A bisubmodular polyhedron is defined in terms of a so-called bisubmodular function on a
family of ordered pairs of disjoint subsets of a finite set. We examine the structures of …

Bisubmodular functions are a natural “directed”, or “signed”, extension of submodular
functions with several applications. Recently Fujishige and Iwata showed how to extend the …

A bidirected graph is a graph each arc of which has either two positive end-vertices (tails),
two negative end-vertices (heads), or one positive end-vertex (a tail) and one negative end …

A k-submodular function is a generalization of submodular and bisubmodular functions. This
paper establishes a compact representation for minimizers of ak-submodular function by a …

(1)Oa == (a]rc (2)Oa = ･in (1)tw(3), (ii)fbrany Page 1 The Operations Research Society of Japan
NII-Electronic Library Service The OpeiationsReseaich Society of Japan Journal of the …

This paper addresses the finest block triangularization of nonsingular skewsymmetric
matrices by simultaneous permutations of rows and columns. Hierarchical relations among …

)U (X2,YD-)= (Xi,}･On (X2,}"2> (1.1){l.2) {U,M}-closed For a {U,n}-closed eaclt (Xi,}'L Page 1 The
Operations Research Society of Japan NII-Electronic Library Service The OpeiationsReseaich …

The problem of making a given directed graph strongly connected was well-investigated by
Eswaran and Tarjan (SIAM J Comput 5: 653–665, 1976). In contrast, the problem of making …