On the Relative Complexity of 15 Problems Related to 0/1-Integer Programming

An integral part of combinatorial optimization and computational complexity consists of establishing relationships between different problems or different versions of the same problem. In. this chapter, we bring together known and new, previously published and unpublished results, which establish that 15 problems related to optimizing a linear function over a 0/1-polytope are polynomial-time equivalent. This list of problems includes optimization and augmentation, testing optimality and primal separation, sensitivity analysis and inverse optimization, as well as several others.