Many birds with one stone: multi-objective approximation algorithms
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Approximating the minimum-degree Steiner tree to within one of optimal
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
A Matter of Degree: Improved Approximation Algorithms for Degree-Bounded Minimum Spanning Trees
SIAM Journal on Computing
Minimum Bounded Degree Spanning Trees
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Survivable network design with degree or order constraints
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Approximating minimum bounded degree spanning trees to within one of optimal
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Additive approximation for bounded degree survivable network design
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Journal of Graph Theory
Degree bounded matroids and submodular flows
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
On the L ∞ -norm of extreme points for crossing supermodular directed network LPs
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Additive approximation for bounded degree survivable network design
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Proceedings of the fifth international workshop on Foundations of mobile computing
A Simple LP Relaxation for the Asymmetric Traveling Salesman Problem
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
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
Novel Algorithms for the Network Lifetime Problem in Wireless Settings
ADHOC-NOW '08 Proceedings of the 7th international conference on Ad-hoc, Mobile and Wireless Networks
Max-Weight Integral Multicommodity Flow in Spiders and High-Capacity Trees
Approximation and Online Algorithms
Network Design with Weighted Degree Constraints
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Online and stochastic survivable network design
Proceedings of the forty-first annual ACM symposium on Theory of computing
Tree embeddings for two-edge-connected network design
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
MixNStream: multi-source video distribution with stream mixers
Proceedings of the 2010 ACM workshop on Advanced video streaming techniques for peer-to-peer networks and social networking
Approximating directed weighted-degree constrained networks
Theoretical Computer Science
Prize-collecting steiner networks via iterative rounding
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Improved algorithm for degree bounded survivable network design problem
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
On generalizations of network design problems with degree bounds
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Hi-index | 0.00 |
We present polynomial-time approximation algorithms for some degree-bounded directed network design problems. Our main result is for intersecting supermodular connectivity with degree bounds: given a directed graph G=(V,E) with non-negative edge-costs, a connectivity requirement specified by an intersecting supermodular function f, and upper bounds av, bvv∈ V on in-degrees and out-degrees of vertices, find a minimum-cost f-connected subgraph of G that satisfies the degree bounds. We give a bicriteria approximation algorithm that for any 0 ≤ ε ≤ 1/2, computes an f-connected subgraph with in-degrees at most ⌈ av/1-ε ⌉ + 4, out-degrees at most ⌈ bv/1-ε ⌉ + 4, and cost at most 1/ε times the optimum. This includes, as a special case, the minimum-cost degree-bounded arborescence problem. We also obtain similar results for the (more general) class of crossing supermodular requirements. Our result extends and improves the (3av+4, 3bv+4, 3)-approximation of Lau et al. Setting ε=0, our result gives the first purely additive guarantee for the unweighted versions of these problems. Our algorithm is based on rounding an LP relaxation for the problem. We also prove that the above cost-degree trade-off (even for the degree-bounded arborescence problem) is optimal relative to the natural LP relaxation. For every 0v/1-ε + O(1) has cost at least 1-o(1)/ε times the optimal LP value. For the special case of finding a minimum degree arborescence (without costs), we give a stronger +2 additive approximation. This improves on a result of Lau et al. [13] that gives a 2Δ*+2 guarantee, and Klein et al. [11] that gives a (1+ε)Δ*+O(log1+ε n) bound, where Δ* is the degree of the optimal arborescence. As a corollary of our result, we (almost) settle a conjecture of Bang-Jensen et al. [1] on low-degree arborescences. Our algorithms use the iterative rounding technique of Jain, which was used by Lau et al. and Singh and Lau in the context of degree-bounded network design. It is however non-trivial to extend these techniques to the directed setting without incurring a multiplicative violation in the degree bounds. This is due to the fact that known polyhedral characterization of arborescences has the cut-constraints which, along with degree-constraints, are unsuitable for arguing the existence of integral variables in a basic feasible solution. We overcome this difficulty by enhancing the iterative rounding steps and by means of stronger counting arguments. Our counting technique is quite general, and it also simplifies the proofs of many previous results. We also apply the technique to undirected graphs. We consider the minimum crossing spanning tree problem: given an undirected edge-weighted graph G, edge-subsets Eii=1k, and non-negative integers bii=1k, find a minimum-cost spanning tree (if it exists) in G that contains at most bi edges from each set Ei. We obtain a +(r-1) additive approximation for this problem, when each edge lies in at most r sets; this considerably improves the result of Bilo et al. A special case of this problem is degree-bounded minimum spanning tree, and our result gives a substantially easier proof of the recent +1 approximation of Singh and Lau.