Q1. What are the contributions in "The b-branching problem in digraphs" ?
In this paper, the authors introduce the concept of b-branchings in digraphs, which is a generalization of branchings serving as a counterpart of b-matchings. The authors demonstrate that b-branchings yield an appropriate generalization of branchings by extending several classical results on branchings. The authors first present a multi-phase greedy algorithm for finding a maximumweight b-branching. The authors then prove a packing theorem extending Edmonds ’ disjoint branchings theorem, and provide a strongly polynomial algorithm for finding optimal disjoint b-branchings. As a consequence of the packing theorem, the authors prove the integer decomposition property of the bbranching polytope. Finally, the authors deal with a further generalization in which a matroid constraint is imposed on the b ( v ) arcs sharing the terminal vertex v. 2012 ACM Subject Classification Mathematics of computing → Graph algorithms