On Degree Sequence Optimization
Combinatorics
2020-11-10 v2 Discrete Mathematics
Data Structures and Algorithms
Optimization and Control
Abstract
We consider the problem of finding a subgraph of a given graph which maximizes a given function evaluated at its degree sequence. While the problem is intractable already for convex functions, we show that it can be solved in polynomial time for convex multi-criteria objectives. We next consider the problem with separable objectives, which is NP-hard already when all vertex functions are the square. We consider a colored extension of the separable problem, which includes the notorious exact matching problem as a special case, and show that it can be solved in polynomial time on graphs of bounded tree-depth for any vertex functions. We mention some of the many remaining open problems.
Cite
@article{arxiv.2003.05141,
title = {On Degree Sequence Optimization},
author = {Shmuel Onn},
journal= {arXiv preprint arXiv:2003.05141},
year = {2020}
}