Evolutionary algorithms and matroid optimization problems
Proceedings of the 9th annual conference on Genetic and evolutionary computation
An algebraic algorithm for weighted linear matroid intersection
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Small Approximate Pareto Sets for Bi-objective Shortest Paths and Other Problems
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
The subdivision-constrained minimum spanning tree problem
Theoretical Computer Science
Monotone Covering Problems with an Additional Covering Constraint
Mathematics of Operations Research
A Survey on Multiple Objective Minimum Spanning Tree Problems
Algorithmics of Large and Complex Networks
Budgeted matching and budgeted matroid intersection via the gasoline puzzle
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Approximation schemes for multi-budgeted independence systems
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Small Approximate Pareto Sets for Biobjective Shortest Paths and Other Problems
SIAM Journal on Computing
On the weight-constrained minimum spanning tree problem
INOC'11 Proceedings of the 5th international conference on Network optimization
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Given an undirected graph G=(V,E) with |V|=n and |E|=m, nonnegative integers ce and de for each edge $e \in E$, and a bound D, the constrained minimum spanning tree problem (CST) is to find a spanning tree T=(V,ET) such that $\sum_{e \in E_T} d_e \leq D$ and $\sum_{e \in E_T} c_e$ is minimized. We present an efficient polynomial time approximation scheme (EPTAS) for this problem. Specifically, for every $\epsilon0$ we present a $(1+\epsilon)$-approximation algorithm with time complexity $O((\frac{1}{\epsilon})^{O(\frac{1}{\epsilon})}n^4)$. Our method is based on Lagrangian relaxation and matroid intersection.