Note: Covering symmetric semi-monotone functions

Authors:
Roland Grappe;Zoltán Szigeti
Affiliations:
G-SCOP, INPGrenoble, UJF, CNRS, 46 avenue Félix Viallet, 38031 Grenoble Cedex, France;G-SCOP, INPGrenoble, UJF, CNRS, 46 avenue Félix Viallet, 38031 Grenoble Cedex, France
Venue:
Discrete Applied Mathematics
Year:
2008

Citing 3
Cited 1

Augmenting graphs to meet edge-connectivity requirements

SIAM Journal on Discrete Mathematics
Minimum augmentation of local edge-connectivity between vertices and vertex subsets in undirected graphs

Discrete Applied Mathematics - Special issue: Discrete algorithms and optimization, in honor of professor Toshihide Ibaraki at his retirement from Kyoto University
Minimum augmentation of edge-connectivity with monotone requirements in undirected graphs

CATS '07 Proceedings of the thirteenth Australasian symposium on Theory of computing - Volume 65

A new approach to splitting-off

IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization

Quantified Score

Hi-index	0.04

Visualization

Abstract

We define a new set of functions called semi-monotone, a subclass of skew-supermodular functions. We show that the problem of augmenting a given graph to cover a symmetric semi-monotone function is NP-complete if all the values of the function are in {0,1} and we provide a minimax theorem if all the values of the function are different from 1. Our problem is equivalent to the node to area augmentation problem. Our contribution is to provide a significantly simpler and shorter proof.