Abstract
We investigate sublinear-space computability relation among the directed graph vertex connectivity problem and its related problems, where by “sublinear-space computability” we mean in this paper \(O(n^{1-\varepsilon })\)-space and polynomial-time computability w.r.t. the number n of vertices. We demonstrate algorithmic techniques to relate the sublinear-space computability of directed graph connectivity and undirected graph length bounded connectivity.
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Notes
- 1.
Any \(O(\log n)\)-space algorithm is (modified to) a polynomial-time algorithm; thus, it is not necessary to require the polynomial-time computability when discussing the log-space computability.
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Acknowledgements
The authors would like to thank Dr. Kotaro Nakagawa for his helpful comments on earlier version of this paper. This work is supported in part by the ELC project (MEXT KAKENHI Grant No. 24106008).
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Imai, T., Watanabe, O. (2016). Relating Sublinear Space Computability Among Graph Connectivity and Related Problems. In: Freivalds, R., Engels, G., Catania, B. (eds) SOFSEM 2016: Theory and Practice of Computer Science. SOFSEM 2016. Lecture Notes in Computer Science(), vol 9587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49192-8_2
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DOI: https://doi.org/10.1007/978-3-662-49192-8_2
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