On Generalizations of Network Design Problems with Degree Bounds

TL;DR

This paper extends iterative relaxation techniques to handle complex degree constraints in network design problems, including laminar crossing spanning trees and matroid intersection, providing new algorithms and bounds.

Contribution

It introduces methods to incorporate degree bounds into various network design problems, expanding the applicability of iterative relaxation.

Findings

New approximation algorithms for degree-constrained problems

Hardness results and integrality gaps established

Improved bounds for laminar crossing spanning trees

Abstract

Iterative rounding and relaxation have arguably become the method of choice in dealing with unconstrained and constrained network design problems. In this paper we extend the scope of the iterative relaxation method in two directions: (1) by handling more complex degree constraints in the minimum spanning tree problem (namely, laminar crossing spanning tree), and (2) by incorporating `degree bounds' in other combinatorial optimization problems such as matroid intersection and lattice polyhedra. We give new or improved approximation algorithms, hardness results, and integrality gaps for these problems.