{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T11:10:07Z","timestamp":1788779407129,"version":"build-2803163510"},"publisher-location":"Cham","reference-count":39,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032376633","type":"print"},{"value":"9783032376640","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T00:00:00Z","timestamp":1788825600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T00:00:00Z","timestamp":1788825600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2027]]},"DOI":"10.1007\/978-3-032-37664-0_2","type":"book-chapter","created":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T10:20:17Z","timestamp":1788776417000},"page":"20-36","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Scaling Weisfeiler\u2013Leman Expressiveness Analysis to\u00a0Massive Graphs with\u00a0GPUs"],"prefix":"10.1007","author":[{"given":"Filippo","family":"Biondi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mirco","family":"Tribastone","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Max","family":"Tschaikowski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,9,8]]},"reference":[{"key":"2_CR1","doi-asserted-by":"crossref","unstructured":"Argyris, G., Lluch-Lafuente, A., Leguizamon-Robayo, A., Tribastone, M., Tschaikowski, M., Vandin, A.: Minimization of dynamical systems over monoids. In: LICS (2023)","DOI":"10.1109\/LICS56636.2023.10175697"},{"key":"2_CR2","doi-asserted-by":"crossref","unstructured":"Bacci, G., Bacci, G., Larsen, K.G., Tribastone, M., Tschaikowski, M., Vandin, A.: Efficient local computation of differential bisimulations via coupling and up-to methods. In: LICS (2021)","DOI":"10.1109\/LICS52264.2021.9470555"},{"key":"2_CR3","doi-asserted-by":"crossref","unstructured":"Berkholz, C., Bonsma, P., Grohe, M.: Tight lower and upper bounds for the complexity of canonical colour refinement. In: ESA (2013)","DOI":"10.1007\/978-3-642-40450-4_13"},{"issue":"5","key":"2_CR4","first-page":"681","volume":"27","author":"A Bishnoi","year":"2018","unstructured":"Bishnoi, A., Clark, P.L., Potukuchi, A., Schmitt, J.R.: On zeros of a polynomial in a finite grid. Comb. Probab. Comput. 27(5), 681\u2013699 (2018)","journal-title":"Comb. Probab. Comput."},{"key":"2_CR5","doi-asserted-by":"crossref","unstructured":"Blackman, D., Vigna, S.: Scrambled linear pseudorandom number generators. ACM Trans. Math. Softw. 47(4) (2021)","DOI":"10.1145\/3460772"},{"key":"2_CR6","doi-asserted-by":"crossref","unstructured":"Blom, S., Haverkort, B.R., Kuntz, M., van\u00a0de Pol, J.: Distributed markovian bisimulation reduction aimed at CSL model checking. In: PDMC (2008)","DOI":"10.1016\/j.entcs.2008.11.012"},{"key":"2_CR7","doi-asserted-by":"crossref","unstructured":"Boldi, P., Codenotti, B., Santini, M., Vigna, S.: Ubicrawler: a scalable fully distributed web crawler. Softw.: Pract. Exp. 34(8), 711\u2013726 (2004)","DOI":"10.1002\/spe.587"},{"key":"2_CR8","doi-asserted-by":"crossref","unstructured":"Boldi, P., Marino, A., Santini, M., Vigna, S.: BUbiNG: massive crawling for the masses. In: WWW (Companion Volume) (2014)","DOI":"10.1145\/2567948.2577304"},{"key":"2_CR9","doi-asserted-by":"crossref","unstructured":"Boldi, P., Rosa, M., Santini, M., Vigna, S.: Layered label propagation: a multiresolution coordinate-free ordering for compressing social networks. In: WWW (2011)","DOI":"10.1145\/1963405.1963488"},{"key":"2_CR10","doi-asserted-by":"crossref","unstructured":"Boldi, P., Vigna, S.: The WebGraph framework I: compression techniques. In: WWW (2004)","DOI":"10.1145\/988672.988752"},{"issue":"11","key":"2_CR11","doi-asserted-by":"publisher","first-page":"6557","DOI":"10.1109\/TAC.2023.3244093","volume":"68","author":"L Cardelli","year":"2023","unstructured":"Cardelli, L., Grosu, R., Larsen, K.G., Tribastone, M., Tschaikowski, M., Vandin, A.: Algorithmic minimization of uncertain continuous-time markov chains. IEEE Trans. Autom. Control 68(11), 6557\u20136572 (2023)","journal-title":"IEEE Trans. Autom. Control"},{"key":"2_CR12","doi-asserted-by":"crossref","unstructured":"Cardelli, L., Squillace, G., Tribastone, M., Tschaikowski, M., Vandin, A.: Formal lumping of polynomial differential equations through approximate equivalences. J. Log. Algebraic Methods Program (2023)","DOI":"10.2139\/ssrn.4160059"},{"key":"2_CR13","doi-asserted-by":"publisher","unstructured":"Cardelli, L., Tribastone, M., Tschaikowski, M., Vandin, A.: ERODE: a tool for the evaluation and reduction of ordinary differential equations. In: Legay, A., Margaria, T. (eds.) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2017. LNCS, vol. 10206, pp. 310\u2013328. Springer, Berlin, Heidelberg (2017). https:\/\/doi.org\/10.1007\/978-3-662-54580-5_19","DOI":"10.1007\/978-3-662-54580-5_19"},{"issue":"38","key":"2_CR14","doi-asserted-by":"publisher","first-page":"10029","DOI":"10.1073\/pnas.1702697114","volume":"114","author":"L Cardelli","year":"2017","unstructured":"Cardelli, L., Tribastone, M., Tschaikowski, M., Vandin, A.: Maximal aggregation of polynomial dynamical systems. Proc. Natl. Acad. Sci. 114(38), 10029\u201310034 (2017). https:\/\/doi.org\/10.1073\/pnas.1702697114","journal-title":"Proc. Natl. Acad. Sci."},{"key":"2_CR15","doi-asserted-by":"crossref","unstructured":"Cardelli, L., Tribastone, M., Tschaikowski, M., Vandin, A.: Guaranteed error bounds on approximate model abstractions through reachability analysis. In: QEST (2018)","DOI":"10.1007\/978-3-319-99154-2_7"},{"key":"2_CR16","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1016\/j.tcs.2019.03.018","volume":"777","author":"L Cardelli","year":"2019","unstructured":"Cardelli, L., Tribastone, M., Tschaikowski, M., Vandin, A.: Symbolic computation of differential equivalences. Theor. Comput. Sci. 777, 132\u2013154 (2019)","journal-title":"Theor. Comput. Sci."},{"key":"2_CR17","doi-asserted-by":"crossref","unstructured":"Chen, D., van Breugel, F., Worrell, J.: On the complexity of computing probabilistic bisimilarity. In: FOSSACS, pp. 437\u2013451 (2012)","DOI":"10.1007\/978-3-642-28729-9_29"},{"key":"2_CR18","doi-asserted-by":"crossref","unstructured":"Davis, T.A., Hu, Y.: The university of florida sparse matrix collection. ACM Trans. Math. Softw. 38(1) (2011)","DOI":"10.1145\/2049662.2049663"},{"key":"2_CR19","doi-asserted-by":"crossref","unstructured":"van Dijk, T., van\u00a0de Pol, J.: Multi-core symbolic bisimulation minimisation. In: TACAS, pp. 332\u2013348 (2016)","DOI":"10.1007\/978-3-662-49674-9_19"},{"key":"2_CR20","unstructured":"Fey, M., Lenssen, J.E.: Fast graph representation learning with pytorch geometric. CoRR abs\/1903.02428 (2019). http:\/\/arxiv.org\/abs\/1903.02428"},{"issue":"1\u20133","key":"2_CR21","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/S0024-3795(97)83595-1","volume":"255","author":"CD Godsil","year":"1997","unstructured":"Godsil, C.D.: Compact graphs and equitable partitions. Linear Algebra Appl. 255(1\u20133), 259\u2013266 (1997)","journal-title":"Linear Algebra Appl."},{"key":"2_CR22","doi-asserted-by":"crossref","unstructured":"Grohe, M.: The logic of graph neural networks. In: LICS (2021)","DOI":"10.1109\/LICS52264.2021.9470677"},{"issue":"3","key":"2_CR23","doi-asserted-by":"publisher","DOI":"10.1002\/ctd2.104","volume":"2","author":"M Ilieva","year":"2022","unstructured":"Ilieva, M., Tschaikowski, M., Vandin, A., Uchida, S.: The current status of gene expression profilings in covid-19 patients. Clin. Transl. Discovery 2(3), e104 (2022)","journal-title":"Clin. Transl. Discovery"},{"issue":"3","key":"2_CR24","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1016\/0022-5193(69)90015-0","volume":"22","author":"S Kauffman","year":"1969","unstructured":"Kauffman, S.: Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22(3), 437\u2013467 (1969)","journal-title":"J. Theor. Biol."},{"key":"2_CR25","doi-asserted-by":"crossref","unstructured":"Kersting, K., Mladenov, M., Garnett, R., Grohe, M.: Power iterated color refinement. AAAI (2014)","DOI":"10.1609\/aaai.v28i1.8992"},{"key":"2_CR26","doi-asserted-by":"crossref","unstructured":"Kunegis, J.: Konect: the koblenz network collection. In: WWW Companion (2013)","DOI":"10.1145\/2487788.2488173"},{"issue":"1","key":"2_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0890-5401(91)90030-6","volume":"94","author":"KG Larsen","year":"1991","unstructured":"Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Inf. Comput. 94(1), 1\u201328 (1991)","journal-title":"Inf. Comput."},{"issue":"333","key":"2_CR28","first-page":"1","volume":"24","author":"C Morris","year":"2023","unstructured":"Morris, C., et al.: Weisfeiler and Leman go machine learning: the story so far. J. Mach. Learn. Res. 24(333), 1\u201359 (2023)","journal-title":"J. Mach. Learn. Res."},{"key":"2_CR29","doi-asserted-by":"crossref","unstructured":"Morris, C., et al.: Weisfeiler and leman go neural: higher-order graph neural networks. In: AAAI (2019)","DOI":"10.1609\/aaai.v33i01.33014602"},{"issue":"6","key":"2_CR30","doi-asserted-by":"publisher","first-page":"973","DOI":"10.1137\/0216062","volume":"16","author":"R Paige","year":"1987","unstructured":"Paige, R., Tarjan, R.E.: Three partition refinement algorithms. SIAM J. Comput. 16(6), 973\u2013989 (1987)","journal-title":"SIAM J. Comput."},{"issue":"4","key":"2_CR31","doi-asserted-by":"publisher","first-page":"701","DOI":"10.1145\/322217.322225","volume":"27","author":"JT Schwartz","year":"1980","unstructured":"Schwartz, J.T.: Fast probabilistic algorithms for verification of polynomial identities. J. ACM (JACM) 27(4), 701\u2013717 (1980)","journal-title":"J. ACM (JACM)"},{"key":"2_CR32","doi-asserted-by":"crossref","unstructured":"Squillace, G., Tribastone, M., Tschaikowski, M., Vandin, A.: Efficient network embedding by approximate equitable partitions. In: ICDM (2024)","DOI":"10.1109\/ICDM59182.2024.00051"},{"key":"2_CR33","doi-asserted-by":"crossref","unstructured":"Steele, G.L., Lea, D., Flood, C.H.: Fast splittable pseudorandom number generators, pp. 453\u2013472. OOPSLA \u201914, ACM (2014)","DOI":"10.1145\/2660193.2660195"},{"key":"2_CR34","doi-asserted-by":"crossref","unstructured":"Tognazzi, S., Tribastone, M., Tschaikowski, M., Vandin, A.: Egac: a genetic algorithm to compare chemical reaction networks. In: GECCO (2017)","DOI":"10.1145\/3071178.3071265"},{"key":"2_CR35","doi-asserted-by":"crossref","unstructured":"Tognazzi, S., Tribastone, M., Tschaikowski, M., Vandin, A.: Backward invariance for linear differential algebraic equations. In: CDC (2018)","DOI":"10.1109\/CDC.2018.8619710"},{"key":"2_CR36","doi-asserted-by":"crossref","unstructured":"Valmari, A., Franceschinis, G.: Simple O(m logn) time markov chain lumping. In: TACAS (2010)","DOI":"10.1007\/978-3-642-12002-2_4"},{"key":"2_CR37","doi-asserted-by":"crossref","unstructured":"Wang, Y., et al.: Gunrock: GPU graph analytics. ACM Trans. Parallel Comput. 4(1) (2017)","DOI":"10.1145\/3108140"},{"key":"2_CR38","unstructured":"Xu, K., Hu, W., Leskovec, J., Jegelka, S.: How powerful are graph neural networks? In: ICLR (2019)"},{"key":"2_CR39","doi-asserted-by":"crossref","unstructured":"Yang, C., Bulu\u00e7, A., Owens, J.D.: Graphblast: a high-performance linear algebra-based graph framework on the GPU. ACM Trans. Math. Softw. (2022)","DOI":"10.1145\/3466795"}],"container-title":["Lecture Notes in Computer Science","Machine Learning and Knowledge Discovery in Databases. Research Track"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-37664-0_2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T10:20:33Z","timestamp":1788776433000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-37664-0_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,8]]},"ISBN":["9783032376633","9783032376640"],"references-count":39,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-37664-0_2","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,8]]},"assertion":[{"value":"8 September 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ECML PKDD","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Joint European Conference on Machine Learning and Knowledge Discovery in Databases","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Naples","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Italy","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2026","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7 September 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 September 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ecml2026","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/ecmlpkdd.org\/2026\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}