Abstract
A problem characteristic common to a number of important integer programming problems is that of precedence constraints: a transitive collection of constraints of the form x j ≤ x i with 0 ≤ x i ≤ 1, 0 ≤ x j ≤ 1, x i , x j integer. Precedence constraints are of interest both because they arise frequently in integer programming applications and because the convex hull of feasible integer points is the same as the region obtained by relaxing the integrality restrictions. This paper investigates the polyhedral structure of the convex hull of feasible integer points when the precedence constraints are complicated by an additional constraint or, more generally, by additional constraints defining an independence system. Sequential lifting for independence systems with precedence constraints is discussed and extensions of the cover and 1-configuration inequalities known for the knapsack polytope are presented. A general procedure for inducing facets called rooting is introduced and a variety of facets based on rooting are developed. The paper concludes by discussing a procedure for coalescing constraints related to minimal covers into facets.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
