Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
The connectivity carcass of a vertex subset in a graph and its incremental maintenance
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
On Halin subgraphs and supergraphs
Discrete Applied Mathematics
Performance guarantees for the TSP with a parameterized triangle inequality
Information Processing Letters
Discrete Mathematics
A survey of very large-scale neighborhood search techniques
Discrete Applied Mathematics
Estimating the Traffic on Weighted Cactus Networks in Linear Time
IV '05 Proceedings of the Ninth International Conference on Information Visualisation
Vertex disjoint paths on clique-width bounded graphs
Theoretical Computer Science
Efficient algorithms for center problems in cactus networks
Theoretical Computer Science
Complexity of the directed spanning cactus problem
Discrete Applied Mathematics
Approximating the minmax subtree cover problem in a cactus
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
The minimum spanning tree problem with conflict constraints and its variations
Discrete Optimization
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We show that testing if an undirected graph contains a bridgeless spanning cactus is NP-hard. As a consequence, the minimum spanning cactus problem (MSCP) on an undirected graph with 0-1 edge weights is NP-hard. For any subgraph S of K"n, we give polynomially testable necessary and sufficient conditions for S to be extendable to a cactus in K"n and the weighted version of this problem is shown to be NP-hard. A spanning tree is shown to be extendable to a cactus in K"n if and only if it has at least one node of even degree. When S is a spanning tree, we show that the weighted version can also be solved in polynomial time. Further, we give an O(n^3) algorithm for computing a minimum cost spanning tree with at least one vertex of even degree on a graph on n nodes. Finally, we show that for a complete graph with edge-costs satisfying the triangle inequality, the MSCP is equivalent to a general class of optimization problems that properly includes the traveling salesman problem and they all have the same approximation hardness.