Peter L. Hammer

Pseudo-boolean optimization

This survey examines the state of the art of a variety of problems related to pseudo-Boolean optimization, i.e. to the optimization of set functions represented by closed algebraic expressions. The main parts of the survey examine general pseudo-Boolean optimization, the specially important case of quadratic pseudo-Boolean optimization (to which every pseudo-Boolean optimization can be reduced), several other important special classes, and approximation algorithms.

Aggregation of inequalities in integer programming.

Given an m

Roof duality, complementation and persistency in quadratic 0–1 optimization

\times

Facet of regular 0–1 polytopes

n zero-one matrix

Logical analysis of numerical data

\underset\tilde\to A

Cause-effect relationships and partially defined Boolean functions

we ask whether there is a single linear inequality

Completely separable graphs

\underset\tilde\to a \underset\tilde\to x \leq b

The splittance of a graph

whose zero-one solutions are precisely the zero-one solutions of

Consensus algorithms for the generation of all maximal bicliques

\underset\tilde\to A \underset\tilde\to x \leq e

Boolean Models and Methods in Mathematics, Computer Science, and Engineering

. We develop an algorithm for answering this question in O(m