The interval order polytope of a digraph

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:36312

Mueller, R; Schulz, A

Interval orders and their cocomparability graphs, the interval graphs, are of significant importance as structures of solutions for several combinatorial optimization problems. This is due to the fact that each element is associated with an interval, which may be interpreted as a time interval, for example in a schedule, or as a substring in a string of items, for example, a substring of a DNA string in molecular biology. In the talk we show that the interval order polytope of a digraph may serve as a basis for a polyhedral combinatorial approach to this class of problems. We present results on odd cycle and clique based valid inequalities and discuss the complexity of their separation problem. We show that well-known valid inequalities of the linear ordering polytope, as, e.g., Mobius ladder inequalities and fence inequalities obtain a natural interpretation in terms of these inequalities of the interval order polytope.

• OSTI ID: 36312
• Report Number(s): CONF-9408161--
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
MATRICES
NONLINEAR PROBLEMS
NONLINEAR PROGRAMMING
NUMERICAL SOLUTION
PARAMETRIC ANALYSIS