scholarly journals Penyelesaian Permainan Sudoku Menggunakan Algoritma Backtracking Berbasis Artificial Intelligence

Journal ICTEE ◽  
2021 ◽  
Vol 2 (2) ◽  
pp. 50
Author(s):  
Alya Aulia Hanafi ◽  
Naseh Hibban ◽  
Fawwaz Muhammad Zulfikar ◽  
Faisal Dharma Adhinata
Keyword(s):  
Artificial Intelligence ◽  
Np Complete

Kebutuhan teknologi untuk mempermudah dan menyelesaikan suatu permasalahan menjadi efisien sangat diperlukan di era modern ini. Salah satu bidang ilmu yang sering digunakan untuk memecahkan masalah dengan meniru kebiasaan manusia adalah Artificial Intelligence (AI). Permainan Sudoku merupakan permainan dengan jenis teka teki logika. Sudoku termasuk pada permasalahan NP – complete, sehingga sulit atau bahkan tidak bisa untuk diselesaikan dengan waktu yang sama. Dari permasalahan tersebut, dibutuhkan sebuah algoritma AI untuk menyelesaikan Permainan Sudoku. Salah satu algoritmanya adalah Backtracking (runut-balik). Hasil percobaan menunjukkan semakin banyak jumlah proses backtracking berbanding lurus dengan semakin banyaknya waktu yang dibutuhkan untuk menyelesaikan permainan Puzzel Sudoku. Kemudian, tingkat akurasi pada program sudoku solving dengan algortima backtracking mencapai 100% dengan kotak kosong berjumlah 43.

scholarly journals The Complexity Landscape of Resource-Constrained Scheduling

2020 ◽  
Author(s):  
Robert Ganian ◽  
Thekla Hamm ◽  
Guillaume Mescoff
Keyword(s):  
Artificial Intelligence ◽  
Polynomial Time ◽  
Project Scheduling ◽  
Scheduling Problem ◽  
Comprehensive Understanding ◽  
Resource Constrained ◽  
Special Cases ◽  
Project Scheduling Problem ◽  
Np Complete ◽  
New Algorithms

The Resource-Constrained Project Scheduling Problem (RCPSP) and its extension via activity modes (MRCPSP) are well-established scheduling frameworks that have found numerous applications in a broad range of settings related to artificial intelligence. Unsurprisingly, the problem of finding a suitable schedule in these frameworks is known to be NP-complete; however, aside from a few results for special cases, we have lacked an in-depth and comprehensive understanding of the complexity of the problems from the viewpoint of natural restrictions of the considered instances. In the first part of our paper, we develop new algorithms and give hardness-proofs in order to obtain a detailed complexity map of (M)RCPSP that settles the complexity of all 1024 considered variants of the problem defined in terms of explicit restrictions of natural parameters of instances. In the second part, we turn to implicit structural restrictions defined in terms of the complexity of interactions between individual activities. In particular, we show that if the treewidth of a graph which captures such interactions is bounded by a constant, then we can solve MRCPSP in polynomial time.

scholarly journals The Complexity of Reasoning about Spatial Congruence

1999 ◽  
Vol 11 ◽  
pp. 361-390 ◽  
Author(s):  
M. Cristani
Keyword(s):  
Artificial Intelligence ◽  
Recent Literature ◽  
Research Effort ◽  
Complete Classification ◽  
Spatial Knowledge ◽  
Np Complete ◽  
Temporal And Spatial ◽  
Spatial Congruence ◽  
Full Algebra

In the recent literature of Artificial Intelligence, an intensive research effort has been spent, for various algebras of qualitative relations used in the representation of temporal and spatial knowledge, on the problem of classifying the computational complexity of reasoning problems for subsets of algebras. The main purpose of these researches is to describe a restricted set of maximal tractable subalgebras, ideally in an exhaustive fashion with respect to the hosting algebras. In this paper we introduce a novel algebra for reasoning about Spatial Congruence, show that the satisfiability problem in the spatial algebra MC-4 is NP-complete, and present a complete classification of tractability in the algebra, based on the individuation of three maximal tractable subclasses, one containing the basic relations. The three algebras are formed by 14, 10 and 9 relations out of 16 which form the full algebra.

scholarly journals Complexity of n-Queens Completion (Extended Abstract)

2018 ◽  
Author(s):  
Ian P. Gent ◽  
Christopher Jefferson ◽  
Peter Nightingale
Keyword(s):  
Artificial Intelligence ◽  
Phase Transition ◽  
Decision Problem ◽  
Completion Problem ◽  
Complete Problems ◽  
Random Instances ◽  
Np Complete

The n-Queens problem is to place n chess queens on an n by n chessboard so that no two queens are on the same row, column or diagonal. The n-Queens Completion problem is a variant, dating to 1850, in which some queens are already placed and the solver is asked to place the rest, if possible. We show that n-Queens Completion is both NP-Complete and #P-Complete. A corollary is that any non-attacking arrangement of queens can be included as a part of a solution to a larger n-Queens problem. We introduce generators of random instances for n-Queens Completion and the closely related Blocked n-Queens and Excluded Diagonals Problem. We describe three solvers for these problems, and empirically analyse the hardness of randomly generated instances. For Blocked n-Queens and the Excluded Diagonals Problem, we show the existence of a phase transition associated with hard instances as has been seen in other NP-Complete problems, but a natural generator for n-Queens Completion did not generate consistently hard instances. The significance of this work is that the n-Queens problem has been very widely used as a benchmark in Artificial Intelligence, but conclusions on it are often disputable because of the simple complexity of the decision problem. Our results give alternative benchmarks which are hard theoretically and empirically, but for which solving techniques designed for n-Queens need minimal or no change.

NUMBER OF SOLUTIONS OF SATISFIABILITY INSTANCES—APPLICATIONS TO KNOWLEDGE BASES

1989 ◽  
Vol 03 (01) ◽  
pp. 53-65 ◽  
Author(s):  
J.C. SIMON ◽  
O. DUBOIS
Keyword(s):  
Artificial Intelligence ◽  
Propositional Logic ◽  
Statistical Approach ◽  
Knowledge Bases ◽  
Zero Order ◽  
Number Of Solutions ◽  
Exponential Process ◽  
Complete Problems ◽  
Np Complete ◽  
Logical Rules

In propositional logic (zero order) a system of logical rules may be put under the form of a conjunction of disjunction, i.e. a “satisfiability” or SAT-problem. SAT is central to NP-complete problems. Any result obtained on SAT would have consequences for a lot of problems important in artificial intelligence. We deal with the question of the number N of solutions of SAT. Firstly, any system of SAT clauses may be transformed in a system of independent clauses by an exponential process; N may be computed exactly. Secondly, by a statistical approach, results are obtained showing that for a given SAT-instance, it should be possible to find an estimate of N with a margin of confidence in polynomial time. Thirdly, we demonstrate the usefulness of these ideas on large knowledge bases.

scholarly journals IS PROTEIN FOLDING PROBLEM REALLY A NP-COMPLETE ONE? FIRST INVESTIGATIONS

2014 ◽  
Vol 12 (01) ◽  
pp. 1350017 ◽  
Author(s):  
CHRISTOPHE GUYEUX ◽  
NATHALIE M.-L. CÔTÉ ◽  
JACQUES M. BAHI ◽  
WOJCIECH BIENIA
Keyword(s):  
Artificial Intelligence ◽  
Amino Acids ◽  
Free Energy ◽  
Protein Folding ◽  
Research Work ◽  
Prediction Problem ◽  
Np Completeness ◽  
Np Complete ◽  
Backbone Structure ◽  
Self Avoiding Walk

To determine the 3D conformation of proteins is a necessity to understand their functions or interactions with other molecules. It is commonly admitted that, when proteins fold from their primary linear structures to their final 3D conformations, they tend to choose the ones that minimize their free energy. To find the 3D conformation of a protein knowing its amino acid sequence, bioinformaticians use various models of different resolutions and artificial intelligence tools, as the protein folding prediction problem is a NP complete one. More precisely, to determine the backbone structure of the protein using the low resolution models (2D HP square and 3D HP cubic), by finding the conformation that minimizes free energy, is intractable exactly. Both proofs of NP-completeness and the 2D prediction consider that acceptable conformations have to satisfy a self-avoiding walk (SAW) requirement, as two different amino acids cannot occupy a same position in the lattice. It is shown in this document that the SAW requirement considered when proving NP-completeness is different from the SAW requirement used in various prediction programs, and that they are different from the real biological requirement. Indeed, the proof of NP completeness and the predictions in silico consider conformations that are not possible in practice. Consequences of this fact are investigated in this research work.

scholarly journals Complexity of n-Queens Completion

2017 ◽  
Vol 59 ◽  
pp. 815-848 ◽  
Author(s):  
Ian P. Gent ◽  
Christopher Jefferson ◽  
Peter Nightingale
Keyword(s):  
Artificial Intelligence ◽  
Phase Transition ◽  
Decision Problem ◽  
Completion Problem ◽  
Complete Problems ◽  
Random Instances ◽  
Np Complete

The n-Queens problem is to place n chess queens on an n by n chessboard so that no two queens are on the same row, column or diagonal. The n-Queens Completion problem is a variant, dating to 1850, in which some queens are already placed and the solver is asked to place the rest, if possible. We show that n-Queens Completion is both NP-Complete and #P-Complete. A corollary is that any non-attacking arrangement of queens can be included as a part of a solution to a larger n-Queens problem. We introduce generators of random instances for n-Queens Completion and the closely related Blocked n-Queens and Excluded Diagonals Problem. We describe three solvers for these problems, and empirically analyse the hardness of randomly generated instances. For Blocked n-Queens and the Excluded Diagonals Problem, we show the existence of a phase transition associated with hard instances as has been seen in other NP-Complete problems, but a natural generator for n-Queens Completion did not generate consistently hard instances. The significance of this work is that the n-Queens problem has been very widely used as a benchmark in Artificial Intelligence, but conclusions on it are often disputable because of the simple complexity of the decision problem. Our results give alternative benchmarks which are hard theoretically and empirically, but for which solving techniques designed for n-Queens need minimal or no change.

scholarly journals Computational Complexity of Arranging Music

2017 ◽  
Author(s):  
Erik D. Demaine ◽  
William S. Moses
Keyword(s):  
Artificial Intelligence ◽  
Dynamic Programming ◽  
Computational Complexity ◽  
Data Structures ◽  
Music Theory ◽  
Algorithms And Data Structures ◽  
Rock Band ◽  
Computer Scientists ◽  
Np Complete ◽  
Single Instrument

Music has long been a subject of analysis for mathematicians and has led to interesting questions in music theory and other fields. For the most part, computer scientists have looked into applying artificial intelligence to music and finding algorithms and data structures to solve various musical problems. These problems tend to be solvable in polynomial time using dynamic programming and have various applications. This chapter takes an additional step in this direction, asking what sorts of problems in music cannot be efficiently computed. Specifically, it asks how various constraints affect the computational complexity of arranging music originally written for one set of instruments for a single instrument instead. It then applies these results to other domains, including musical choreography (such as ice skating and ballet) as well as to creating levels for rhythm games (such as Rock Band). It proves that all of the problems are NP-complete.

Artificial Intelligence

2009 ◽  
Author(s):  
David L. Poole ◽  
Alan K. Mackworth
Keyword(s):  
Artificial Intelligence
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