TY - JOUR
ID - 36279
TI - Some Results about the Contractions and the Pendant Pairs of a Submodular System
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Hanifehnezhad, Saeid
AU - Dolati, Ardeshir
AD - Department of Mathematics, Shahed University, Tehran, Iran.
AD - Department of Computer Science, Shahed University, Tehran, Iran.
Y1 - 2019
PY - 2019
VL - 16
IS - 1
SP - 119
EP - 128
KW - Submodular system
KW - Submodular optimization
KW - Maximum adjacency ordering
KW - Posimodular functions
KW - Pendant pairs
KW - st-cut
DO - 10.22130/scma.2018.91924.481
N2 - Submodularity is an important property of set functions with deep theoretical results and various applications. Submodular systems appear in many applicable area, for example machine learning, economics, computer vision, social science, game theory and combinatorial optimization. Nowadays submodular functions optimization has been attracted by many researchers. Pendant pairs of a symmetric submodular system play essential role in finding a minimizer of this system. In this paper, we investigate some relations between pendant pairs of a submodular system and pendant pairs of its contractions. For a symmetric submodular system $left(V,fright)$ we construct a suitable sequence of $left|Vright|-1$ pendant pairs of its contractions. By using this sequence, we present some properties of the system and its contractions. Finally, we prove some results about the minimizers of a posimodular function.
UR - http://scma.maragheh.ac.ir/article_36279.html
L1 - http://scma.maragheh.ac.ir/article_36279_8d135d8fd6e9c532ae60aff53488a3d6.pdf
ER -