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Algorithms"],"published-print":{"date-parts":[[2012,4]]},"abstract":"<jats:p>We consider testing directed graphs Eulerianity in the orientation model introduced in Halevy et al. [2005]. Despite the local nature of the Eulerian property, it turns out to be significantly harder to test than other properties studied in the orientation model. We show a nonconstant lower bound on the query complexity of 2-sided tests and a linear lower bound on the query complexity of 1-sided tests for this property. On the positive side, we give several 1-sided and 2-sided tests, including a sublinear query complexity 2-sided test, for general graphs. For special classes of graphs, including bounded-degree graphs and expander graphs, we provide improved results. In particular, we give a 2-sided test with constant query complexity for dense graphs, as well as for expander graphs with a constant expansion parameter.<\/jats:p>","DOI":"10.1145\/2151171.2151178","type":"journal-article","created":{"date-parts":[[2012,4,24]],"date-time":"2012-04-24T18:41:10Z","timestamp":1335292870000},"page":"1-41","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["On the query complexity of testing orientations for being Eulerian"],"prefix":"10.1145","volume":"8","author":[{"given":"Eldar","family":"Fischer","sequence":"first","affiliation":[{"name":"Technion, Israel Institute of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oded","family":"Lachish","sequence":"additional","affiliation":[{"name":"Birkbeck, University of London"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arie","family":"Matsliah","sequence":"additional","affiliation":[{"name":"IBM Research and Technion, Israel Institute of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ilan","family":"Newman","sequence":"additional","affiliation":[{"name":"University of Haifa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Orly","family":"Yahalom","sequence":"additional","affiliation":[{"name":"ORT Braude College, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2012,4,25]]},"reference":[{"doi-asserted-by":"publisher","key":"e_1_2_1_1_1","DOI":"10.1016\/j.jcss.2004.04.008"},{"doi-asserted-by":"publisher","key":"e_1_2_1_2_1","DOI":"10.5555\/1109557.1109648"},{"doi-asserted-by":"publisher","key":"e_1_2_1_3_1","DOI":"10.1137\/S0097539704445445"},{"doi-asserted-by":"publisher","key":"e_1_2_1_4_1","DOI":"10.1002\/rsa.10023.abs"},{"doi-asserted-by":"publisher","key":"e_1_2_1_5_1","DOI":"10.1016\/0022-0000(93)90044-W"},{"volume-title":"Proceedings of the 7th ALENEX. SIAM Press, 259--262","author":"Brightwell G. R.","unstructured":"Brightwell , G. R. and Winkler , P . 2005. Counting Eulerian circuits is &num;P-complete . In Proceedings of the 7th ALENEX. SIAM Press, 259--262 . Brightwell, G. R. and Winkler, P. 2005. Counting Eulerian circuits is &num;P-complete. In Proceedings of the 7th ALENEX. SIAM Press, 259--262.","key":"e_1_2_1_6_1"},{"doi-asserted-by":"publisher","key":"e_1_2_1_7_1","DOI":"10.1007\/978-3-540-74208-1_28"},{"doi-asserted-by":"crossref","unstructured":"Fischer E. 2004. The art of uninformed decisions: A primer to property testing. In Current Trends in Theoretical Computer Science: The Challenge of the New Century World Scientific 229--264.  Fischer E. 2004. The art of uninformed decisions: A primer to property testing. In Current Trends in Theoretical Computer Science: The Challenge of the New Century World Scientific 229--264.","key":"e_1_2_1_8_1","DOI":"10.1142\/9789812562494_0014"},{"doi-asserted-by":"publisher","key":"e_1_2_1_9_1","DOI":"10.1007\/s00453-009-9368-2"},{"volume-title":"Eulerian graphs and related topics part 1","author":"Fleishcner H.","unstructured":"Fleishcner , H. 1990. Eulerian graphs and related topics part 1 , vol. 1 . Ann. Discrete Math. 45, Elsevier . Fleishcner, H. 1990. Eulerian graphs and related topics part 1, vol. 1. Ann. Discrete Math. 45, Elsevier.","key":"e_1_2_1_10_1"},{"volume-title":"Eulerian graphs and related topics part 1","author":"Fleishcner H.","unstructured":"Fleishcner , H. 1991. Eulerian graphs and related topics part 1 . vol. 2 . Ann. Discrete Math. 50, Elsevier . Fleishcner, H. 1991. Eulerian graphs and related topics part 1. vol. 2. Ann. Discrete Math. 50, Elsevier.","key":"e_1_2_1_11_1"},{"doi-asserted-by":"publisher","key":"e_1_2_1_12_1","DOI":"10.1145\/285055.285060"},{"doi-asserted-by":"publisher","key":"e_1_2_1_13_1","DOI":"10.1007\/s00453-001-0078-7"},{"unstructured":"Halevy S. Lachish O. Newman I. and Tsur D. 2005. Testing orientation properties. Tech. rep. TR05-153 Electronic Colloquium on Computational Complexity (ECCC).  Halevy S. Lachish O. Newman I. and Tsur D. 2005. Testing orientation properties. Tech. rep. TR05-153 Electronic Colloquium on Computational Complexity (ECCC).","key":"e_1_2_1_14_1"},{"doi-asserted-by":"publisher","key":"e_1_2_1_15_1","DOI":"10.1109\/CCC.2007.31"},{"doi-asserted-by":"publisher","key":"e_1_2_1_16_1","DOI":"10.1007\/PL00009811"},{"doi-asserted-by":"publisher","key":"e_1_2_1_17_1","DOI":"10.1137\/S0097539703436424"},{"doi-asserted-by":"publisher","key":"e_1_2_1_18_1","DOI":"10.1007\/BF01902503"},{"doi-asserted-by":"crossref","unstructured":"Mihail M. and Winkler P. 1996. On the number of Eulerian orientations of a graph. Algorithmica 16 4\/5 402--414.  Mihail M. and Winkler P. 1996. On the number of Eulerian orientations of a graph. Algorithmica 16 4\/5 402--414.","key":"e_1_2_1_19_1","DOI":"10.1007\/BF01940872"},{"doi-asserted-by":"publisher","key":"e_1_2_1_20_1","DOI":"10.1137\/S009753970038211X"},{"doi-asserted-by":"publisher","key":"e_1_2_1_21_1","DOI":"10.1002\/rsa.10013.abs"},{"doi-asserted-by":"publisher","key":"e_1_2_1_22_1","DOI":"10.1073\/pnas.171285098"},{"volume-title":"Proof Techniques in Graph Theory","author":"Robinson R. W.","unstructured":"Robinson , R. W. 1969. Enumeration of Euler graphs . In Proof Techniques in Graph Theory , Academic Press , New York , 147--153. Robinson, R. W. 1969. Enumeration of Euler graphs. In Proof Techniques in Graph Theory, Academic Press, New York, 147--153.","key":"e_1_2_1_23_1"},{"volume-title":"Handbook of Randomized Computing","author":"Ron D.","unstructured":"Ron , D. 2001. Property testing (a tutorial) . In Handbook of Randomized Computing , Vol. II , Kluwer Press , Amsterdam , 597--643. Ron, D. 2001. Property testing (a tutorial). In Handbook of Randomized Computing, Vol. II, Kluwer Press, Amsterdam, 597--643.","key":"e_1_2_1_24_1"},{"doi-asserted-by":"publisher","key":"e_1_2_1_25_1","DOI":"10.1137\/S0097539793255151"},{"volume-title":"Graph Theory","author":"Tutte T.","unstructured":"Tutte , T. 1984. Graph Theory . Addison-Wesley , New York . Tutte, T. 1984. Graph Theory. 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