Approximation Algorithm for the Minimum Degree Spanning Tree Problem

TL;DR: With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility.

TL;DR: Algorithmic and hardness results for network design problems with degree or order constraints are presented and it is shown that the vertex-connectivity Survivable Network Design problem with degree constraints is hard to approximate, even when the cost of every edge is zero.

TL;DR: An algorithm that constructs a schedule with O(log k · b* + k1/2) rounds for the directed k-multicast problem, where b* is the value of the optimum solution, is devised, which is the first algorithm with a non-trivial approximation guarantee for this problem.

TL;DR: A polynomial time algorithm is proposed for the minimum degree spanning tree problem in directed acyclic graphs that starts with an arbitrary spanning tree, and iteratively reduces the number of vertices of maximum degree to result in an optimal tree.