On the mixed set covering, packing and partitioning polytope

Set Covering, Packing and Partitioning Problems

where A is a mxn matrix of zeroes and ones, e = (1,...,1) is a vector of m ones and c is a vector of n (arbitrary) rational components. This pure 0-1 linear programming problem is called the set covering problem. When the inequalities are replaced by equations the problem is called the set partitioning problem, and when all of the ≥ constraints are replaced by ≤ constraints, the problem is call...

Packing, Partitioning, and Covering Symresacks

In this paper, we consider symmetric binary programs that contain set packing, partitioning, or covering (ppc) inequalities. To handle symmetries as well as ppc-constraints simultaneously, we introduce constrained symresacks which are the convex hull of all binary points that are lexicographically not smaller than their image w.r.t. a coordinate permutation and which fulfill some ppc-constraint...

Online Mixed Packing and Covering

In many problems, the inputs to the problem arrive over time. As each input is received, it must be dealt with irrevocably. Such problems are online problems. An increasingly common method of solving online problems is to solve the corresponding linear program, obtained either directly for the problem or by relaxing the integrality constraints. If required, the fractional solution obtained is t...

New facets for the set packing polytope

Sequential and Parallel Algorithms for Mixed Packing and Covering

We describe sequential and parallel algorithms that approximately solve linear programs with no negative coefficients (a.k.a. mixed packing and covering problems). For explicitly given problems, our fastest sequential algorithm returns a solution satisfying all constraints within a 1 ± ǫ factor in O(md log(m)/ǫ) time, where m is the number of constraints and d is the maximum number of constrain...