{"id":152841,"date":"2005-05-01T00:00:00","date_gmt":"2005-05-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/an-efficient-decision-procedure-for-utvpi-constraints\/"},"modified":"2018-10-16T20:18:47","modified_gmt":"2018-10-17T03:18:47","slug":"an-efficient-decision-procedure-for-utvpi-constraints","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/an-efficient-decision-procedure-for-utvpi-constraints\/","title":{"rendered":"An Efficient Decision Procedure for UTVPI Constraints"},"content":{"rendered":"<div class=\"asset-content\">\n<p>A unit two variable per inequality (UTVPI) constraint is of the form a.x+b.y \u0142eq d where x and y are integer variables, the coefficients a,b \u2208 \\-1,0,1$ and the bound d is an integer constant. This paper presents an efficient decision procedure for UTVPI constraints. Given m such constraints over n variables, the procedure checks the satisfiability of the constraints in O(n.m) time and O(n+m) space. This improves upon the previously known O(n<sup>2<\/sup>.m) time and O(n<sup>2<\/sup>) space algorithm based on transitive closure. Our decision procedure is also equality generating, proof generating, and model generating.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A unit two variable per inequality (UTVPI) constraint is of the form a.x+b.y \u0142eq d where x and y are integer variables, the coefficients a,b \u2208 \\-1,0,1$ and the bound d is an integer constant. This paper presents an efficient decision procedure for UTVPI constraints. Given m such constraints over n variables, the procedure checks [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13561],"msr-publication-type":[193718],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-152841","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_publishername":"Springer Verlag","msr_edition":"Frontiers of Combining Systems (FroCos 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