On Independent Cliques and Linear Complementarity Problems
Abstract
In recent work (Pandit and Kulkarni [Discrete Applied Mathematics, 244 (2018), pp. 155--169]), the independence number of a graph was characterized as the maximum of the norm of solutions of a Linear Complementarity Problem (\LCP) defined suitably using parameters of the graph. Solutions of this LCP have another relation, namely, that they corresponded to Nash equilibria of a public goods game. Motivated by this, we consider a perturbation of this LCP and identify the combinatorial structures on the graph that correspond to the maximum norm of solutions of the new LCP. We introduce a new concept called independent clique solutions which are solutions of the LCP that are supported on independent cliques and show that for small perturbations, such solutions attain the maximum norm amongst all solutions of the new LCP.
Cite
@article{arxiv.1811.09798,
title = {On Independent Cliques and Linear Complementarity Problems},
author = {Karan N. Chadha and Ankur A. Kulkarni},
journal= {arXiv preprint arXiv:1811.09798},
year = {2018}
}
Comments
Submitted to the SIAM Journal on Discrete Mathematics