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Abstract: We consider the problem (MSSS) of finding the minimum number of arcs in a spanning strongly connected subgraph of a strongly connected digraph. This problem is NP-hard for general digraphs since it generalizes the hamiltonian cycle problem. We characterize the number of arcs in a minimum spanning strong subgraph for digraphs which are either extended semicomplete or semicomplete bipartite. Our proofs lead to polynomial algorithms for finding an optimal subgraph for every digraph from each of... (Update)
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.... Recently it was shown that the MSSS problem is solvable in polynomial time for several classes which contain tournaments as a subclass [4, 5]. In the last section of this paper we also discuss briefly some approximation algorithms for this problem for general digraphs. Suppose...
...can be solved e#ciently for a much larger superclass of semicomplete digraphs than just quasi transitive digraphs. We remark that in [9], the MSSS problem was solved for various generalizations of tournaments. In particular polynomial algorithms were given for the classes of...
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Strongly Connected Spanning Subgraphs with the Minimum.. - Bang-Jensen, Huang, Yeo (2000) (Correct)
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BibTeX entry: (Update)
J. Bang-Jensen, J. Huang and A. Yeo, Strongly connected spanning subgraphs with the minimum number of arcs in quasi-transitive digraphs, submitted. http://citeseer.ist.psu.edu/bang-jensen99strongly.html More
@techreport{ bangjensen99strongly,
author = "Jørgen Bang-Jensen and Jing Huang and Anders Yeo",
title = "Strongly Connected Spanning Subgraphs with the Minimum Number of Arcs in Quasi-transitive Digraphs",
number = "PP-1999-05",
month = "9,",
year = "1999",
url = "citeseer.ist.psu.edu/bang-jensen99strongly.html" }
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16 One-diregular subgraphs in semicomplete multipartite digraph.. - Yeo - 1997
15 Quasi-transitive digraphs (context) - Bang-Jensen, Huang - 1995
13 Approximating the minimum equivalent digraph - Khuller, Raghavachari et al. - 1995
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9 Transitive compaction in parallel via branchings (context) - Gibbons, Karp et al.
7 A sufficient condition for a semicomplete multipartite digra.. (context) - Bang-Jensen, Gutin et al. - 1996
7 Huang and E (context) - Bang-Jensen - 1993
6 A polynomialalgorithm for the Hamiltonian cycle problem in s.. (context) - Bang-Jensen, Gutin et al. - 1998
6 Cycles and paths in complete multipartite digraphs (context) - Gutin - 1995
6 Vertex heaviest paths and cycles in quasi-transitive digraph.. (context) - Bang-Jensen, Gutin - 1996
6 Sufficient Conditions for a Digraph to be Hamiltonian (context) - Bang-Jensen, Gutin et al. - 1996
5 The complexity of finding generalized paths in tournaments (context) - Hell, Rosenfeld - 1983
5 Generalizations of tournaments: A survey (context) - Bang-Jensen, Gutin - 1998
4 Digraphs with the path-merging property (context) - Bang-Jensen - 1995
4 trees and cycles in tournaments (context) - Bang-Jensen, Gutin - 1996
4 Fast algorithms for finding hamiltonian paths and cycles in .. (context) - Bang-Jensen, Hell - 1991
3 Paths and cycles in extended and decomposable digraphs (context) - Bang-Jensen, Gutin - 1997
3 Parallel algorithms for hamiltonian paths with specified (context) - Bang-Jensen, Haddad
2 Strongly connected spanning subgraphs with the minimum numbe.. (context) - Bang-Jensen, Huang et al. - 1999
2 Parallel algorithms for the hamiltonian cycle and hamiltonia.. (context) - Bang-Jensen, Haddad et al. - 1997
2 A Polynomial Algorithm for finding a cycle covering a given .. - Yeo
2 the complexity of hamiltonian path and cycle problems in cer.. (context) - Bang-Jensen, Gutin
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