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
Spanning trees with minimum weighted degrees
Information Processing Letters
An algebraic algorithm for weighted linear matroid intersection
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
A constant factor approximation algorithm for k-median clustering with outliers
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Additive approximation for bounded degree survivable network design
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Additive guarantees for degree bounded directed 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
The "Not-Too-Heavy Spanning Tree" Constraint
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
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
Parameterizing above or below guaranteed values
Journal of Computer and System Sciences
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
Degree-bounded minimum spanning trees
Discrete Applied Mathematics
A primal branch-and-cut algorithm for the degree-constrained minimum spanning tree problem
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Degree bounded matroids and submodular flows
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Parameterized complexity of the smallest degree-constrained subgraph problem
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Multi-objective problems in terms of relational algebra
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
ACM Transactions on Sensor Networks (TOSN)
An O(log n/ log log n)-approximation algorithm for the asymmetric traveling salesman problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximating directed weighted-degree constrained networks
Theoretical Computer Science
Next generation session management for 3D teleimmersive interactive environments
Multimedia Tools and Applications
k-edge-connectivity: approximation and LP relaxation
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Additive Guarantees for Degree-Bounded Directed Network Design
SIAM Journal on Computing
Network-design with degree constraints
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Degree Bounded Network Design with Metric Costs
SIAM Journal on Computing
Matroidal degree-bounded minimum spanning trees
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Parameterized complexity of finding small degree-constrained subgraphs
Journal of Discrete Algorithms
Discrete Applied Mathematics
Sharp separation and applications to exact and parameterized algorithms
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
The asymmetric traveling salesman problem on graphs with bounded genus
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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
Matroids and integrality gaps for hypergraphic steiner tree relaxations
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Operations Research Letters
Network design with weighted degree constraints
Discrete Optimization
On some network design problems with degree constraints
Journal of Computer and System Sciences
Chain-Constrained spanning trees
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
Bounded-degree minimum-radius spanning trees in wireless sensor networks
Theoretical Computer Science
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We consider the minimum cost spanning tree problem under the restriction that all degrees must be at most a given value k. We show that we can efficiently find a spanning tree of maximum degree at most k+2 whose cost is at most the cost of the optimum spanning tree of maximum degree at most k. This is almost best possible. The approach uses a sequence of simple algebraic, polyhedral and combinatorial arguments. It illustrates many techniques and ideas in combinatorial optimization as it involves polyhedral characterizations, uncrossing, matroid intersection, and graph orientations (or packing of spanning trees). The result generalizes to the setting where every vertex has both upper and lower bounds and gives then a spanning tree which violates the bounds by at most two units and whose cost is at most the cost of the optimum tree. It also gives a better understanding of the subtour relaxation for both the symmetric and asymmetric traveling salesman problems. The generalization to l-edge-connected subgraphs is briefly discussed.