{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:41:17Z","timestamp":1777596077497,"version":"3.51.4"},"reference-count":38,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2017,10,31]],"date-time":"2017-10-31T00:00:00Z","timestamp":1509408000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Comput. Logic"],"published-print":{"date-parts":[[2017,10,31]]},"abstract":"<jats:p>\n            We study the problem of conjunctive query evaluation relative to a class of queries. This problem is formulated here as the relational homomorphism problem relative to a class of structures\n            <jats:italic>A<\/jats:italic>\n            , in which each instance must be a pair of structures such that the first structure is an element of\n            <jats:italic>A<\/jats:italic>\n            . We present a comprehensive complexity classification of these problems, which strongly links graph-theoretic properties of\n            <jats:italic>A<\/jats:italic>\n            to the complexity of the corresponding homomorphism problem. In particular, we define a binary relation on graph classes, which is a preorder, and completely describe the resulting hierarchy given by this relation. This relation is defined in terms of a notion that we call\n            <jats:italic>graph deconstruction<\/jats:italic>\n            and that is a variant of the well-known notion of tree decomposition. We then use this hierarchy of graph classes to infer a complexity hierarchy of homomorphism problems that is comprehensive up to a computationally very weak notion of reduction, namely, a parameterized version of quantifier-free, first-order reduction. In doing so, we obtain a significantly refined complexity classification of homomorphism problems as well as a unifying, modular, and conceptually clean treatment of existing complexity classifications. We then present and develop the theory of Ehrenfeucht-Fra\u00efss\u00e9-style pebble games, which solve the homomorphism problems where the cores of the structures in\n            <jats:italic>A<\/jats:italic>\n            have bounded tree depth. This condition characterizes those classical homomorphism problems decidable in logarithmic space, assuming a hypothesis from parameterized space complexity. Finally, we use our framework to classify the complexity of model checking existential sentences having bounded quantifier rank.\n          <\/jats:p>","DOI":"10.1145\/3143805","type":"journal-article","created":{"date-parts":[[2017,11,6]],"date-time":"2017-11-06T13:30:18Z","timestamp":1509975018000},"page":"1-37","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["One Hierarchy Spawns Another"],"prefix":"10.1145","volume":"18","author":[{"given":"Hubie","family":"Chen","sequence":"first","affiliation":[{"name":"Universidad del Pa\u00eds Vasco and IKERBASQUE, Basque Foundation for Science, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Moritz","family":"M\u00fcller","sequence":"additional","affiliation":[{"name":"Kurt G\u00f6del Research Center, University of Vienna, Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2017,11,3]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Foundations of Databases","author":"Abiteboul Serge","unstructured":"Serge Abiteboul , Richard Hull , and Victor Vianu . 1995. 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Graph Theory , 4 th Edition. Graduate Texts in Mathematics, Vol. 173 . Springer . I--XVIII, 1--436 pages. Reinhard Diestel. 2012. Graph Theory, 4th Edition. Graduate Texts in Mathematics, Vol. 173. Springer. I--XVIII, 1--436 pages.","edition":"4"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-5559-1"},{"key":"e_1_2_1_20_1","volume-title":"Finite Model Theory","author":"Ebbinghaus Heinz-Dieter","unstructured":"Heinz-Dieter Ebbinghaus and J\u00f6rg Flum . 1995. Finite Model Theory . Springer . Heinz-Dieter Ebbinghaus and J\u00f6rg Flum. 1995. Finite Model Theory. 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Nicole Schweikardt, Thomas Schwentick, and Luc Segoufin. 2009. Database theory: Query languages. In Algorithms and Theory of Computation Handbook (2nd ed.), Mikhail J. Atallah and Marina Blanton (Eds.). Vol. 2: Special Topics and Techniques. CRC Press, Boca Raton, FL.","edition":"2"}],"container-title":["ACM Transactions on Computational Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/dl.acm.org\/doi\/10.1145\/3143805","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/dl.acm.org\/doi\/pdf\/10.1145\/3143805","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T02:13:22Z","timestamp":1750212802000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/dl.acm.org\/doi\/10.1145\/3143805"}},"subtitle":["Graph Deconstructions and the Complexity Classification of Conjunctive Queries"],"short-title":[],"issued":{"date-parts":[[2017,10,31]]},"references-count":38,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,10,31]]}},"alternative-id":["10.1145\/3143805"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1145\/3143805","relation":{},"ISSN":["1529-3785","1557-945X"],"issn-type":[{"value":"1529-3785","type":"print"},{"value":"1557-945X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,10,31]]},"assertion":[{"value":"2016-03-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-09-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-11-03","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}