Titlebook: Compact Extended Linear Programming Models; Giuseppe Lancia,Paolo Serafini Textbook 2018 Springer International Publishing AG 2018 ILP.com

叢林

General Techniques for Compact Formulations,ld a compact extended formulation. Some examples are immediately brought to the attention of the reader so that the technique can be better understood. Also the role of the nonnegative factorization of the slack matrix is explained and some preliminary examples are shown.

poliosis

The Permutahedron,st one is based on LP techniques and the second one on a simple projection of a polyhedron whose vertices are integral. Both these formulations require a quadratic number of variables and inequalities. A better compact extended formulation can be obtained via sorting networks for which a . formulati

nepotism

The Parity Polytope,e convex hull of all 0-1 vectors with an odd number of ones. We show two alternative compact extended formulations for both polytopes, one based on the union of polyhedra and the other one on LP. Whereas the former is a quadratic extension, the latter is only linear. This result seems to be new.

entice

Trees,iner tree problem. We then describe the well-known minimum spanning tree problem, for which there exist polynomial algorithms and exponential-size models. We use both LP techniques and nonnegative rank factorization to provide compact extended formulations. Finally we present two NP-hard problems re

Barrister

Stable Sets,can be given an exact representation, although with an exponential number of inequalities. When the graphs are perfect, however, compact extended formulations are possible for the stable set polytope. We give an example of such situation by describing a compact extended formulation, obtained by LP t

circumvent

Traveling Salesman Problems, this problem have been proposed since a long time, but most of them are not effective for computational purposes. We describe an effective compact model which expresses the subtour inequalities via the max-flow/min-cut theorem. In this chapter we also present a new formulation for the TSP that show

改良

heckle

VEIL

粗糙