{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T06:10:24Z","timestamp":1697868624844},"reference-count":8,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2007,3,21]],"date-time":"2007-03-21T00:00:00Z","timestamp":1174435200000},"content-version":"vor","delay-in-days":7749,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems &amp;amp; Computers in Japan"],"published-print":{"date-parts":[[1986,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Nontrivial lower bounds of the time complexity are given for a class of problems on graphs. Specifically, given a complete graph with weighted edges, the problem of finding a subgraph satisfying a property \u03c0 and having edge\u2010weights that sum exactly to unity is considered. An \u03c9(<jats:italic>n<\/jats:italic><jats:sup>3<\/jats:sup> log <jats:italic>n<\/jats:italic>) lower bound is established under the algebraic decision tree model for a property \u03c0 that satisfies the degree constraint and is closed with respect to isomorphism, where <jats:italic>n<\/jats:italic> is the number of vertices in an input graph. This result is a proper generalization of that of Nakayama et al. [8], in which the same lower bound was obtained for \u03c0 that is hereditary on subgraphs and determined by components. Furthermore, an \u03c9(<jats:italic>n<\/jats:italic><jats:sup>3<\/jats:sup>) lower bound is shown for \u03c0 = \u201cclique\u201d that does not satisfy the degree constraint and hence the above result can not be applied.<\/jats:p>","DOI":"10.1002\/scj.4690170611","type":"journal-article","created":{"date-parts":[[2007,7,7]],"date-time":"2007-07-07T12:03:35Z","timestamp":1183809815000},"page":"95-102","source":"Crossref","is-referenced-by-count":0,"title":["Lower bounds on time complexity for some subgraph detection problems"],"prefix":"10.1002","volume":"17","author":[{"given":"Masanari","family":"Arai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Masafumi","family":"Yamashita","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tomio","family":"Hirata","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Toshihide","family":"Ibaraki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Namio","family":"Honda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,3,21]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"The Design and Analysis of Computer Algorithms","author":"Aho A. V.","year":"1974"},{"key":"e_1_2_1_3_2","unstructured":"D.Dobkin. A nonlinear lower bound on linear search tree program for solving knapsack problems Yale Computer Science Research Report No. 52 (1975)."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(78)90026-0"},{"key":"e_1_2_1_5_2","unstructured":"H.Machida. A lower bound on the complexity of knapsack problem Proceedings of the Seventh I. B. M. Symposium on Mathematical Foundation of Computer Science pp.1\u201323(1982)."},{"key":"e_1_2_1_6_2","first-page":"8","volume-title":"A polynomial linear search algorithm for the n\u2010dimensional knapsack problem","author":"Meyer auf der Heide F."},{"key":"e_1_2_1_7_2","volume-title":"Threshold Logic and Its Applications","author":"Muroga S.","year":"1971"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(82)90002-5"},{"key":"e_1_2_1_9_2","first-page":"9","article-title":"Lower bounds for some graph problems","volume":"66","author":"Nakayama H.","year":"1983","journal-title":"Trans. I.E.C.E., Japan"}],"container-title":["Systems and Computers in Japan"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fscj.4690170611","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/scj.4690170611","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T16:59:31Z","timestamp":1697821171000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/scj.4690170611"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1986,1]]},"references-count":8,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1986,1]]}},"alternative-id":["10.1002\/scj.4690170611"],"URL":"https:\/\/doi.org\/10.1002\/scj.4690170611","archive":["Portico"],"relation":{},"ISSN":["0882-1666","1520-684X"],"issn-type":[{"value":"0882-1666","type":"print"},{"value":"1520-684X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1986,1]]}}}