A note on the Frank—Tardos bi-truncation algorithm for crossing-submodular functions

Abstract

Recently, Frank and Tardos (1988) presented an algorithm, called the bi-truncation algorithm, for discerning whether a polyhedron defined by

$$Q(b) = \{ x|x \in ^s ,\forall X \subseteq S:x(X) \le b(X),X(S) = b(S)\}$$

is nonempty, whereb″ is a crossing-submodular function on 2^s. We point out an error in their algorithm and show how it is corrected.