Additive guarantees for degree bounded directed network design
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Approximating Directed Weighted-Degree Constrained Networks
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Approximating directed weighted-degree constrained networks
Theoretical Computer Science
Additive Guarantees for Degree-Bounded Directed Network Design
SIAM Journal on Computing
Note: Arc-disjoint paths and trees in 2-regular digraphs
Discrete Applied Mathematics
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Using a suitable orientation, we give a short proof of a strengthening of a result of Czumaj and Strothmann [4]: Every 2-edge-connected graph G contains a spanning tree T with the property that $d_T(v)\le {d_T(v)+\,3 \over 2}$ for every vertex v. As an analogue of this result in the directed case, we prove that every 2-arc-strong digraph D has an out-branching B such that $d^+_B(x)\le {d^+_D(x)+ \over 2}+1$. A corollary of this is that every k-arc-strong digraph D has an out-branching B such that $d^+_B(v)\le {d^+_D(v)+ \over 2^r}+r$, where $r=\lfloor \log_2k\rfloor$. We conjecture that in this case $d^+_B(x)\le {d^+_D(x)+ \over k}+1$ would be the right (and best possible) answer. If true, this would again imply a strengthening of a result from [4] concerning spanning trees with small degrees in k-connected graphs when k ≥ 2. We prove that for acyclic digraphs the existence of an out-branching satisfying prescribed bounds on the out-degrees of each vertex can be checked in polynomial time. A corollary of this is that the existence of arc-disjoint branchings $F^+_s$,$F^-_t$, where the first is an out-branching rooted at s and the second an in-branching rooted at t, can be checked in polynomial time for the class of acyclic digraphs © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 297–307, 2003 This work was initiated while the authors attended the DCI 2001 workshop on tournaments at DIMACS. We gratefully acknowledge financial support by DIMACS.