Edge-disjoint in- and out-branchings in tournaments and related path problems
Journal of Combinatorial Theory Series B
Transitive compaction in parallel via branchings
Journal of Algorithms
Approximating the Minimum Equivalent Digraph
SIAM Journal on Computing
On strongly connected digraphs with bounded cycle length
Discrete Applied Mathematics
An Algorithm for Finding a Minimal Equivalent Graph of a Digraph
Journal of the ACM (JACM)
Approximating the minimum strongly connected subgraph via a matching lower bound
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Strongly Connected Spanning Subdigraphs with the Minimum Number of Arcs in Quasi-transitive Digraphs
SIAM Journal on Discrete Mathematics
Finding a Minimal Transitive Reduction in a Strongly Connected Digraph within Linear Time
WG '89 Proceedings of the 15th International Workshop on Graph-Theoretic Concepts in Computer Science
Every strong digraph has a spanning strong subgraph with at most n+2α-2 arcs
Journal of Combinatorial Theory Series B
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Invitation to data reduction and problem kernelization
ACM SIGACT News
Parameterized Complexity
Minimum Leaf Out-Branching Problems
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Minimum leaf out-branching and related problems
Theoretical Computer Science
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A digraph D is strong if it contains a directed path from x to y for every choice of vertices x,y in D. We consider the problem (MSSS) of finding the minimum number of arcs in a spanning strong subdigraph of a strong digraph. It is easy to see that every strong digraph D on n vertices contains a spanning strong subdigraph on at most 2n-2 arcs. By reformulating the MSSS problem into the equivalent problem of finding the largest positive integer k@?n-2 so that D contains a spanning strong subdigraph with at most 2n-2-k arcs, we obtain a problem which we prove is fixed parameter tractable. Namely, we prove that there exists an O(f(k)n^c) algorithm for deciding whether a given strong digraph D on n vertices contains a spanning strong subdigraph with at most 2n-2-k arcs. We furthermore prove that if k=1 and D has no cut vertex then it has a kernel of order at most (2k-1)^2. We finally discuss related problems and conjectures.