Abstract
We lay out a refined framework to discuss various approximation algorithms for combinatorial optimization problems residing inside the optimization class PO. We are focused on optimization problems characterized by computation models of uniform NC1-circuits, uniform-AC0, and logarithmic-space Turing machines. We present concrete optimization problems and prove that they are indeed complete under reasonably weak reductions. We also show collapses and separations among refined optimization classes.
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References
Àlvarez, C., Jenner, B.: A very hard log-space counting class. Theoret. Comput. Sci. 107, 3–30 (1993)
Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties. Springer (2003)
Gabow, H.N.: A matroid approach to finding edge connectivity and packing arborescences. In: STOC 1991, pp. 112–122. ACM Press (1991)
Goldschlager, L.M., Shaw, R.A., Staples, J.: The maximum flow problem is log space complete for P. Theoret. Comput. Sci. 21, 105–111 (1982)
Karger, D.R.: Global min-cuts in RNC, and other ramifications of a simple min-cut algorithm. In: SODA 1993, pp. 21–30 (1993)
Reingold, O.: Undirected connectivity in log-space. J. ACMÂ 55, article 17 (2008)
Tantau, T.: Logspace optimisation problems and their approximation properties. Theory Comput. Syst. 41, 327–350 (2007)
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Yamakami, T. (2013). Uniform-Circuit and Logarithmic-Space Approximations of Refined Combinatorial Optimization Problems. In: Widmayer, P., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2013. Lecture Notes in Computer Science, vol 8287. Springer, Cham. https://doi.org/10.1007/978-3-319-03780-6_28
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DOI: https://doi.org/10.1007/978-3-319-03780-6_28
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03779-0
Online ISBN: 978-3-319-03780-6
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