763:). This solver adopts a constraint programming approach, using bit-parallel data structures and specialized propagation algorithms for performance. It supports most common variations of the problem and is capable of counting or enumerating solutions as well as deciding whether one exists.
1007:
It is known since the mid-70's that the isomorphism problem is solvable in polynomial time for plane graphs. However, it has also been noted that the subisomorphism problem is still N P-complete, in particular because the
Hamiltonian cycle problem is NP-complete for planar
342:
552:
1207:
710:
describes a recursive backtracking procedure for solving the subgraph isomorphism problem. Although its running time is, in general, exponential, it takes polynomial time for any fixed choice of
424:
1248:
Han, Myoungji; Kim, Hyunjoon; Gu, Geonmo; Park, Kunsoo; Han, Wookshin (2019), "Efficient
Subgraph Matching: Harmonizing Dynamic Programming, Adaptive Matching Order, and Failing Set Together",
213:
1713:
McCreesh, Ciaran; Prosser, Patrick; Trimble, James (2020), "The
Glasgow Subgraph Solver: Using Constraint Programming to Tackle Hard Subgraph Isomorphism Problem Variants",
375:
218:
161:
1760:
750:
proposed in 2004 another algorithm based on
Ullmann's, VF2, which improves the refinement process using different heuristics and uses significantly less memory.
429:
1636:
Carletti, V.; Foggia, P.; Saggese, A.; Vento, M. (2018), "Challenging the time complexity of exact subgraph isomorphism for huge and dense graphs with VF3",
1160:
886:
680:
1681:
Graph-Based
Representations in Pattern Recognition - 12th IAPR-TC-15 International Workshop, GbRPR 2019, Tours, France, June 19-21, 2019, Proceedings
1317:
Ohlrich, Miles; Ebeling, Carl; Ginting, Eka; Sather, Lisa (1993), "SubGemini: identifying subcircuits using a fast subgraph isomorphism algorithm",
1732:
1696:
1378:
1336:
1299:
1217:
795:
881:
876:
1715:
Graph
Transformation - 13th International Conference, ICGT 2020, Held as Part of STAF 2020, Bergen, Norway, June 25-26, 2020, Proceedings
611:
956:
1431:
Snijders, T. A. B.; Pattison, P. E.; Robins, G.; Handcock, M. S. (2006), "New specifications for exponential random graph models",
1120:
84:
is also used for the same problem. This name puts emphasis on finding such a subgraph as opposed to the bare decision problem.
1228:
1400:; Jurisica, I. (2006), "Efficient estimation of graphlet frequency distributions in protein–protein interaction networks",
1750:
1515:
383:
1503:
Jamil, Hasan (2011), "Computing
Subgraph Isomorphic Queries using Structural Unification and Minimum Graph Structures",
31:
766:
For large graphs, state-of-the art algorithms include CFL-Match and
Turboiso, and extensions thereupon such as DAF by
695:); that is, solving the subgraph isomorphism requires an algorithm to check the presence or absence in the input of Ω(
1755:
649:
166:
1513:
Ullmann, Julian R. (2010), "Bit-vector algorithms for binary constraint satisfaction and subgraph isomorphism",
1358:
618:
93:
54:
972:
de la
Higuera, Colin; Janodet, Jean-Christophe; Samuel, Émilie; Damiand, Guillaume; Solnon, Christine (2013),
818:
1600:
Bonnici, V.; Giugno, R. (2013), "A subgraph isomorphism algorithm and its application to biochemical data",
1354:
871:
851:
1152:
910:
782:
to find similarities between chemical compounds from their structural formula; often in this area the term
1563:
1524:
1440:
1277:
1092:
759:
The current state of the art solver for moderately-sized, hard instances is the
Glasgow Subgraph Solver (
832:
756:
proposed a better algorithm, which improves the initial order of the vertices using some heuristics.
1568:
1529:
1445:
1282:
836:
783:
347:
1702:
1661:
1589:
1542:
1491:
1472:
1458:
1342:
1305:
1261:
1187:
1169:
1136:
337:{\displaystyle G_{0}=(V_{0},E_{0})\mid V_{0}\subseteq V,E_{0}\subseteq E\cap (V_{0}\times V_{0})}
676:
is true. However the complexity-theoretic status of graph isomorphism remains an open question.
1673:
1728:
1692:
1653:
1625:
1581:
1419:
1374:
1332:
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1213:
952:
727:
70:
58:
946:
128:
1718:
1684:
1645:
1615:
1605:
1573:
1554:
Cordella, Luigi P. (2004), "A (sub) graph isomorphism algorithm for matching large graphs",
1534:
1481:
1450:
1409:
1366:
1322:
1287:
1253:
1203:
1199:
1179:
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988:
859:
855:
787:
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The proof of subgraph isomorphism being NP-complete is simple and based on reduction of the
100:
39:
1388:
1002:
1384:
998:
973:
844:
840:
779:
668:
both have the same numbers of vertices and edges and the subgraph isomorphism problem for
547:{\displaystyle \{\,v_{1},v_{2}\,\}\in E_{0}\iff \{\,f(v_{1}),f(v_{2})\,\}\in E^{\prime }}
77:. However certain other cases of subgraph isomorphism may be solved in polynomial time.
1620:
1148:
1020:
822:
814:
684:
574:
558:
66:
1744:
1706:
1454:
1397:
1265:
642:
1546:
1495:
1462:
1414:
645:, this shows that subgraph isomorphism remains NP-complete even in the planar case.
17:
1665:
1346:
1309:
1191:
1140:
1112:
805:
The closely related problem of counting the number of isomorphic copies of a graph
723:
1717:, Lecture Notes in Computer Science, vol. 12150, Springer, pp. 316–324,
1593:
1723:
1688:
1610:
1096:
735:
74:
1683:, Lecture Notes in Computer Science, vol. 11510, Springer, pp. 1–13,
1649:
1370:
993:
913:
already showed subgraph isomorphism to be NP-complete, using a reduction from
1291:
1272:
Kuramochi, Michihiro; Karypis, George (2001), "Frequent subgraph discovery",
1538:
1257:
378:
1657:
1629:
1585:
1423:
1577:
1486:
1365:, Algorithms and Combinatorics, vol. 28, Springer, pp. 400–401,
1327:
1131:
744:
is a substantial update to the 1976 subgraph isomorphism algorithm paper.
581:
vertices. To translate this to a subgraph isomorphism problem, simply let
99:
To prove subgraph isomorphism is NP-complete, it must be formulated as a
1183:
561:, an NP-complete decision problem in which the input is a single graph
1209:
Computers and Intractability: A Guide to the Theory of NP-Completeness
1174:
1093:
http://www.aaai.org/Papers/Symposia/Fall/2006/FS-06-02/FS06-02-007.pdf
974:"Polynomial algorithms for open plane graph and subgraph isomorphisms"
1361:(2012), "18.3 The subgraph isomorphism problem and Boolean queries",
799:
791:
734:
is fixed, the running time of subgraph isomorphism can be reduced to
660:: the answer to the graph isomorphism problem is true if and only if
1470:
Ullmann, Julian R. (1976), "An algorithm for subgraph isomorphism",
691:
showed that any subgraph isomorphism problem has query complexity Ω(
1319:
Proceedings of the 30th international Design Automation Conference
914:
858:
in graphs problems; an extension of subgraph isomorphism known as
786:
is used. A query structure is often defined graphically using a
641:. Because the Hamiltonian cycle problem is NP-complete even for
625:
which is to be tested for Hamiltonicity into the pair of graphs
948:
Complexity Theory: Exploring the Limits of Efficient Algorithms
1638:
IEEE Transactions on Pattern Analysis and Machine Intelligence
1556:
IEEE Transactions on Pattern Analysis and Machine Intelligence
1080:
1153:"Subgraph isomorphism in planar graphs and related problems"
539:
411:
197:
184:
1229:"On the randomized complexity of monotone graph properties"
1116:
828:
594:; then the answer to the subgraph isomorphism problem for
1674:"Experimental Evaluation of Subgraph Isomorphism Solvers"
103:. The input to the decision problem is a pair of graphs
933:
813:
has been applied to pattern discovery in databases, the
778:
As subgraph isomorphism has been applied in the area of
831:
describe an application of subgraph isomorphism in the
65:. Subgraph isomorphism is a generalization of both the
794:
based database systems typically define queries using
760:
69:
and the problem of testing whether a graph contains a
1068:
614:
shows that subgraph isomorphism is also NP-complete.
432:
386:
350:
221:
169:
131:
419:{\displaystyle f\colon V_{0}\rightarrow V^{\prime }}
49:are given as input, and one must determine whether
843:(the most runtime-intensive), and thus offered by
546:
418:
369:
336:
207:
155:
714:(with a polynomial that depends on the choice of
637:is a cycle having the same number of vertices as
602:is equal to the answer to the clique problem for
1274:1st IEEE International Conference on Data Mining
1056:
817:of protein-protein interaction networks, and in
648:Subgraph isomorphism is a generalization of the
610:. Since the clique problem is NP-complete, this
1122:Proc. 3rd ACM Symposium on Theory of Computing
1117:"The complexity of theorem-proving procedures"
1097:https://e-reports-ext.llnl.gov/pdf/332302.pdf
854:, where it is considered part of an array of
753:
88:Decision problem and computational complexity
8:
1363:Sparsity: Graphs, Structures, and Algorithms
1161:Journal of Graph Algorithms and Applications
767:
528:
482:
461:
433:
887:Maximum common subgraph isomorphism problem
208:{\displaystyle H=(V^{\prime },E^{\prime })}
111:. The answer to the problem is positive if
481:
477:
1722:
1619:
1609:
1567:
1528:
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1444:
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839:. Subgraph matching is also a substep in
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92:For broader coverage of this topic, see
1505:26th ACM Symposium on Applied Computing
1045:
898:
741:
707:
27:Problem in theoretical computer science
1761:Computational problems in graph theory
1033:
934:Nešetřil & Ossona de Mendez (2012)
761:McCreesh, Prosser & Trimble (2020)
688:
1069:PrĹľulj, Corneil & Jurisica (2006)
925:
923:
38:is a computational task in which two
7:
1516:Journal of Experimental Algorithmics
1032:For an experimental evaluation, see
906:
882:Maximum common edge subgraph problem
877:Induced subgraph isomorphism problem
821:methods for mathematically modeling
850:The problem is also of interest in
862:is also of interest in that area.
681:Aanderaa–Karp–Rosenberg conjecture
617:An alternative reduction from the
612:polynomial-time many-one reduction
25:
377:? I. e., does there exist a
1455:10.1111/j.1467-9531.2006.00176.x
699:) different edges in the graph.
215:be graphs. Is there a subgraph
115:is isomorphic to a subgraph of
1057:Kuramochi & Karypis (2001)
726:(or more generally a graph of
687:of monotone graph properties,
569:, and the question is whether
524:
511:
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331:
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202:
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1:
1415:10.1093/bioinformatics/btl030
1227:Gröger, Hans Dietmar (1992),
1724:10.1007/978-3-030-51372-6_19
981:Theoretical Computer Science
370:{\displaystyle G_{0}\cong H}
36:subgraph isomorphism problem
32:theoretical computer science
1689:10.1007/978-3-030-20081-7_1
1611:10.1186/1471-2105-14-s7-s13
754:Bonnici & Giugno (2013)
621:problem translates a graph
1777:
1672:Solnon, Christine (2019),
1650:10.1109/TPAMI.2017.2696940
119:, and negative otherwise.
91:
1371:10.1007/978-3-642-27875-4
1359:Ossona de Mendez, Patrice
994:10.1016/j.tcs.2013.05.026
650:graph isomorphism problem
1604:, 14(Suppl7) (13): S13,
1433:Sociological Methodology
1292:10.1109/ICDM.2001.989534
951:, Springer, p. 81,
819:exponential random graph
94:Computational complexity
1539:10.1145/1671970.1921702
1258:10.1145/3299869.3319880
872:Frequent subtree mining
852:artificial intelligence
156:{\displaystyle G=(V,E)}
1095:; expanded version at
1081:Snijders et al. (2006)
945:Wegener, Ingo (2005),
909:paper that proves the
679:In the context of the
585:be the complete graph
548:
420:
371:
338:
209:
157:
67:maximum clique problem
1578:10.1109/tpami.2004.75
1487:10.1145/321921.321925
1328:10.1145/157485.164556
1223:. A1.4: GT48, pg.202.
1132:10.1145/800157.805047
833:computer-aided design
829:Ohlrich et al. (1993)
652:, which asks whether
549:
421:
372:
339:
210:
158:
1751:NP-complete problems
1507:, pp. 1058–1063
1125:, pp. 151–158,
1019:Here Ω invokes
430:
384:
348:
219:
167:
129:
18:Subgraph isomorphism
845:graph rewrite tools
837:electronic circuits
784:substructure search
80:Sometimes the name
73:, and is therefore
1602:BMC Bioinformatics
1473:Journal of the ACM
1355:Nešetřil, Jaroslav
1321:, pp. 31–37,
1184:10.7155/jgaa.00014
1021:Big Omega notation
917:involving cliques.
911:Cook–Levin theorem
809:in a larger graph
544:
416:
367:
334:
205:
153:
1734:978-3-030-51371-9
1698:978-3-030-20080-0
1562:(10): 1367–1372,
1380:978-3-642-27874-7
1338:978-0-89791-577-9
1301:978-0-7695-1119-1
1219:978-0-7167-1045-5
1204:Johnson, David S.
1200:Garey, Michael R.
768:Han et al. (2019)
728:bounded expansion
656:is isomorphic to
619:Hamiltonian cycle
575:complete subgraph
122:Formal question:
82:subgraph matching
71:Hamiltonian cycle
16:(Redirected from
1768:
1756:Graph algorithms
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1236:Acta Cybernetica
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1212:, W.H. Freeman,
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856:pattern matching
788:structure editor
685:query complexity
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101:decision problem
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1512:
1502:
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1302:
1276:, p. 313,
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1149:Eppstein, David
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930:Eppstein (1999)
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841:graph rewriting
823:social networks
780:cheminformatics
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748:Cordella (2004)
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1446:10.1.1.62.7975
1428:
1408:(8): 974–980,
1402:Bioinformatics
1398:Corneil, D. G.
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1283:10.1.1.22.4992
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559:clique problem
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1439:(1): 99–153,
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905:The original
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860:graph mining
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765:
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724:planar graph
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1113:Cook, S. A.
907:Cook (1971)
802:extension.
736:linear time
573:contains a
75:NP-complete
53:contains a
1745:Categories
1106:References
703:Algorithms
426:such that
344:such that
59:isomorphic
1707:128270779
1564:CiteSeerX
1525:CiteSeerX
1441:CiteSeerX
1278:CiteSeerX
1266:195259296
987:: 76–99,
790:program;
540:′
532:∈
479:⟺
465:∈
412:′
404:→
391::
379:bijection
362:≅
319:×
303:∩
297:⊆
278:⊆
265:∣
198:′
185:′
1658:28436848
1630:23815292
1586:15641723
1547:15021184
1496:17268751
1463:10800726
1424:16452112
1206:(1979),
1151:(1999),
1115:(1971),
866:See also
718:). When
633:, where
57:that is
55:subgraph
1666:3709576
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1389:2920058
1347:5889119
1310:8684662
1192:2303110
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1008:graphs.
1003:3083515
683:on the
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800:SMILES
796:SMARTS
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1703:S2CID
1677:(PDF)
1662:S2CID
1590:S2CID
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1492:S2CID
1459:S2CID
1343:S2CID
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1188:S2CID
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