Graph Learning for Combinatorial Optimization: A Survey of State-of-the-Art

Graphs have been widely used to represent complex data in many applications, such as e-commerce, social networks, and bioinformatics. Efficient and effective analysis of graph data is important for graph-based applications. However, most graph analysis tasks are combinatorial optimization (CO) probl...

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Published in:Data Science and Engineering Vol. 6; no. 2; pp. 119 - 141
Main Authors: Peng, Yun, Choi, Byron, Xu, Jianliang
Format: Journal Article
Language:English
Published: Singapore Springer Singapore 01.06.2021
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Abstract Graphs have been widely used to represent complex data in many applications, such as e-commerce, social networks, and bioinformatics. Efficient and effective analysis of graph data is important for graph-based applications. However, most graph analysis tasks are combinatorial optimization (CO) problems, which are NP-hard. Recent studies have focused a lot on the potential of using machine learning (ML) to solve graph-based CO problems. Most recent methods follow the two-stage framework. The first stage is graph representation learning, which embeds the graphs into low-dimension vectors. The second stage uses machine learning to solve the CO problems using the embeddings of the graphs learned in the first stage. The works for the first stage can be classified into two categories, graph embedding methods and end-to-end learning methods. For graph embedding methods, the learning of the the embeddings of the graphs has its own objective, which may not rely on the CO problems to be solved. The CO problems are solved by independent downstream tasks. For end-to-end learning methods, the learning of the embeddings of the graphs does not have its own objective and is an intermediate step of the learning procedure of solving the CO problems. The works for the second stage can also be classified into two categories, non-autoregressive methods and autoregressive methods. Non-autoregressive methods predict a solution for a CO problem in one shot. A non-autoregressive method predicts a matrix that denotes the probability of each node/edge being a part of a solution of the CO problem. The solution can be computed from the matrix using search heuristics such as beam search. Autoregressive methods iteratively extend a partial solution step by step. At each step, an autoregressive method predicts a node/edge conditioned to current partial solution, which is used to its extension. In this survey, we provide a thorough overview of recent studies of the graph learning-based CO methods. The survey ends with several remarks on future research directions.
AbstractList Graphs have been widely used to represent complex data in many applications, such as e-commerce, social networks, and bioinformatics. Efficient and effective analysis of graph data is important for graph-based applications. However, most graph analysis tasks are combinatorial optimization (CO) problems, which are NP-hard. Recent studies have focused a lot on the potential of using machine learning (ML) to solve graph-based CO problems. Most recent methods follow the two-stage framework. The first stage is graph representation learning, which embeds the graphs into low-dimension vectors. The second stage uses machine learning to solve the CO problems using the embeddings of the graphs learned in the first stage. The works for the first stage can be classified into two categories, graph embedding methods and end-to-end learning methods. For graph embedding methods, the learning of the the embeddings of the graphs has its own objective, which may not rely on the CO problems to be solved. The CO problems are solved by independent downstream tasks. For end-to-end learning methods, the learning of the embeddings of the graphs does not have its own objective and is an intermediate step of the learning procedure of solving the CO problems. The works for the second stage can also be classified into two categories, non-autoregressive methods and autoregressive methods. Non-autoregressive methods predict a solution for a CO problem in one shot. A non-autoregressive method predicts a matrix that denotes the probability of each node/edge being a part of a solution of the CO problem. The solution can be computed from the matrix using search heuristics such as beam search. Autoregressive methods iteratively extend a partial solution step by step. At each step, an autoregressive method predicts a node/edge conditioned to current partial solution, which is used to its extension. In this survey, we provide a thorough overview of recent studies of the graph learning-based CO methods. The survey ends with several remarks on future research directions.
Audience Academic
Author Peng, Yun
Choi, Byron
Xu, Jianliang
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  organization: Department of Computer Science, Hong Kong Baptist University
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Cites_doi 10.1145/2623330.2623732
10.1145/2783258.2783417
10.2200/S00928ED1V01Y201906DTM061
10.1038/nature14236
10.24963/ijcai.2019/312
10.1109/ICDE.2016.7498232
10.1109/TKDE.2014.2316818
10.1145/3308558.3313488
10.1145/3292500.3330986
10.1145/3178876.3186120
10.1609/aaai.v34i04.5720
10.1145/2939672.2939754
10.1109/SFCS.2001.959936
10.1145/3219819.3220068
10.24963/ijcai.2019/569
10.24963/ijcai.2020/679
10.1109/TBDATA.2018.2850013
10.1145/2939672.2939751
10.1609/aaai.v31i1.10750
10.1109/TSC.2013.42
10.1109/BigData47090.2019.9005670
10.1287/ijoc.11.1.15
10.1109/DSW.2018.8439919
10.1145/2806416.2806512
10.1007/978-3-319-93031-2_12
10.1017/CBO9780511815478
10.1093/bioinformatics/btz718
10.1007/s41019-019-0092-x
10.1007/s00493-006-0008-z
10.1145/2783258.2783307
10.1017/ATSIP.2020.13
10.1109/ICDE.2019.00059
10.1109/TKDE.2018.2849727
10.1109/ICDE.2019.00125
10.1145/2939672.2939753
10.1007/978-3-030-04221-9_48
10.1007/BF02392825
10.1109/ICCV.2019.00315
10.1145/2736277.2741093
10.1609/aaai.v33i01.33014731
10.1145/227683.227684
10.1007/BF00339943
10.1007/s41019-019-0097-5
10.1145/2939672.2939673
10.1109/TKDE.2018.2807452
10.1109/ICTAI.2019.00125
10.1145/3097983.3098061
10.1145/3289600.3290967
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References Hamilton WL, Ying R, Leskovec J (2017) Inductive representation learning on large graphs. In: Proceedings of international conference on neural information processing systems (NIPS’17), pp 1025–1035
ChenFWangYCWangBKuoCCJGraph representation learning: a surveyAPSIPA Trans Signal Inf Process20209e1510.1017/ATSIP.2020.13
HopfieldJTankDNeural computation of decisions in optimisation problemsBiol Cybern1985521411520572.68041
FanZPengYChoiBXuJBhowmickSSTowards efficient authenticated subgraph query service in outsourced graph databasesIEEE Trans Serv Comput20147469671310.1109/TSC.2013.42
Wang D, Cui P, Zhu W (2016) Structural deep network embedding. In: Proceedings of ACM SIGKDD International conference on knowledge discovery and data mining (KDD’16), pp 1225–1234
Li Z, Chen Q, Koltun V (2018) Combinatorial optimization with graph convolutional networks and guided tree search. In: Proceedings of international conference on neural information processing systems (NIPS’18), pp 537–546
YueXWangZHuangJParthasarathySMoosavinasabSHuangYLinSMZhangWZhangPSunHGraph embedding on biomedical networks: methods, applications and evaluationsBioinformatics201936412411251
Chang L (2019) Efficient maximum clique computation over large sparse graphs. In: Proceedings of ACM SIGKDD international conference on knowledge discovery and data mining (KDD’19), pp 529–538
Sato R, Yamada M, Kashima H (2019) Approximation ratios of graph neural networks for combinatorial problems. In: Proceedings of the neural information processing systems (NIPS’19)
PapadimitriouCHVempalaSOn the approximability of the traveling salesman problemCombinatorica2006261101120220128710.1007/s00493-006-0008-z
Wu Z, Pan S, Chen F, Long G, Zhang C, Yu PS (2019) A comprehensive survey on graph neural networks. CoRR arXiv:1901.00596
Tu K, Cui P, Wang X, Yu PS, Zhu W (2018) Deep recursive network embedding with regular equivalence. In: Proceedings of ACM SIGKDD international conference on knowledge discovery & data mining (KDD’18), pp 2357–2366
Nguyen H, Murata T (2017) Motif-aware graph embeddings. In: Proceedings of international joint conference on artificial intelligence (IJCAI’17), pp 1–1
Huang W, Zhang T, Rong Y, Huang J (2018) Adaptive sampling towards fast graph representation learning. In: Proceedings of international conference on neural information processing systems (NIPS’18), pp 4563–4572
Mikolov T, Sutskever I, Chen K, Corrado G, Dean J (2013) Distributed representations of words and phrases and their compositionality. In: Proceedings of the 26th international conference on neural information processing systems (NIPS’13), pp 3111–3119
Tang J, Qu M, Wang M, Zhang M, Yan J, Mei Q (2015) LINE: Large-scale information network embedding. In: Proceedings of international conference on world wide web (WWW’15), pp 1067–1077
Veličković P, Cucurull G, Casanova A, Romero A, Liò P, Bengio Y (2018) Graph Attention Networks. In: International conference on learning representations (ICLR)
CaiHZhengVWChangKA comprehensive survey of graph embedding: problems, techniques, and applicationsIEEE Trans Knowl Data Eng201830091616163710.1109/TKDE.2018.2807452
Cao S, Lu W, Xu Q (2015) GraRep: learning graph representations with global structural information. In: Proceedings of ACM international on conference on information and knowledge management (CIKM’15), pp 891–900
DaveVSZhangBChenPYAl HasanMNeural-brane: neural bayesian personalized ranking for attributed network embeddingData Sci Eng20194211913110.1007/s41019-019-0092-x
Ribeiro LF, Saverese PH, Figueiredo DR (2017) Struc2Vec: Learning node representations from structural identity. In: Proceedings of ACM SIGKDD international conference on knowledge discovery and data mining (KDD’17), pp 385–394
Khot S (2001) Improved inapproximability results for maxclique, chromatic number and approximate graph coloring. In: Proceedings IEEE symposium on foundations of computer science, pp 600–609
JinWBarzilayRJaakkolaTJunction tree variational autoencoder for molecular graph generationProc Int Conf Mach Learn20188023232332
Li Y, Gu C, Dullien T, Vinyals O, Kohli P (2019) Graph matching networks for learning the similarity of graph structured objects. In: Proceedings of international conference on machine learning (ICML’19), pp 3835–3845
Wu Y, Song W, Cao Z, Zhang J, Lim A (2019) Learning improvement heuristics for solving the travelling salesman problem. CoRR arXiv:1912.05784
HåstadJClique is hard to approximate within n1-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n^{1-\varepsilon }$$\end{document}Acta Math19991821105142168733110.1007/BF02392825
Ou M, Cui P, Pei J, Zhang Z, Zhu W (2016) Asymmetric transitivity preserving graph embedding. In: Proceedings of ACM SIGKDD international conference on knowledge discovery and data mining (KDD’16), pp 1105–1114
Meng L, Zhang J (2019) IsoNN: Isomorphic neural network for graph representation learning and classification. CoRR arXiv:1907.09495
Tang J, Qu M, Mei Q (2015) PTE: Predictive text embedding through large-scale heterogeneous text networks. In: Proceedings of ACM SIGKDD international conference on knowledge discovery and data mining (KDD’15), pp 1165–1174
Bengio Y, Lodi A, Prouvost A (2018) Machine learning for combinatorial optimization: A methodological tour d’horizon. arXiv:1811.06128
Wang R, Yan J, Yang X (2019) Learning combinatorial embedding networks for deep graph matching. In: Proceedings of the IEEE international conference on computer vision (ICCV’19), pp 3056–3065
Yang Y, Wang X, Song M, Yuan J, Tao D (2019) SPAGAN: Shortest path graph attention network. In: Proceedings of international joint conference on artificial intelligence (IJCAI’19), pp 4099–4105
Joshi CK, Cappart Q, Rousseau LM, Laurent T, Bresson X (2020) Learning TSP requires rethinking generalization. arXiv:2006.07054
Nazi A, Hang W, Goldie A, Ravi S, Mirhoseini A (2019) GAP : Generalizable approximate graph partitioning framework. URL ICLR workshop
Chami I, Abu-El-Haija S, Perozzi B, Ré C, Murphy K (2020) Machine learning on graphs: a model and comprehensive taxonomy. arXiv:2005.03675
Kool W, van Hoof H, Welling M (2019) Attention, learn to solve routing problems! In: International conference on learning representations
Yanardag P, Vishwanathan S (2015) Deep graph kernels. In: Proceedings of ACM sigkdd international conference on knowledge discovery and data mining (KDD’15), pp 1365–1374
PengYFanZChoiBXuJBhowmickSSAuthenticated subgraph similarity searchin outsourced graph databasesIEEE Trans Knowl Data Eng20152771838186010.1109/TKDE.2014.2316818
Deudon M, Cournut P, Lacoste A, Adulyasak Y, Rousseau LM (2018) Learning heuristics for the TSP by policy gradient. In: International conference on the integration of constraint programming, artificial intelligence, and operations research, pp 170–181
VinyalsOFortunatoMJaitlyNPointer networksAdv Neural Inf Process Syst20152826922700
Joshi CK, Laurent T, Bresson X (2019) An efficient graph convolutional network technique for the travelling salesman problem. CoRR arXiv:1906.01227
SuttonRSBartoAGReinforcement learning: an introduction2018CambridgeMIT Press1407.68009
Abe K, Xu Z, Sato I, Sugiyama M (2019) Solving np-hard problems on graphs with extended alphago zero. arXiv:1905.11623
HuangXLakshmananLVXuJCommunity search over big graphs2019New YorkMorgan & Claypool Publishers10.2200/S00928ED1V01Y201906DTM061
Mazyavkina N, Sviridov S, Ivanov S, Burnaev E (2020) Reinforcement learning for combinatorial optimization: a survey. arXiv:2003.03600
DevlinJChangMWLeeKToutanovaKBERT: Pre-training of deep bidirectional transformers for language understandingProc Conf N Am Chapter Assoc Comput Linguist Hum Lang Technol2019141714186
Hamilton WL, Ying R, Leskovec J (2017) Representation learning on graphs: methods and applications. IEEE Data Eng Bull
Huang J, Patwary MMA, Diamos GF (2019) Coloring big graphs with alphagozero. CoRR arXiv:1902.10162
Grover A, Leskovec J (2016) Node2Vec: Scalable feature learning for networks. In: Proceedings of ACM SIGKDD international conference on knowledge discovery and data mining (KDD’16), pp 855–864
Dareddy MR, Das M, Yang H (2019) Motif2Vec: Motif aware node representation learning for heterogeneous networks. In: 2019 IEEE international conference on big data (Big Data’19), pp 1052–1059
Peng Y, Choi B, He B, Zhou S, Xu R, Yu X (2016) VColor: A practical vertex-cut based approach for coloring large graphs. In: IEEE international conference on data engineering (ICDE’16), pp 97–108
DuvenaudDKMaclaurinDIparraguirreJBombarellRHirzelTAspuru-GuzikAAdamsRPConvolutional networks on graphs for learning molecular fingerprintsAdv Neural Inf Process Syst20152822242232
Yu Y, Lu Z, Liu J, Zhao G, Wen J (2019) RUM: Network representation learning using motifs. In: IEEE international conference on data engineering (ICDE’19), pp 1382–1393
WassermanSFaustKSocial network analysis: methods and applications1994CambridgeCambridge University Press10.1017/CBO9780511815478
MnihVKavukcuogluKSilverDRusuAAVenessJBellemareMGGravesARiedmillerMFidjelandAKOstrovskiGHuman-level control through deep reinforcement learningNature2015518754052953310.1038/nature14236
Dai H, Khalil EB, Zhang Y, Dilkina B, Song L (2017) Learning combinatorial optimization algorithms over graphs. In: Proceedings of international conference on neural information processing systems (NIPS’17), pp 6351–6361
Smith-MilesKNeural networks for combinatorial optimization: a review of more than a decade of researchINFORMS J Comput1999111534168812410.1287/ijoc.11.1.15
Nowak A, Villar S, Bandeira AS, Bruna J (2017) A note on learning algorithms for quadratic assignment with graph neural networks. In: Proceeding of international conference on machine learning (ICML’17), pp 22–22
Tsitsulin A, Mottin D, Karras P, Müller E (2018) VERSE: Versatile graph embeddings from similarity measures. In: Proceedings of
RS Sutton (155_CR61) 2018
CH Papadimitriou (155_CR53) 2006; 26
H Cai (155_CR7) 2018; 30
S Wasserman (155_CR70) 1994
J Hopfield (155_CR28) 1985; 52
155_CR39
155_CR38
155_CR37
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155_CR36
155_CR46
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155_CR75
155_CR30
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155_CR73
155_CR72
155_CR71
References_xml – reference: Mikolov T, Sutskever I, Chen K, Corrado G, Dean J (2013) Distributed representations of words and phrases and their compositionality. In: Proceedings of the 26th international conference on neural information processing systems (NIPS’13), pp 3111–3119
– reference: MnihVKavukcuogluKSilverDRusuAAVenessJBellemareMGGravesARiedmillerMFidjelandAKOstrovskiGHuman-level control through deep reinforcement learningNature2015518754052953310.1038/nature14236
– reference: Chami I, Abu-El-Haija S, Perozzi B, Ré C, Murphy K (2020) Machine learning on graphs: a model and comprehensive taxonomy. arXiv:2005.03675
– reference: Ou M, Cui P, Pei J, Zhang Z, Zhu W (2016) Asymmetric transitivity preserving graph embedding. In: Proceedings of ACM SIGKDD international conference on knowledge discovery and data mining (KDD’16), pp 1105–1114
– reference: SuttonRSBartoAGReinforcement learning: an introduction2018CambridgeMIT Press1407.68009
– reference: Yang Y, Wang X, Song M, Yuan J, Tao D (2019) SPAGAN: Shortest path graph attention network. In: Proceedings of international joint conference on artificial intelligence (IJCAI’19), pp 4099–4105
– reference: Yanardag P, Vishwanathan S (2015) Deep graph kernels. In: Proceedings of ACM sigkdd international conference on knowledge discovery and data mining (KDD’15), pp 1365–1374
– reference: Milan A, Rezatofighi SH, Garg R, Dick A, Reid I (2017) Data-driven approximations to np-hard problems. In: Thirty-first AAAI conference on artificial intelligence
– reference: Li Z, Chen Q, Koltun V (2018) Combinatorial optimization with graph convolutional networks and guided tree search. In: Proceedings of international conference on neural information processing systems (NIPS’18), pp 537–546
– reference: Kool W, van Hoof H, Welling M (2019) Attention, learn to solve routing problems! In: International conference on learning representations
– reference: Chang L (2019) Efficient maximum clique computation over large sparse graphs. In: Proceedings of ACM SIGKDD international conference on knowledge discovery and data mining (KDD’19), pp 529–538
– reference: Du X, Yan J, Zha H (2019) Joint link prediction and network alignment via cross-graph embedding. In: Proceedings of international joint conference on artificial intelligence, IJCAI’19, pp 2251–2257
– reference: HopfieldJTankDNeural computation of decisions in optimisation problemsBiol Cybern1985521411520572.68041
– reference: PapadimitriouCHVempalaSOn the approximability of the traveling salesman problemCombinatorica2006261101120220128710.1007/s00493-006-0008-z
– reference: Deudon M, Cournut P, Lacoste A, Adulyasak Y, Rousseau LM (2018) Learning heuristics for the TSP by policy gradient. In: International conference on the integration of constraint programming, artificial intelligence, and operations research, pp 170–181
– reference: Prates M, Avelar P, Lemos H, Lamb L, Vardi M (2019) Learning to solve NP-Complete problems - a graph neural network for decision TSP. In: Proceedings of AAAI conference on artificial intelligence (AAAI’19), pp 4731–4738
– reference: Cao S, Lu W, Xu Q (2015) GraRep: learning graph representations with global structural information. In: Proceedings of ACM international on conference on information and knowledge management (CIKM’15), pp 891–900
– reference: Tang J, Qu M, Mei Q (2015) PTE: Predictive text embedding through large-scale heterogeneous text networks. In: Proceedings of ACM SIGKDD international conference on knowledge discovery and data mining (KDD’15), pp 1165–1174
– reference: Grover A, Leskovec J (2016) Node2Vec: Scalable feature learning for networks. In: Proceedings of ACM SIGKDD international conference on knowledge discovery and data mining (KDD’16), pp 855–864
– reference: Le Q, Mikolov T (2014) Distributed representations of sentences and documents. In: Proceedings of international conference on international conference on machine learning, vol 32, ICML’14, pp II–1188–II–1196
– reference: Peng Y, Choi B, He B, Zhou S, Xu R, Yu X (2016) VColor: A practical vertex-cut based approach for coloring large graphs. In: IEEE international conference on data engineering (ICDE’16), pp 97–108
– reference: Hamilton WL, Ying R, Leskovec J (2017) Inductive representation learning on large graphs. In: Proceedings of international conference on neural information processing systems (NIPS’17), pp 1025–1035
– reference: PengYFanZChoiBXuJBhowmickSSAuthenticated subgraph similarity searchin outsourced graph databasesIEEE Trans Knowl Data Eng20152771838186010.1109/TKDE.2014.2316818
– reference: Bai Y, Ding H, Bian S, Chen T, Sun Y, Wang W (2019) SimGNN: a neural network approach to fast graph similarity computation. In: Proceedings of the ACM international conference on web search and data mining (WSDM’19), pp 384–392
– reference: JinWBarzilayRJaakkolaTJunction tree variational autoencoder for molecular graph generationProc Int Conf Mach Learn20188023232332
– reference: Bengio Y, Lodi A, Prouvost A (2018) Machine learning for combinatorial optimization: A methodological tour d’horizon. arXiv:1811.06128
– reference: Huang W, Zhang T, Rong Y, Huang J (2018) Adaptive sampling towards fast graph representation learning. In: Proceedings of international conference on neural information processing systems (NIPS’18), pp 4563–4572
– reference: Joshi CK, Cappart Q, Rousseau LM, Laurent T, Bresson X (2020) Learning TSP requires rethinking generalization. arXiv:2006.07054
– reference: Perozzi B, Al-Rfou R, Skiena S (2014) DeepWalk: Online learning of social representations. In: Proceedings of ACM SIGKDD international conference on knowledge discovery and data mining (KDD’14), pp 701–710
– reference: WassermanSFaustKSocial network analysis: methods and applications1994CambridgeCambridge University Press10.1017/CBO9780511815478
– reference: Abe K, Xu Z, Sato I, Sugiyama M (2019) Solving np-hard problems on graphs with extended alphago zero. arXiv:1905.11623
– reference: CaiHZhengVWChangKA comprehensive survey of graph embedding: problems, techniques, and applicationsIEEE Trans Knowl Data Eng201830091616163710.1109/TKDE.2018.2807452
– reference: Tsitsulin A, Mottin D, Karras P, Müller E (2018) VERSE: Versatile graph embeddings from similarity measures. In: Proceedings of world wide web conference (WWW’18), pp 539–548
– reference: Lamb LC, Garcez AD, Gori M, Prates MO, Avelar PH, Vardi MY (2020) Graph neural networks meet neural-symbolic computing: a survey and perspective. In: Proceedings of international joint conference on artificial intelligence (IJCAI’20), pp 4877–4884
– reference: VinyalsOFortunatoMJaitlyNPointer networksAdv Neural Inf Process Syst20152826922700
– reference: Zhang F, Yuan NJ, Lian D, Xie X, Ma WY (2016) Collaborative knowledge base embedding for recommender systems. In: Proceedings of ACM SIGKDD international conference on knowledge discovery and data mining (KDD’16), pp 353–362
– reference: Nguyen H, Murata T (2017) Motif-aware graph embeddings. In: Proceedings of international joint conference on artificial intelligence (IJCAI’17), pp 1–1
– reference: Nazi A, Hang W, Goldie A, Ravi S, Mirhoseini A (2019) GAP : Generalizable approximate graph partitioning framework. URL ICLR workshop
– reference: Fan W, Ma Y, Li Q, He Y, Zhao E, Tang J, Yin D (2019) Graph neural networks for social recommendation. In: The world wide web conference, pp 417–426
– reference: Hamilton WL, Ying R, Leskovec J (2017) Representation learning on graphs: methods and applications. IEEE Data Eng Bull
– reference: Lemos H, Prates MOR, Avelar PHC, Lamb LC (2019) Graph colouring meets deep learning: Effective graph neural network models for combinatorial problems. CoRR arXiv:1903.04598
– reference: Nowak A, Villar S, Bandeira AS, Bruna J (2017) A note on learning algorithms for quadratic assignment with graph neural networks. In: Proceeding of international conference on machine learning (ICML’17), pp 22–22
– reference: Ribeiro LF, Saverese PH, Figueiredo DR (2017) Struc2Vec: Learning node representations from structural identity. In: Proceedings of ACM SIGKDD international conference on knowledge discovery and data mining (KDD’17), pp 385–394
– reference: Bai Y, Xu D, Wang A, Gu K, Wu X, Marinovic A, Ro C, Sun Y, Wang W (2020) Fast detection of maximum common subgraph via deep Q-learning. arXiv:2002.03129
– reference: Wu Z, Pan S, Chen F, Long G, Zhang C, Yu PS (2019) A comprehensive survey on graph neural networks. CoRR arXiv:1901.00596
– reference: Tang J, Qu M, Wang M, Zhang M, Yan J, Mei Q (2015) LINE: Large-scale information network embedding. In: Proceedings of international conference on world wide web (WWW’15), pp 1067–1077
– reference: Tu K, Cui P, Wang X, Yu PS, Zhu W (2018) Deep recursive network embedding with regular equivalence. In: Proceedings of ACM SIGKDD international conference on knowledge discovery & data mining (KDD’18), pp 2357–2366
– reference: ZhangDYinJZhuXZhangCNetwork representation learning: a surveyIEEE Trans Big Data20206132810.1109/TBDATA.2018.2850013
– reference: Huang J, Patwary MMA, Diamos GF (2019) Coloring big graphs with alphagozero. CoRR arXiv:1902.10162
– reference: CuiPWangXPeiJZhuWA survey on network embeddingIEEE Trans Knowl Data Eng201931583385210.1109/TKDE.2018.2849727
– reference: BonnerSKureshiIBrennanJTheodoropoulosGMcGoughASObaraBExploring the semantic content of unsupervised graph embeddings: an empirical studyData Sci Eng20194326928910.1007/s41019-019-0097-5
– reference: Kipf TN, Welling M (2017) Semi-supervised classification with graph convolutional networks. In: International conference on learning representations (ICLR’17)
– reference: Wu Y, Song W, Cao Z, Zhang J, Lim A (2019) Learning improvement heuristics for solving the travelling salesman problem. CoRR arXiv:1912.05784
– reference: ChenFWangYCWangBKuoCCJGraph representation learning: a surveyAPSIPA Trans Signal Inf Process20209e1510.1017/ATSIP.2020.13
– reference: Yu Y, Lu Z, Liu J, Zhao G, Wen J (2019) RUM: Network representation learning using motifs. In: IEEE international conference on data engineering (ICDE’19), pp 1382–1393
– reference: Mazyavkina N, Sviridov S, Ivanov S, Burnaev E (2020) Reinforcement learning for combinatorial optimization: a survey. arXiv:2003.03600
– reference: Joshi CK, Laurent T, Bresson X (2019) An efficient graph convolutional network technique for the travelling salesman problem. CoRR arXiv:1906.01227
– reference: Li Y, Gu C, Dullien T, Vinyals O, Kohli P (2019) Graph matching networks for learning the similarity of graph structured objects. In: Proceedings of international conference on machine learning (ICML’19), pp 3835–3845
– reference: DaveVSZhangBChenPYAl HasanMNeural-brane: neural bayesian personalized ranking for attributed network embeddingData Sci Eng20194211913110.1007/s41019-019-0092-x
– reference: HuangXLakshmananLVXuJCommunity search over big graphs2019New YorkMorgan & Claypool Publishers10.2200/S00928ED1V01Y201906DTM061
– reference: Meng L, Zhang J (2019) IsoNN: Isomorphic neural network for graph representation learning and classification. CoRR arXiv:1907.09495
– reference: Wang R, Yan J, Yang X (2019) Learning combinatorial embedding networks for deep graph matching. In: Proceedings of the IEEE international conference on computer vision (ICCV’19), pp 3056–3065
– reference: YueXWangZHuangJParthasarathySMoosavinasabSHuangYLinSMZhangWZhangPSunHGraph embedding on biomedical networks: methods, applications and evaluationsBioinformatics201936412411251
– reference: DevlinJChangMWLeeKToutanovaKBERT: Pre-training of deep bidirectional transformers for language understandingProc Conf N Am Chapter Assoc Comput Linguist Hum Lang Technol2019141714186
– reference: HåstadJClique is hard to approximate within n1-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n^{1-\varepsilon }$$\end{document}Acta Math19991821105142168733110.1007/BF02392825
– reference: Bai Y, Ding H, Gu K, Sun Y, Wang W (2020) Learning-based efficient graph similarity computation via multi-scale convolutional set matching. In: Proceedings of the AAAI conference on artificial intelligence (AAAI’20), pp 3219–3226
– reference: DuvenaudDKMaclaurinDIparraguirreJBombarellRHirzelTAspuru-GuzikAAdamsRPConvolutional networks on graphs for learning molecular fingerprintsAdv Neural Inf Process Syst20152822242232
– reference: Veličković P, Cucurull G, Casanova A, Romero A, Liò P, Bengio Y (2018) Graph Attention Networks. In: International conference on learning representations (ICLR)
– reference: GoemansMXWilliamsonDPImproved approximation algorithms for maximum cut and satisfiability problems using semidefinite programmingJ ACM199542611151145141222810.1145/227683.227684
– reference: Chen H, Yin H, Chen T, Nguyen QVH, Peng W, Li X (2019) Exploiting centrality information with graph convolutions for network representation learning. In: IEEE international conference on data engineering (ICDE’19), pp 590–601
– reference: FanZPengYChoiBXuJBhowmickSSTowards efficient authenticated subgraph query service in outsourced graph databasesIEEE Trans Serv Comput20147469671310.1109/TSC.2013.42
– reference: Dareddy MR, Das M, Yang H (2019) Motif2Vec: Motif aware node representation learning for heterogeneous networks. In: 2019 IEEE international conference on big data (Big Data’19), pp 1052–1059
– reference: Narayanan A, Chandramohan M, Chen L, Liu Y, Saminathan S, Subgraph2Vec: learning distributed representations of rooted sub-graphs from large graphs
– reference: Smith-MilesKNeural networks for combinatorial optimization: a review of more than a decade of researchINFORMS J Comput1999111534168812410.1287/ijoc.11.1.15
– reference: Wang D, Cui P, Zhu W (2016) Structural deep network embedding. In: Proceedings of ACM SIGKDD International conference on knowledge discovery and data mining (KDD’16), pp 1225–1234
– reference: Khot S (2001) Improved inapproximability results for maxclique, chromatic number and approximate graph coloring. In: Proceedings IEEE symposium on foundations of computer science, pp 600–609
– reference: Dai H, Khalil EB, Zhang Y, Dilkina B, Song L (2017) Learning combinatorial optimization algorithms over graphs. In: Proceedings of international conference on neural information processing systems (NIPS’17), pp 6351–6361
– reference: Sato R, Yamada M, Kashima H (2019) Approximation ratios of graph neural networks for combinatorial problems. In: Proceedings of the neural information processing systems (NIPS’19)
– ident: 155_CR56
  doi: 10.1145/2623330.2623732
– ident: 155_CR73
  doi: 10.1145/2783258.2783417
– ident: 155_CR4
– volume-title: Community search over big graphs
  year: 2019
  ident: 155_CR31
  doi: 10.2200/S00928ED1V01Y201906DTM061
– ident: 155_CR33
– volume: 518
  start-page: 529
  issue: 7540
  year: 2015
  ident: 155_CR47
  publication-title: Nature
  doi: 10.1038/nature14236
– ident: 155_CR19
  doi: 10.24963/ijcai.2019/312
– ident: 155_CR54
  doi: 10.1109/ICDE.2016.7498232
– volume: 27
  start-page: 1838
  issue: 7
  year: 2015
  ident: 155_CR55
  publication-title: IEEE Trans Knowl Data Eng
  doi: 10.1109/TKDE.2014.2316818
– ident: 155_CR21
  doi: 10.1145/3308558.3313488
– ident: 155_CR10
  doi: 10.1145/3292500.3330986
– ident: 155_CR14
– ident: 155_CR64
  doi: 10.1145/3178876.3186120
– ident: 155_CR3
  doi: 10.1609/aaai.v34i04.5720
– ident: 155_CR24
  doi: 10.1145/2939672.2939754
– ident: 155_CR37
– ident: 155_CR71
– ident: 155_CR35
  doi: 10.1109/SFCS.2001.959936
– ident: 155_CR65
  doi: 10.1145/3219819.3220068
– ident: 155_CR74
  doi: 10.24963/ijcai.2019/569
– ident: 155_CR1
– ident: 155_CR38
  doi: 10.24963/ijcai.2020/679
– ident: 155_CR26
– volume: 6
  start-page: 3
  issue: 1
  year: 2020
  ident: 155_CR77
  publication-title: IEEE Trans Big Data
  doi: 10.1109/TBDATA.2018.2850013
– ident: 155_CR52
  doi: 10.1145/2939672.2939751
– ident: 155_CR46
  doi: 10.1609/aaai.v31i1.10750
– volume: 7
  start-page: 696
  issue: 4
  year: 2014
  ident: 155_CR22
  publication-title: IEEE Trans Serv Comput
  doi: 10.1109/TSC.2013.42
– ident: 155_CR43
– ident: 155_CR15
  doi: 10.1109/BigData47090.2019.9005670
– volume: 11
  start-page: 15
  year: 1999
  ident: 155_CR60
  publication-title: INFORMS J Comput
  doi: 10.1287/ijoc.11.1.15
– ident: 155_CR51
  doi: 10.1109/DSW.2018.8439919
– volume: 28
  start-page: 2692
  year: 2015
  ident: 155_CR67
  publication-title: Adv Neural Inf Process Syst
– ident: 155_CR8
  doi: 10.1145/2806416.2806512
– ident: 155_CR17
  doi: 10.1007/978-3-319-93031-2_12
– ident: 155_CR36
– volume-title: Social network analysis: methods and applications
  year: 1994
  ident: 155_CR70
  doi: 10.1017/CBO9780511815478
– ident: 155_CR29
– volume: 36
  start-page: 1241
  issue: 4
  year: 2019
  ident: 155_CR76
  publication-title: Bioinformatics
  doi: 10.1093/bioinformatics/btz718
– volume: 1
  start-page: 4171
  year: 2019
  ident: 155_CR18
  publication-title: Proc Conf N Am Chapter Assoc Comput Linguist Hum Lang Technol
– ident: 155_CR48
– ident: 155_CR25
– volume: 4
  start-page: 119
  issue: 2
  year: 2019
  ident: 155_CR16
  publication-title: Data Sci Eng
  doi: 10.1007/s41019-019-0092-x
– volume: 26
  start-page: 101
  issue: 1
  year: 2006
  ident: 155_CR53
  publication-title: Combinatorica
  doi: 10.1007/s00493-006-0008-z
– ident: 155_CR62
  doi: 10.1145/2783258.2783307
– volume: 9
  start-page: e15
  year: 2020
  ident: 155_CR11
  publication-title: APSIPA Trans Signal Inf Process
  doi: 10.1017/ATSIP.2020.13
– ident: 155_CR12
  doi: 10.1109/ICDE.2019.00059
– volume: 31
  start-page: 833
  issue: 5
  year: 2019
  ident: 155_CR13
  publication-title: IEEE Trans Knowl Data Eng
  doi: 10.1109/TKDE.2018.2849727
– ident: 155_CR44
– ident: 155_CR75
  doi: 10.1109/ICDE.2019.00125
– ident: 155_CR9
– ident: 155_CR50
– ident: 155_CR39
– volume-title: Reinforcement learning: an introduction
  year: 2018
  ident: 155_CR61
– ident: 155_CR68
  doi: 10.1145/2939672.2939753
– ident: 155_CR30
– ident: 155_CR42
  doi: 10.1007/978-3-030-04221-9_48
– volume: 182
  start-page: 105
  issue: 1
  year: 1999
  ident: 155_CR27
  publication-title: Acta Math
  doi: 10.1007/BF02392825
– ident: 155_CR5
– ident: 155_CR69
  doi: 10.1109/ICCV.2019.00315
– ident: 155_CR63
  doi: 10.1145/2736277.2741093
– ident: 155_CR57
  doi: 10.1609/aaai.v33i01.33014731
– ident: 155_CR45
– ident: 155_CR49
– volume: 42
  start-page: 1115
  issue: 6
  year: 1995
  ident: 155_CR23
  publication-title: J ACM
  doi: 10.1145/227683.227684
– ident: 155_CR66
– volume: 52
  start-page: 141
  year: 1985
  ident: 155_CR28
  publication-title: Biol Cybern
  doi: 10.1007/BF00339943
– ident: 155_CR41
– volume: 4
  start-page: 269
  issue: 3
  year: 2019
  ident: 155_CR6
  publication-title: Data Sci Eng
  doi: 10.1007/s41019-019-0097-5
– ident: 155_CR78
  doi: 10.1145/2939672.2939673
– volume: 28
  start-page: 2224
  year: 2015
  ident: 155_CR20
  publication-title: Adv Neural Inf Process Syst
– volume: 80
  start-page: 2323
  year: 2018
  ident: 155_CR32
  publication-title: Proc Int Conf Mach Learn
– volume: 30
  start-page: 1616
  issue: 09
  year: 2018
  ident: 155_CR7
  publication-title: IEEE Trans Knowl Data Eng
  doi: 10.1109/TKDE.2018.2807452
– ident: 155_CR40
  doi: 10.1109/ICTAI.2019.00125
– ident: 155_CR72
– ident: 155_CR34
– ident: 155_CR58
  doi: 10.1145/3097983.3098061
– ident: 155_CR2
  doi: 10.1145/3289600.3290967
– ident: 155_CR59
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Snippet Graphs have been widely used to represent complex data in many applications, such as e-commerce, social networks, and bioinformatics. Efficient and effective...
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SubjectTerms Algorithm Analysis and Problem Complexity
Artificial Intelligence
Bioinformatics
Carbon monoxide
Chemistry and Earth Sciences
Combinatorial analysis
Computer Science
Data Mining and Knowledge Discovery
Database Management
Embedding
Graph representations
Graphical representations
Graphs
Machine learning
Optimization
Physics
Social networks
Statistics for Engineering
Surveys
Systems and Data Security
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