A better approximation ratio for the minimum k-edge-connected spanning subgraph problem
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Approximating the minimum strongly connected subgraph via a matching lower bound
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Calculating a Relational Program for Transitive Reductions of Strongly Connected Graphs
ReIMICS '01 Revised Papers from the 6th International Conference and 1st Workshop of COST Action 274 TARSKI on Relational Methods in Computer Science
Every strong digraph has a spanning strong subgraph with at most n+2α-2 arcs
Journal of Combinatorial Theory Series B
A linear time 5/3-approximation for the minimum strongly-connected spanning subgraph problem
Information Processing Letters
Special edges, and approximating the smallest directed k-edge connected spanning subgraph
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Redundancy in logic II: 2CNF and Horn propositional formulae
Artificial Intelligence
ACM Transactions on Algorithms (TALG)
The minimum spanning strong subdigraph problem is fixed parameter tractable
Discrete Applied Mathematics
Approximating Transitive Reductions for Directed Networks
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
A generic program for minimal subsets with applications
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
Property-aware program sampling
Proceedings of the 9th ACM SIGPLAN-SIGSOFT workshop on Program analysis for software tools and engineering
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
A novel method for signal transduction network inference from indirect experimental evidence
WABI'07 Proceedings of the 7th international conference on Algorithms in Bioinformatics
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The MEG (minimum equivalent graph) problem is the following: "Given a directed graph, find a smallest subset of the edges that maintains all reachability relations between nodes." This problem is NP-hard; this paper gives an approximation algorithm achieving a performance guarantee of about 1.64 in polynomial time. The algorithm achieves a performance guarantee of 1.75 in the time required for transitive closure. The heart of the MEG problem is the minimum SCSS (strongly connected spanning subgraph) problem --- the MEG problem restricted to strongly connected digraphs. For the minimum SCSS problem, the paper gives a practical, nearly linear-time implementation achieving a performance guarantee of 1.75. The algorithm and its analysis are based on the simple idea of contracting long cycles. The analysis applies directly to $2$-\Exchange, a general "local improvement" algorithm, showing that its performance guarantee is 1.75.