) ◽  
pp. 4607
Author(s):  
Xiaozhou Guo ◽  
Yi Liu ◽  
Kaijun Tan ◽  
Wenyu Mao ◽  
Min Jin ◽  
...  
Keyword(s):  
Markov Model ◽  
Repetition Rate ◽  
Random Sampling ◽  
High Probability ◽  
Deterministic Algorithm ◽  
High Repetition Rate ◽  
Generation Process ◽  
Dynamic Distribution ◽  
Model Based ◽  
Optimal Adjustment

In password guessing, the Markov model is still widely used due to its simple structure and fast inference speed. However, the Markov model based on random sampling to generate passwords has the problem of a high repetition rate, which leads to a low cover rate. The model based on enumeration has a lower cover rate for high-probability passwords, and it is a deterministic algorithm that always generates the same passwords in the same order, making it vulnerable to attack. We design a dynamic distribution mechanism based on the random sampling method. This mechanism enables the probability distribution of passwords to be dynamically adjusted and tend toward uniform distribution strictly during the generation process. We apply the dynamic distribution mechanism to the Markov model and propose a dynamic Markov model. Through comparative experiments on the RockYou dataset, we set the optimal adjustment degree α. Compared with the Markov model without the dynamic distribution mechanism, the dynamic Markov model reduced the repetition rate from 75.88% to 66.50% and increased the cover rate from 37.65% to 43.49%. In addition, the dynamic Markov model had the highest cover rate for high-probability passwords. Finally, the model avoided the lack of a deterministic algorithm, and when it was run five times, it reached almost the same cover rate as OMEN.

scholarly journals A Primal-Dual Online Deterministic Algorithm for Matching with Delays

2018 ◽  
pp. 51-68 ◽  
Author(s):  
Marcin Bienkowski ◽  
Artur Kraska ◽  
Hsiang-Hsuan Liu ◽  
Paweł Schmidt
Keyword(s):  
Deterministic Algorithm ◽  
Primal Dual

scholarly journals DETERMINISTIC ANTS IN LABYRINTH — INFORMATION GAINED BY MAP SHARING

2013 ◽  
Vol 24 (06) ◽  
pp. 1350035
Author(s):  
JANUSZ MALINOWSKI ◽  
JAN W. KANTELHARDT ◽  
KRZYSZTOF KUŁAKOWSKI
Keyword(s):  
Complete Information ◽  
Deterministic Algorithm ◽  
Numerical Results ◽  
Square Lattice ◽  
Scaling Relations

A few ant robots are placed in a labyrinth, formed by a square lattice with a small number of corridors removed. Ants move according to a deterministic algorithm designed to explore all corridors. Each ant remembers the shape of corridors which it has visited. Once two ants meet, they share the information acquired. We evaluate how the time of getting a complete information by an ant depends on the number of ants, and how the length known by an ant depends on time. Numerical results are presented in the form of scaling relations.

scholarly journals Refined Deterministic Algorithm for Biplane Construction

2010 ◽  
Vol 18 (1) ◽  
pp. 45
Author(s):  
Ivica Martinjak ◽  
Mario-Osvin Pavcevic
Keyword(s):  
Deterministic Algorithm
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