{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T05:00:18Z","timestamp":1698037218780},"reference-count":10,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2007,9,5]],"date-time":"2007-09-05T00:00:00Z","timestamp":1188950400000},"content-version":"vor","delay-in-days":6821,"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":[[1989,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The consistent labeling problem, which is one of the combinational problems, can be formulated within the framework of the stochastic relaxation process. This paper describes clearly the structure of the stochastic relaxation algorithm obtained from such a formulation. The usefulness of the stochastic relaxation in the consistent labeling problem is demonstrated. The consistent labeling problem belongs to the NP\u2010complete class, and is one of the \u201cdifficult\u201d problems among the combinational problems. The stochastic relaxation method aims at the overall consistency by iterating the adjustment for local consistency. In this sense, in the consistent labeling problem, a consistent label is obtained if the local consistency applies to any part of the system. On the other hand, the stochastic relaxation can be considered as a dynamical system which contains a mutual interaction to adjust the consistency. The steady\u2010state solution of such a dynamical system corresponds to a solution generated by the stochastic relaxation process. This paper describes clearly the structure of the dynamical system specified by the stochastic relaxation, via a theoretical analysis and a computer simulation. As a result, it was verified that an initial state always exists near the equilibrium point, from which the convergence to the optimal steady\u2010state solution is ensured. It was verified that by reducing the neighborhood region, the ratio of the initial state region from which the convergence to the optimal steady\u2010state solution is ensured, is increased.<\/jats:p>","DOI":"10.1002\/scj.4690200307","type":"journal-article","created":{"date-parts":[[2009,11,19]],"date-time":"2009-11-19T22:36:27Z","timestamp":1258670187000},"page":"68-77","source":"Crossref","is-referenced-by-count":0,"title":["Dynamics of Stochastic Relaxation Processes"],"prefix":"10.1002","volume":"20","author":[{"given":"Toshiaki","family":"Ejima","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,9,6]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.1976.4309519"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.1980.4767035"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.1983.4767390"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.1981.4767127"},{"issue":"12","key":"e_1_2_1_6_2","first-page":"2099","article-title":"A study of correction operator in relaxation method","volume":"68","author":"Ejima T.","year":"1985","journal-title":"Trans. (D), I.E.C.E., Japan"},{"issue":"4","key":"e_1_2_1_7_2","first-page":"672","article-title":"Evaluation of convergence in stochastic relaxation","volume":"70","author":"Ejima T.","year":"1987","journal-title":"Trans. (A). I.E.C.E., Japan"},{"issue":"7","key":"e_1_2_1_8_2","first-page":"43","article-title":"Outline of image processing algorithm\u2014Application of relaxation method","volume":"44","author":"Sakagamai","year":"1979","journal-title":"Mem. Electrotech. Lab."},{"issue":"9","key":"e_1_2_1_9_2","first-page":"1167","article-title":"Recognition of handwritten basic Chinese characters by consistent relaxation","volume":"65","author":"Yamamoto K.","year":"1982","journal-title":"Trans. (D), I.E.C.E., Japan"},{"key":"e_1_2_1_10_2","unstructured":"ShimohiraandM.Kimura Recognition of vowel sequence uttered by unspecified speakers using the relation among vowels. Tech. Rep. I.E.C.E. Japan SP86\u201087(1987)."},{"issue":"11","key":"e_1_2_1_11_2","first-page":"1086","article-title":"Perspectives in knowledge information processing\u2014from the viewpoint of pattern understanding","volume":"69","author":"Kosaka Y.","year":"1986","journal-title":"Proc. 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.4690200307","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/scj.4690200307","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T14:28:29Z","timestamp":1697984909000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/scj.4690200307"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,1]]},"references-count":10,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1989,1]]}},"alternative-id":["10.1002\/scj.4690200307"],"URL":"https:\/\/doi.org\/10.1002\/scj.4690200307","archive":["Portico"],"relation":{},"ISSN":["0882-1666","1520-684X"],"issn-type":[{"value":"0882-1666","type":"print"},{"value":"1520-684X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,1]]}}}