Two algorithms for weighted matroid intersection
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Improved Inapproximability Results for MaxClique, Chromatic Number and Approximate Graph Coloring
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Approximating Maximum Clique by Removing Subgraphs
SIAM Journal on Discrete Mathematics
Approximate clustering of fingerprint vectors with missing values
CATS '05 Proceedings of the 2005 Australasian symposium on Theory of computing - Volume 41
Computers and Operations Research
Spanning cactus of a graph: Existence, extension, optimization, and approximation
Discrete Applied Mathematics
The maximum flow problem with disjunctive constraints
Journal of Combinatorial Optimization
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We consider the minimum spanning tree problem with conflict constraints (MSTC). The problem is known to be strongly NP-hard and computing even a feasible solution is NP-hard. When the underlying graph is a cactus, we show that the feasibility problem is polynomially bounded whereas the optimization version is still NP-hard. When the conflict graph is a collection of disjoint cliques, (equivalently, when the conflict relation is transitive) we observe that MSTC can be solved in polynomial time. We also identify other special cases of MSTC that can be solved in polynomial time. Exploiting these polynomially solvable special cases we derive strong lower bounds. Also, various heuristic algorithms and feasibility tests are discussed along with preliminary experimental results. As a byproduct of this investigation, we show that if an @e-optimal solution to the maximum clique problem can be obtained in polynomial time, then a (3@e-1)-optimal solution to the maximum edge clique partitioning (Max-ECP) problem can be obtained in polynomial time. As a consequence, we have a polynomial time approximation algorithm for the Max-ECP with performance ratio O(n(loglogn)^2log^3n), improving the best previously known bound of O(n).