Chemical graph generator

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generation step. In other words, structure reduction is efficient when structural constraints are provided, and structure assembly is faster without constraints. First, the useless connections are eliminated, and then the substructures are assembled to build structures. Thus, GEN copes with the constraints in a more efficient way by combining these methods. GEN removes the connections creating the forbidden structures, and then the connection matrices are filled based on substructure information. The method does not accept overlaps among substructures. Once the structure is built in the matrix representation, the saturated molecule is stored in the output list. The COCOA method was further improved and a new generator was built, HOUDINI. It relies on two data structures: a square matrix of compounds representing all bonds in a hyper structure is constructed, and second, substructure representation is used to list atom-centred fragments. In the structure generation, HOUDINI maps all the atom-centred fragments onto the hyper structure.

328:. Orderly generation is performed to cope with this exhaustivity. Many assembly algorithms, such as OMG, MOLGEN and Jean-Loup Faulon's structure generator, are orderly generation methods. Jean-Loup Faulon's structure generator relies on equivalence classes over atoms. Atoms with the same interaction type and element are grouped in the same equivalence class. Rather than extending all atoms in a molecule, one atom from each class is connected with other atoms. Similar to the former generator, Julio Peironcely's structure generator, OMG, takes atoms and substructures as inputs and extends the structures using a 310: 2049: 158:'s orderly generation method. Although their reports are from the 1970s, these studies are still the fundamental references for structure generators. In the orderly generation method, specific order-check functions are performed on graph representatives, such as vectors. For example, MOLGEN performs a descending order check while filling rows of adjacency matrices. This descending order check is based on an input valence distribution. The literature classifies generators into two major types: structure assembly and structure reduction. The 459: 223:

the algorithm assembles substructures with overlaps to construct structures. ASSEMBLE overcomes overlapping by including a “neighbouring atom tag”. The generator is purely mathematical and does not involve the interpretation of any spectral data. Spectral data are used for structure scoring and substructure information. Based on the molecular formula, the generator forms bonds between pairs of atoms, and all the extensions are checked against the given constraints. If the process is considered as a

367:. MASS, SMOG and Ivan Bangov's algorithm are good examples in the literature. MASS is a method of mathematical synthesis. First, it builds all incidence matrices for a given molecular formula. The atom valences are then used as the input for matrix generation. The matrices are generated by considering all the possible interactions among atoms with respect to the constraints and valences. The benefit of constructive search algorithms is their low memory usage. SMOG is a successor of MASS. 80: 394:'s research group. As a type of assembly method, building blocks, such as ring systems and atom fragments, are used in the structure generation. Every intermediate structure is extended by adding building blocks in all possible ways. To reduce the number of duplicates, Brendan McKay's canonical path augmentation method is used. To overcome the combinatorial explosion in the generation, applicability domain and ring systems are detected based on inverse 260:

filling in missing bond information. This platform could generate structures with any arbitrary size of molecules; however, molecular formulas with more than 30 heavy atoms are too time consuming for practical applications. This limitation highlighted the need for a new CASE system. SENECA was developed to eliminate the shortcomings of LUCY. To overcome the limitations of the exhaustive approach, SENECA was developed as a

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starts with the hypergraph, and the structures decrease in size at each step. Bonds are deleted based on the substructures. If a substructure is no longer in the hypergraph, the substructure is removed from the constraints. Overlaps in the substructures were also considered due to the hypergraphs. The earliest reduction-based structure generator is COCOA, an exhaustive and

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analysis. The applicability domain, or target area, is described based on given biological as well as pharmaceutical activity information from QSPR/QSAR. In that study, monotonically changed descriptors (MCD) are used to describe applicability domains. For every extension in intermediate structures,

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The structure generator GEN by Simona Bohanec combines two tasks: structure assembly and structure reduction. Like COCOA, the initial state of the problem is a hyper structure. Both assembly and reduction methods have advantages and disadvantages, and the GEN tool avoids these disadvantages in the

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bond-removal method. Generated fragments are described as atom-centred fragments to optimize storage, comparable to circular fingerprints and atom signatures. Rather than storing structures, only the list of first neighbours of each atom is stored. The main disadvantage of reduction methods is the

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Substantial contributions were made by Craig Shelley and Morton Munk, who published a large number of CASE papers in this field. The first of these papers reported a structure generator, ASSEMBLE. The algorithm is considered one of the earliest assembly methods in the field. As the name indicates,

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Unlike these assembly methods, reduction methods make all the bonds between atom pairs, generating a hypergraph. Then, the size of the graph is reduced with respect to the constraints. First, the existence of substructures in the hypergraph is checked. Unlike assembly methods, the generation tree

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based on the given reaction rules. Its core algorithm is a breadth-first method, generating structures by applying reaction rules to each source compound. Structure generation and enumeration are performed based on Brendan McKay's canonical augmentation method. RetroPath 2.0 provides a variety of

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OMG generates structures based on the canonical augmentation method from Brendan McKay's NAUTY package. The algorithm calculates canonical labelling and then extends structures by adding one bond. To keep the extension canonical, canonical bonds are added. Although NAUTY is an efficient tool for

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data; second, the assembly of these substructures based on a set of construction rules. Hidetsugu Abe and the other contributors published the first paper on CHEMICS, which is a CASE tool comprising several structure generation methods. The program relies on a predefined non-overlapping fragment

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structure elucidation method based on the HMBC data of unknown molecules, and involves an exhaustive 2-step structure generation process where first all combinations of interpretations of HMBC signals are implemented in a connectivity matrix, which is then completed by a deterministic generator

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and fragments. These generators are the core of CASE systems. In a generator, the molecular formula is the basic input. If fragments are obtained from the experimental data, they can also be used as inputs to accelerate structure generation. The first structure generators were versions of graph

227:, the first node of the tree is an atom set with substructures if any are provided by the spectral data. By extending the molecule with a bond, an intermediate structure is built. Each intermediate structure can be represented by a node in the generation tree. ASSEMBLE was developed with a 280:

is reached. In the generation, this transformation relies on equations based on Jean-Loup Faulon's rules. LSD (Logic for Structure Determination) is an important contribution from French scientists. The tool uses spectral data information such as HMBC and

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data of an unknown molecule. Compared to many other generators, MOLGEN approaches the problem from different angles. The key feature of MOLGEN is generating structures without building all the intermediate structures and without generating duplicates.

382:. MOLGEN is an orderly generation method. Many different versions of MOLGEN have been developed, and they provide various functions. Based on the users' needs, different types of inputs can be used. For example, MOLGEN-MS allows users to input 601:, due to the computational explosion, many structure generators output only connected chemical graphs. Thus, the connectivity check is one of the mandatory intermediate steps in structure generation because the aim is to generate fully 305:

into fragments, components and segments was performed as an application of integer partitioning. These fragments were then used as building blocks in the structure generator. This structure generator was part of a CASE system, ESESOC.

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and, notably, one of the developers of MASS, Mikhail Elyashberg. COCON is another NMR based structure generator, relying on theoretical data sets for structure generation. Except J-HMBC and J-COSY, all NMR types can be used as inputs.

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Shin-ichi Sasaki; Hidetsugu Abe; Yuji Hirota; Yoshiaki Ishida; Yoshihiro Kudo; Shukichi Ochiai; Keiji Saito; Tohru Yamasaki (1 November 1978). "CHEMICS-F: A Computer Program System for Structure Elucidation of Organic Compounds".

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Robert C Glem; Andreas Bender; Catrin H Arnby; Lars Carlsson; Scott Boyer; James Smith (1 March 2006). "Circular fingerprints: flexible molecular descriptors with applications from physical chemistry to ADME".

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K. A. Blinov; M. E. Elyashberg; S. G. Molodtsov; A. J. Williams; E. R. Martirosian (1 April 2001). "An expert system for automated structure elucidation utilizing 1H-1H, 13C-1H and 15N-1H 2D NMR correlations".

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The efficiency and exhaustivity of generators are also related to the data structures. Unlike previous methods, AEGIS was a list-processing generator. Compared to adjacency matrices, list data requires less

219:. The secondary and tertiary component sets are built layer-by-layer starting with these primary components. These component sets are represented as vectors and are used as building blocks in the process. 1773:. In molecular graphs, canonical labelling and molecular symmetry detection are implementations of automorphism groups. Although there are well known canonical labelling methods in the field, such as 3461:

Mohammad Mahdi Jaghoori; Sung-Shik T.Q. Jongmans; Frank de Boer; Julio Peironcely; Jean-Loup Faulon; Theo Reijmers; Thomas Hankemeier (December 2013). "PMG: Multi-core Metabolite Identification".

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labelling and duplicate checks. As for many other generators, the tree approach is the skeleton of Jean-Loup Faulon's structure generators. However, considering all possible extensions leads to a

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generation algorithms. In contrast to previous methods, these methods build all the connectivity matrices without building intermediate structures. In these algorithms, canonicity criteria and

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massive size of the hypergraphs. Indeed, for molecules with unknown structures, the size of the hyper structure becomes extremely large, resulting in a proportional increase in the run time.

2697:(April 1981). "Applications of artificial intelligence for chemical inference. 37. GENOA: a computer program for structure elucidation utilizing overlapping and alternative substructures". 4647: 146:

After DENDRAL, another mathematical method, MASS, a tool for mathematical synthesis and analysis of molecular structures, was reported. As with CONGEN, the MASS algorithm worked as an

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I. P. Bangov; K. D. Kanev (February 1988). "Computer-assisted structure generation from a gross formula: II. Multiple bond unsaturated and cyclic compounds. Employment of fragments".

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Hidetsugu. Abe; Peter C. Jurs (September 1975). "Automated chemical structure analysis of organic molecules with a molecular structure generator and pattern recognition techniques".

4642: 243:. As no spectral data was interpreted in this system, the user needed to provide substructures as inputs. Structure generators can also vary based on the type of data used, such as 344:, and the developers released PMG (Parallel Molecule Generator). MOLGEN outperforms PMG using only 1 core; however, PMG outperforms MOLGEN by increasing the number of cores to 10. 1502: 589:, and the maximum number of bonds a chemical element can make. For example, carbon's valence is 4. In a chemical graph, an atom is saturated if it reaches its valence. A graph is 854: 3227:

Jean-Loup Faulon; Carla J Churchwell; Donald P Visco (1 May 2003). "The signature molecular descriptor. 2. Enumerating molecules from their extended valence sequences".

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to facilitate use. The second version of ASSEMBLE was released in 2000. Another assembly method is GENOA. Compared to ASSEMBLE and many other generators, GENOA is a

3906:(13 July 2017). "druGAN: An Advanced Generative Adversarial Autoencoder Model for de Novo Generation of New Molecules with Desired Molecular Properties in Silico". 1349: 1002: 4135:

Jean-Loup Faulon; Michael J Collins; Robert D Carr (1 March 2004). "The signature molecular descriptor. 4. Canonizing molecules using extended valence sequences".

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library. CHEMICS generates different types of component sets ranked from primary to tertiary based on component complexity. The primary set contains atoms, i.e.,

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in the generation makes the generation process more efficient. For example, a well-known tool called RetroPath is used for molecular structure enumeration and

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Molecular structure generation is explained step by step. Starting from a set of atoms, bonds are added between atom pairs until reaching saturated structures.

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the MCDs are updated. The usage of MCDs reduces the search space in the generation process. In the QSPR/QSAR based structure generation, there is the lack of

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is calculated to evaluate the structure and its spectral properties. By transforming this structure into another structure, the process continues until the

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Jean-Loup Faulon (January 1996). "Stochastic Generator of Chemical Structure. 2. Using Simulated Annealing To Search the Space of Constitutional Isomers".

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Baudoin Delépine; Thomas Duigou; Pablo Carbonell; Jean-Loup Faulon (9 December 2017). "RetroPath2.0: A retrosynthesis workflow for metabolic engineers".

248: 2836:(November 2001). "SENECA: A Platform-Independent, Distributed, and Parallel System for Computer-Assisted Structure Elucidation in Organic Chemistry". 1319:

of the graph. An automorphism permutes the vertices of a graph; in other words, it maps a graph onto itself. This action is edge-vertex preserving. If

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Jean-Loup Faulon (1 September 1994). "Stochastic Generator of Chemical Structure. 1. Application to the Structure Elucidation of Large Molecules".

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Julio E Peironcely; Miguel Rojas-Chertó; Davide Fichera; Theo Reijmers; Leon Coulier; Jean-Loup Faulon; Thomas Hankemeier (17 September 2012).

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A series of stochastic generators was reported by Jean-Loup Faulon. The software, MOLSIG, was integrated into this stochastic generator for

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M. S. Molchanova; V. V. Shcherbukhin; N. S. Zefirov (January 1996). "Computer Generation of Molecular Structures by the SMOG Program".

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Christie BD; Munk ME (1 May 1988). "Structure generation by reduction: a new strategy for computer-assisted structure elucidation".

2060: 3594:"MOLGEN-MS: Evaluation of low resolution electron impact mass spectra with MS classification and exhaustive structure generation" 60: 2332:

Karina A. Gulyaeva; Irina L. Artemieva (2020). "The Ontological Approach in Organic Chemistry Intelligent System Development".

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Junfeng Hao; Lu Xu; Changyu Hu (October 2000). "Expert system for elucidation of structures of organic compounds (ESESOC)".

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H.J. Luinge; J.H. Van Der Maas (June 1990). "AEGIS, an algorithm for the exhaustive generation of irredundant structures".

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to search for life on Mars. CONGEN dealt well with overlaps in substructures. The overlaps among substructures rather than

4518:"MAYGEN: an open-source chemical structure generator for constitutional isomers based on the orderly generation principle" 115:

generators modified for chemical purposes. One of the first structure generators was CONGEN, originally developed for the

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Martin Badertscher; Andrew Korytko; Klaus-Peter Schulz; et al. (May 2000). "Assemble 2.0: a structure generator".

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method, such as Igor Faradjev's algorithm, and an additional solution to memory problems. Branch-and-bound methods are

194:-based structure generator. The algorithm had two steps: first, the prediction of the substructure from low-resolution 4186:

Simona Bohanec (1 May 1995). "Structure Generation by the Combination of Structure Reduction and Structure Assembly".

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Jean Loup Faulon (1 July 1992). "On using graph-equivalent classes for the structure elucidation of large molecules".

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V.V. Serov; M.E. Elyashberg; L.A. Gribov (April 1976). "Mathematical synthesis and analysis of molecular structures".

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Chang-Yu Hu; Lu Xu (November 1994). "Principles for structure generation of organic isomers from molecular formula".

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and ALATIS, NAUTY is a commonly used software package for automorphism group calculations and canonical labelling.

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Craig A. Shelley; Morton E. Munk (November 1981). "Case, a computer model of the structure elucidation process".

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substructure search-based algorithm, and it assembles different substructures by also considering the overlaps.

2207:(1 January 1987). "Prediction of the folding of short polypeptide segments by uniform conformational sampling". 2516: 2373: 290: 3390: 370:

Unlike previous methods, MOLGEN is the only maintained efficient generic structure generator, developed as a

63:(CASE). CASE systems again have regained interest for the structure elucidation of unknowns in computational 4284:

G. Massiot; J. M. Nuzillard (July 1992). "Computer-assisted elucidation of structures of natural products".

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The second line of this table shows a permutation of the first line. The multiplication of permutations,

590: 289:. A well-known commercial CASE system, StrucEluc, also features a NMR based generator. This tool is from 4382: 3839: 3284: 3033: 2079: 379: 286: 285:

data to generate all possible structures. LSD is an open source structure generator released under the

2278: 794: 4455: 2287:(June 1993). "DENDRAL: A case study of the first expert system for scientific hypothesis formation". 420: 175: 585:

of a vertex is its number of connections. In a chemical graph, the maximum degree of an atom is its

4662: 1315:, called blocks of the set. The set of permutations preserving the set system is used to build the 273: 159: 2790:(20 September 1996). "LUCY—A Program for Structure Elucidation from NMR Correlation Experiments". 336:

graph canonical labelling, OMG is approximately 2000 times slower than MOLGEN. The problem is the

3908: 2444: 404: 325: 56: 3835:"Molecular structures enumeration and virtual screening in the chemical space with RetroPath2.0" 3277: 2064: 4286: 3670:(26 November 2014). "Ring-System-Based Exhaustive Structure Generation for Inverse-QSPR/QSAR". 3098: 2692: 2605: 2497:"Algorithms for group actions: Homomorphism principle and orderly generation applied to graphs" 232: 28: 2647: 1082: 3969: 3729: 3672: 2932: 2209: 1644: 1549: 1354: 582: 503: 481: 337: 216: 68: 4444: 3779: 3615:(14 June 2016). "Ring system-based chemical graph generation for de novo molecular design". 1721: 1589: 1229: 1150: 1052: 309: 4376:

Stephen R Heller; Alan McNaught; Igor Pletnev; Stephen Stein; Dmitrii Tchekhovskoi (2015).

3958: 2157: 1322: 1124: 975: 883: 786: 371: 352: 329: 256: 240: 3424: 2930:

Jean-Marc Nuzillard; Massiot Georges (January 1991). "Logic for structure determination".

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method. This tree extension terminates when all the branches reach saturated structures.

8: 3832: 2974: 2833: 2787: 2070: 586: 485: 277: 265: 224: 191: 107: 2161: 1264: 190:

in the molecule. One of the earliest attempts was made by Hidetsugu Abe in 1975 using a

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generation problems. Molecular structures are graphs with chemical constraints such as

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connected to consider all possible extensions. If substructures are obtained from the

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Mathilde Koch; Thomas Duigou; Pablo Carbonell; Jean-Loup Faulon (19 December 2017).

2048: 186:, the generation starts with these substructures. These substructures provide known 4590: 4580: 4539: 4529: 4498: 4480: 4464: 4427: 4409: 4391: 4358: 4342: 4311: 4295: 4266: 4242: 4211: 4195: 4168: 4144: 4117: 4073: 4049: 4022: 4004: 3988: 3941: 3917: 3903: 3884: 3866: 3848: 3815: 3791: 3762: 3738: 3705: 3681: 3648: 3624: 3574: 3558: 3531: 3515: 3488: 3472: 3428: 3420: 3404: 3372: 3356: 3329: 3311: 3293: 3260: 3236: 3209: 3193: 3166: 3150: 3123: 3107: 3078: 3060: 3042: 3009: 2985: 2957: 2941: 2912: 2896: 2869: 2845: 2815: 2799: 2769: 2753: 2724: 2708: 2675: 2659: 2630: 2614: 2585: 2569: 2541: 2525: 2477: 2469: 2453: 2435: 2398: 2382: 2353: 2337: 2314: 2298: 2284: 2242: 2218: 2175: 2165: 2124: 2106: 2088: 1959: 1116: 886: 348: 302: 151: 147: 36: 4230: 2170: 2093: 493: 136: 124: 44: 32: 4451:"Unique identifiers for small molecules enable rigorous labeling of their atoms" 3795: 3476: 3226: 2341: 488:

represent atoms and bonds, respectively. The bond order corresponds to the edge

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Besides these mathematical structure generation methods, the implementations of

4585: 4534: 4333:(March 1999). "Combinatorial algorithms: generation, enumeration, and search". 3724: 3667: 3612: 3505: 2439: 2204: 2055: 593:

if there is at least one path between each pair of vertices. Although chemical

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method to find optimal solutions. The systems comprise two stochastic methods:

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McKay, Brendan D.; Yirik, Mehmet Aziz; Steinbeck, Christoph (December 2022).

4476: 4405: 4354: 4307: 4254: 4207: 4156: 4105: 4061: 4000: 3960: 3929: 3862: 3803: 3750: 3693: 3636: 3570: 3527: 3484: 3416: 3368: 3307: 3248: 3205: 3162: 3119: 3056: 2997: 2953: 2908: 2857: 2811: 2765: 2720: 2694: 2671: 2626: 2581: 2537: 2465: 2394: 2349: 2310: 2262:"DENDRAL-a computer program for generating and filtering chemical structures" 2230: 2102: 375: 187: 179: 4362: 3722: 3578: 3492: 3170: 2357: 2128: 4604: 4553: 4516:

Yirik, Mehmet Aziz; Sorokina, Maria; Steinbeck, Christoph (December 2021).

4494: 4446: 4423: 4330: 4299: 4262: 4164: 4113: 4018: 3992: 3937: 3880: 3811: 3758: 3742: 3727:(1 January 2010). "Exhaustive Structure Generation for Inverse-QSPR/QSAR". 3701: 3685: 3665: 3644: 3610: 3325: 3298: 3256: 3074: 3047: 3005: 2865: 2803: 2457: 2189: 2120: 859: 413: 364: 195: 64: 4502: 4468: 4431: 4346: 4315: 4270: 4215: 4172: 4121: 4077: 4069: 4026: 3945: 3888: 3819: 3766: 3709: 3652: 3535: 3432: 3376: 3333: 3264: 3213: 3127: 3082: 3013: 2989: 2961: 2916: 2873: 2819: 2773: 2728: 2679: 2634: 2589: 2545: 2481: 2442:(1979). "Orderly algorithms for generating restricted classes of graphs". 2416:

Faradzev, IA (1978). "Constructive enumeration of combinatorial objects".

2402: 2318: 2246: 2238: 2222: 1995: 614: 424: 356: 261: 79: 40: 4228: 4199: 4053: 3360: 3197: 2712: 2573: 2529: 2017: 3562: 3154: 2693:

Raymond E. Carhart; Dennis H. Smith; Neil A. B. Gray; James G. Nourse;

1289: 111: 4328: 4246: 4148: 3519: 3240: 2900: 2849: 2501:

DIMACS Series in Discrete Mathematics and Theoretical Computer Science

1977: 464: 150:

generator. Many mathematical generators are descendants of efficient

3393:; Adolfo Piperno (January 2014). "Practical graph isomorphism, II". 2370: 2331: 1803: 4229:

A. Korytko; K-P Schulz; M. S. Madison; Munk ME (1 September 2003).

3983: 3965:"Application of Generative Autoencoder in de Novo Molecular Design" 3959:

Thomas Blaschke; Marcus Olivecrona; Ola Engkvist; Jürgen Bajorath;

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The available software packages and their links are listed below.

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molecules. A molecule is saturated if all its atoms are saturated.

204: 31:. The development of such software packages is a research topic of 2929: 1893: 2434: 1127:

of a group is the number of elements in the group. Let us assume

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is a rearrangement of these elements. An example is given below:

598: 594: 116: 4231:"HOUDINI: A New Approach to Computer-Based Structure Generation" 1925: 1147:

is a set of integers. Under the function composition operation,

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workflows such as isomer transformation, enumeration, QSAR and

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Knowledge articles published in peer-reviewed literature (J2W)

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Artur Kadurin; Sergey Nikolenko; Kuzma Khrabrov; Alex Aliper;

3389: 2602: 35:. Chemical graph generators are used in areas such as virtual 23:

is a software package to generate computer representations of

858:

The combination of two permutations is also a permutation. A

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Yirik, Mehmet Aziz; Steinbeck, Christoph (5 January 2021).

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This article was adapted from the following source under a

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The generation process starts with a set of atoms from the

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Knowledge articles published in PLOS Computational Biology

3499: 3271: 3140: 2494: 4283: 3591: 3029:"Theoretical NMR correlations based Structure Discussion" 1780: 252: 4643:

Knowledge articles published in peer-reviewed literature

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of all the intermediate structures. OMG has since been

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project, the first artificial intelligence project in

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