Linear Algorithm for a Cyclic Graph Transformation
- Autores: Lyubetsky V.1,2, Lyubetskaya E.1, Gorbunov K.1
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Afiliações:
- Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)
- Faculty of Mechanics and Mathematics
- Edição: Volume 39, Nº 9 (2018)
- Páginas: 1217-1227
- Seção: Part 1. Special issue “High Performance Data Intensive Computing” Editors: V. V. Voevodin, A. S. Simonov, and A. V. Lapin
- URL: https://journals.rcsi.science/1995-0802/article/view/203121
- DOI: https://doi.org/10.1134/S1995080218090147
- ID: 203121
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Resumo
We propose a linear time and linear space algorithm that constructs a minimal (in the total cost) sequence of operations required to transform a directed graph consisting of disjoint cycles into any graph of the same type. The following operations are allowed: double-cut-and-join of vertices and insertion or deletion of a connected fragment of edges; the latter two operations have the same cost. We present a complete proof that the algorithm finds the corresponding minimum. The problem is a nontrivial particular case of the general problem of transforming a graph into another, which in turn is an instance of a hard optimization problem in graphs. In this general problem, which is known to be NP-complete, each vertex of a graph is of degree 1 or 2, edges with the same name may repeat unlimitedly, and operations belong to a well-known list including the above-mentioned operations. We describe our results for the general problem, but the proof is given for the cyclic case only.
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Sobre autores
V. Lyubetsky
Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute); Faculty of Mechanics and Mathematics
Autor responsável pela correspondência
Email: lyubetsk@iitp.ru
Rússia, Bol’shoi Karetnyi per. 19, str. 1, Moscow, 127051; Moscow, 119991
E. Lyubetskaya
Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)
Email: lyubetsk@iitp.ru
Rússia, Bol’shoi Karetnyi per. 19, str. 1, Moscow, 127051
K. Gorbunov
Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)
Email: lyubetsk@iitp.ru
Rússia, Bol’shoi Karetnyi per. 19, str. 1, Moscow, 127051