Sorting Permutations by Reversals and Eulerian Cycle Decompositions

@article{Caprara1999SortingPB,
  title={Sorting Permutations by Reversals and Eulerian Cycle Decompositions},
  author={Alberto Caprara},
  journal={SIAM J. Discret. Math.},
  year={1999},
  volume={12},
  pages={91-110}
}
  • A. Caprara
  • Published 1999
  • Computer Science
  • SIAM J. Discret. Math.
We analyze the strong relationship among three combinatorial problems, namely, the problem of sorting a permutation by the minimum number of reversals (MIN-SBR), the problem of finding the maximum number of edge-disjoint alternating cycles in a breakpoint graph associated with a given permutation (MAX-ACD), and the problem of partitioning the edge set of an Eulerian graph into the maximum number of cycles (MAX-ECD). We first illustrate a nice characterization of breakpoint graphs, which leads… 
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  • Computer Science, Mathematics
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TLDR
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On the Tightness of the Alternating-Cycle Lower Bound for Sorting by Reversals
  • A. Caprara
  • Mathematics, Computer Science
    J. Comb. Optim.
  • 1999
TLDR
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  • A. Labarre
  • Computer Science, Mathematics
    SIAM J. Discret. Math.
  • 2013
TLDR
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Given an Eulerian graph G, in the Maximum Eulerian Cycle Decomposition problem, we are interested in finding a collection of edge-disjoint cycles {E1, E2, . . . , Ek} in G such that all edges of G
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TLDR
The results show that, although the problem is hard and the exact algorithm proposed has apparently exponential running time even on average, the instances of practical interest can be solved to proven optimality very fast.
Edit Distances and Factorisations of Even Permutations
TLDR
This paper presents an algebraic reinterpretation of the cycle graph of the permutation to sort as an even permutation, and obtains a new lower bound on the prefix transposition distance, which is shown to outperform previous results.
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  • A. Caprara
  • Mathematics, Computer Science
    J. Comb. Optim.
  • 1999
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