{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T03:16:32Z","timestamp":1761621392256},"reference-count":0,"publisher":"AI Access Foundation","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["jair"],"abstract":"<jats:p>When writing a constraint program, we have to choose which variables  should be the decision variables, and how to represent the constraints  on these variables. In many cases, there is considerable choice for  the decision variables.  Consider, for example, permutation problems in which we have as many values as variables, and each variable takes  an unique value. In such problems, we can choose between a primal and a dual viewpoint. In the dual viewpoint, each dual variable  represents one of the primal values, whilst each dual value represents one of the primal variables. Alternatively, by means of channelling  constraints to link the primal and dual variables, we can have a  combined model with both sets of variables. In this paper, we perform  an extensive theoretical and empirical study of such primal, dual and  combined models for two classes of problems: permutation problems and  injection problems. Our results show that it often be advantageous to  use multiple viewpoints, and to have constraints which channel between them to maintain consistency. They also illustrate a general  methodology for comparing different constraint models.<\/jats:p>","DOI":"10.1613\/jair.1351","type":"journal-article","created":{"date-parts":[[2018,7,12]],"date-time":"2018-07-12T13:26:58Z","timestamp":1531402018000},"page":"357-391","source":"Crossref","is-referenced-by-count":25,"title":["Dual Modelling of Permutation and Injection Problems"],"prefix":"10.1613","volume":"21","author":[{"given":"B.","family":"Hnich","sequence":"first","affiliation":[]},{"given":"B. M.","family":"Smith","sequence":"additional","affiliation":[]},{"given":"T.","family":"Walsh","sequence":"additional","affiliation":[]}],"member":"16860","published-online":{"date-parts":[[2004,2,1]]},"container-title":["Journal of Artificial Intelligence Research"],"original-title":[],"link":[{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/jair.org\/index.php\/jair\/article\/download\/10370\/24818","content-type":"application\/postscript","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/jair.org\/index.php\/jair\/article\/download\/10370\/24819","content-type":"application\/zip","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/jair.org\/index.php\/jair\/article\/download\/10370\/24820","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/jair.org\/index.php\/jair\/article\/download\/10370\/24820","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,27]],"date-time":"2019-10-27T22:26:18Z","timestamp":1572215178000},"score":1,"resource":{"primary":{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/jair.org\/index.php\/jair\/article\/view\/10370"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,2,1]]},"references-count":0,"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.1613\/jair.1351","relation":{},"ISSN":["1076-9757"],"issn-type":[{"value":"1076-9757","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,2,1]]}}}