On box totally dual integral polyhedra

On box totally dual integral polyhedra

Edmonds and Giles introduced the class of box totally dual integral polyhedra as a generalization of submodular flow polyhedra. In this paper a geometric characterization of these polyhedra is given. This geometric result is used to show that each TDI defining system for a box TDI polyhedron is in fact a box TDI system, that the class of box TDI polyhedra is in co-NP and is closed under taking ...

On totally dual integral systems

Let A be a rational (m x n)-matrix and b be a rational m-vector. The linear system Ax< b is said to be totally dual integral (TDI) if for all integer n-vectors c, the linear program min{b’v: A’y= c; yr 0} has an integer-valued optimum solution if it has an optimum solution. The contents of this paper can be divided into three parts: First of all an attempt is made to characterize special classe...

Recognizing Totally Dual Integral Systems is Hard

These are notes about Ding, Feng and Zang’s proof [5]. The proof of their result is not new, the only difference with them is the starting point: we work directly on their gadget graph encoding a SAT problem and not on more general graphs. This allows to shortcut some parts of the original proof that become superfluous. After proving their theorem I clarify some points about total dual integral...

Almost quaternionic integral submanifolds and totally umbilic integral submanifolds

In literature (Kobayashi and Nomizu, 1963, 1969; Yano and Ako, 1972; Ishihara, 1974; Özdemir, 2006; Alagöz et al., 2012), almost complex and almost quaternionic structures have been investigated widely. These structures are special structures on the tangent bundle of a manifold. A detailed review can be found in Kirichenko and Arseneva (1997). Let us recall some basic facts and definitions from...

Integral Boundary Points of Convex Polyhedra