scholarly journals Randomized heuristic for the maximum clique problem

2020 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Approximation Algorithm ◽  
Randomized Algorithm ◽  
Maximum Clique ◽  
Constant Factor ◽  
Maximum Clique Problem ◽  
Hard Problem ◽  
Np Hard ◽  
Np Hard Problem ◽  
Java Code ◽  
Clique Problem

<p>A clique in a graph is a set of vertices that are all directly connected</p><p>to each other i.e. a complete sub-graph. A clique of the largest size is</p><p>called a maximum clique. Finding the maximum clique in a graph is an</p><p>NP-hard problem and it cannot be solved by an approximation algorithm</p><p>that returns a solution within a constant factor of the optimum. In this</p><p>work, we present a simple and very fast randomized algorithm for the</p><p>maximum clique problem. We also provide Java code of the algorithm</p><p>in our git repository. Results show that the algorithm is able to find</p><p>reasonably good solutions to some randomly chosen DIMACS benchmark</p><p>graphs. Rather than aiming for optimality, we aim to find good solutions</p><p>very fast.</p>

scholarly journals Randomized heuristic for the maximum clique problem

2020 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Approximation Algorithm ◽  
Randomized Algorithm ◽  
Maximum Clique ◽  
Constant Factor ◽  
Maximum Clique Problem ◽  
Hard Problem ◽  
Np Hard ◽  
Np Hard Problem ◽  
Java Code ◽  
Clique Problem

<p>A clique in a graph is a set of vertices that are all directly connected</p><p>to each other i.e. a complete sub-graph. A clique of the largest size is</p><p>called a maximum clique. Finding the maximum clique in a graph is an</p><p>NP-hard problem and it cannot be solved by an approximation algorithm</p><p>that returns a solution within a constant factor of the optimum. In this</p><p>work, we present a simple and very fast randomized algorithm for the</p><p>maximum clique problem. We also provide Java code of the algorithm</p><p>in our git repository. Results show that the algorithm is able to find</p><p>reasonably good solutions to some randomly chosen DIMACS benchmark</p><p>graphs. Rather than aiming for optimality, we aim to find good solutions</p><p>very fast.</p>

scholarly journals GCLIQUE: An Open Source Genetic Algorithm for the Maximum Clique Problem

2020 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Genetic Algorithm ◽  
Maximum Clique ◽  
Maximum Size ◽  
The Other ◽  
Maximum Clique Problem ◽  
Hard Problem ◽  
Maximum Cliques ◽  
Np Hard Problem ◽  
Optimum Solution ◽  
Clique Problem

<p>A clique in a graph is a set of vertices that are all connected to each</p><p>other. A maximum clique is a clique of maximum size. A graph may have</p><p>more than one maximum cliques. The problem of finding a maximum</p><p>clique is a strongly hard NP-hard problem. It is not possible to find an</p><p>approximation algorithm which finds a maximum clique that is a constant</p><p>factor of the optimum solution. In this work, we present a genetic algorithm</p><p>for the maximum clique problem that is able to find optimum or</p><p>close to optimum solutions to most DIMACS graphs. The genetic algorithm</p><p>uses new crossover mechanisms which are able to find reasonably</p><p>good cliques which can then be used in other applications downstream.</p><p>We also provide C++ code for our algorithm. Results show that our algorithm</p><p>is able to find maximum cliques for most DIMACS instances, and</p><p>if not, close to optimum solutions for the other instances.</p>

scholarly journals GCLIQUE: An Open Source Genetic Algorithm for the Maximum Clique Problem

2020 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Genetic Algorithm ◽  
Maximum Clique ◽  
Maximum Size ◽  
The Other ◽  
Maximum Clique Problem ◽  
Hard Problem ◽  
Maximum Cliques ◽  
Np Hard Problem ◽  
Optimum Solution ◽  
Clique Problem

<p>A clique in a graph is a set of vertices that are all connected to each</p><p>other. A maximum clique is a clique of maximum size. A graph may have</p><p>more than one maximum cliques. The problem of finding a maximum</p><p>clique is a strongly hard NP-hard problem. It is not possible to find an</p><p>approximation algorithm which finds a maximum clique that is a constant</p><p>factor of the optimum solution. In this work, we present a genetic algorithm</p><p>for the maximum clique problem that is able to find optimum or</p><p>close to optimum solutions to most DIMACS graphs. The genetic algorithm</p><p>uses new crossover mechanisms which are able to find reasonably</p><p>good cliques which can then be used in other applications downstream.</p><p>We also provide C++ code for our algorithm. Results show that our algorithm</p><p>is able to find maximum cliques for most DIMACS instances, and</p><p>if not, close to optimum solutions for the other instances.</p>

HEURISTICS FOR THE TRANSPOSITION DISTANCE PROBLEM

2013 ◽  
Vol 11 (05) ◽  
pp. 1350013 ◽  
Author(s):  
ULISSES DIAS ◽  
ZANONI DIAS
Keyword(s):  
Information Retrieval ◽  
Approximation Algorithm ◽  
Computer Science ◽  
Large Scale ◽  
Hard Problem ◽  
Np Hard ◽  
String Processing ◽  
Minimum Number ◽  
Np Hard Problem ◽  
Distance Problem

Transpositions are large-scale mutational events that occur when a block of genes moves from a region of a chromosome to another region within the same chromosome. The transposition distance problem is the minimum number of transpositions required to transform one genome into another. Recently, Bulteau et al. [Bulteau L, Fertin G, Rusu U, Automata, Languages and Programming, Vol. 6755 of Lecture Notes in Computer Science, pp. 654–665, Springer Berlin, Heidelberg, 2011] proved that finding the transposition distance is a NP-Hard problem. Some approximation algorithm for this problem have been presented to date [Bafna V, Pevzner PA, SIAM J Discr Math11(2):224–240, 1998; Elias I, Hartman T, IEEE/ACM Trans Comput Biol Bioinform3(4):369–379, 2006; Mira CVG, Dias Z, Santos HP, Pinto GA, Walter ME, Proc 3rd Brazilian Symp Bioinformatics (BSB'2008), pp. 115–126, Santo André, Brazil, 2008; Walter MEMT, Dias Z, Meidanis J, Proc String Processing and Information Retrieval (SPIRE'2000), pp. 199–208, Coruña, Spain, 2000]. Here we focus on developing heuristics to provide an improved approximated solution. Our approach outperforms other algorithms on small sized permutations. We also show that our algorithm keeps the good performance on longer permutations.

Clique Finder

2022 ◽  
Vol 13 (2) ◽  
pp. 0-0
Keyword(s):  
Error Function ◽  
Computing Time ◽  
Maximum Clique ◽  
Maximum Clique Problem ◽  
Np Hard ◽  
Exact Methods ◽  
Real World Applications ◽  
Np Hard Problem ◽  
Hard Problems ◽  
Cooling Schedule

The Maximum Clique Problem (MCP) is a classical NP-hard problem that has gained considerable attention due to its numerous real-world applications and theoretical complexity. It is inherently computationally complex, and so exact methods may require prohibitive computing time. Nature-inspired meta-heuristics have proven their utility in solving many NP-hard problems. In this research, we propose a simulated annealing-based algorithm that we call Clique Finder algorithm to solve the MCP. Our algorithm uses a logarithmic cooling schedule and two moves that are selected in an adaptive manner. The objective (error) function is the total number of missing links in the clique, which is to be minimized. The proposed algorithm was evaluated using benchmark graphs from the open-source library DIMACS, and results show that the proposed algorithm had a high success rate.

scholarly journals Clique Finder

2022 ◽  
Vol 13 (2) ◽  
pp. 1-22
Author(s):  
Sarab Almuhaideb ◽  
Najwa Altwaijry ◽  
Shahad AlMansour ◽  
Ashwaq AlMklafi ◽  
AlBandery Khalid AlMojel ◽  
...  
Keyword(s):  
Error Function ◽  
Computing Time ◽  
Maximum Clique ◽  
Maximum Clique Problem ◽  
Np Hard ◽  
Exact Methods ◽  
Real World Applications ◽  
Np Hard Problem ◽  
Hard Problems ◽  
Cooling Schedule

The Maximum Clique Problem (MCP) is a classical NP-hard problem that has gained considerable attention due to its numerous real-world applications and theoretical complexity. It is inherently computationally complex, and so exact methods may require prohibitive computing time. Nature-inspired meta-heuristics have proven their utility in solving many NP-hard problems. In this research, we propose a simulated annealing-based algorithm that we call Clique Finder algorithm to solve the MCP. Our algorithm uses a logarithmic cooling schedule and two moves that are selected in an adaptive manner. The objective (error) function is the total number of missing links in the clique, which is to be minimized. The proposed algorithm was evaluated using benchmark graphs from the open-source library DIMACS, and results show that the proposed algorithm had a high success rate.

Pointer Network Based Deep Learning Algorithm for the Maximum Clique Problem

2021 ◽  
Vol 30 (01) ◽  
pp. 2140004
Author(s):  
Shenshen Gu ◽  
Hanmei Yao
Keyword(s):  
Reinforcement Learning ◽  
Supervised Learning ◽  
Learning Strategy ◽  
Learning Algorithm ◽  
Maximum Clique ◽  
Exact Algorithm ◽  
Maximum Clique Problem ◽  
Deep Learning Algorithm ◽  
Np Hard Problem ◽  
Clique Problem

The maximum clique problem (MCP) is a famous NP-hard problem, which is difficult for the exact algorithm to solve when the dimension is large. In this paper, we applied the pointer network based method to solve this problem. First, we illustrated how to train the network with supervised learning strategy to obtain the solution to the maximum clique problem. We then further trained the pointer network with reinforcement learning strategy to obtain the vertices from the graph. For both strategies, backtracking algorithm is used to reselect the vertices. From the experimental results, we can see that both supervised learning and reinforcement learning work well. Promising results can be obtained up to 100 dimensions. This illustrates that the deep neural network based algorithms have great potentials for solving the maximum clique problem effectively and efficiently.

scholarly journals Using Machine Learning for Quantum Annealing Accuracy Prediction

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 187
Author(s):  
Aaron Barbosa ◽  
Elijah Pelofske ◽  
Georg Hahn ◽  
Hristo N. Djidjev
Keyword(s):  
Machine Learning ◽  
Maximum Clique ◽  
Classification Model ◽  
Maximum Clique Problem ◽  
Problem Instance ◽  
Np Hard ◽  
Machine Learning Classification ◽  
Hard Problems ◽  
Problem Instances ◽  
D Wave

Quantum annealers, such as the device built by D-Wave Systems, Inc., offer a way to compute solutions of NP-hard problems that can be expressed in Ising or quadratic unconstrained binary optimization (QUBO) form. Although such solutions are typically of very high quality, problem instances are usually not solved to optimality due to imperfections of the current generations quantum annealers. In this contribution, we aim to understand some of the factors contributing to the hardness of a problem instance, and to use machine learning models to predict the accuracy of the D-Wave 2000Q annealer for solving specific problems. We focus on the maximum clique problem, a classic NP-hard problem with important applications in network analysis, bioinformatics, and computational chemistry. By training a machine learning classification model on basic problem characteristics such as the number of edges in the graph, or annealing parameters, such as the D-Wave’s chain strength, we are able to rank certain features in the order of their contribution to the solution hardness, and present a simple decision tree which allows to predict whether a problem will be solvable to optimality with the D-Wave 2000Q. We extend these results by training a machine learning regression model that predicts the clique size found by D-Wave.

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