Abstract
Galperin and Wigderson proposed a succinct representation for graphs, that uses number of bits that is logarithmic in the number of nodes. They proved complexity results for various decision problems on graph properties, when the graph is given in a succinct representation. Later, Papadimitriou and Yannakakis showed, that under the same succinct encoding method, certain class of decision problems on graph properties becomes exponentially hard. In this paper we consider the complexity of the Permanent problem when the graph/matrix is given in a restricted succinct representation. We present an optical architecture that is based on the holographic concept for solving balanced succinct permanent problem. Holography enables to have exponential copying (roughly, n ×n in each iteration) rather than constant copying (e.g., doubling in each iteration).
Partially supported by the Lynne and William Frankel Center for Computer Science, Ben-Gurion University of the Negev, Israel. ICT Programme of the European Union under contract number FP7-21570 (FRONTS), and Rita Altura Trust Chair in Computer Sciences.
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References
Anter, A., Dolev, S.: Optical solution for hard on average #p-complete instances (using exponential space for solving instances of the permanent). Natural Computing 9, 891–902 (2010)
Dolev, S., Fitoussi, H.: Masking traveling beams: Optical solutions for np-complete problems, trading space for time. Theor. Comput. Sci. 411(6), 837–853 (2010)
Galperin, H., Wigderson, A.: Succinct representations of graphs. Inf. Control 56, 183–198 (1984)
Lipton, R.: New directions in testing. In: Distributed Computing and Cryptography. DIMACS Series on Discrete Mathematicsand Theoretical Computer Science, vol. 2, pp. 191–202 (1991)
Moon, C.R., Mattos, L.S., Foster, B.K., Zeltzer, G., Ko, W., Manoharan, H.C.: Quantum Phase Extraction in Isospectral Electronic Nanostructures. Science 319(5864), 782–787 (2008)
Papadimitriou, C.H., Yannakakis, M.: A note on succinct representations of graphs. Inf. Control 71, 181–185 (1986)
Valiant, L.G.: The complexity of computing the permanent. Theoretical Computer Science 8(2), 189–201 (1979)
Wegener, I.: The complexity of Boolean functions. Wiley-Feubner Series in Computer Science. B. G. Teubner and John Wiley & Sons, Chichester (1987)
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Dolev, S., Fandina, N., Rosen, J. (2011). Holographic Computation of Balanced Succinct Permanent Instances. In: Dolev, S., Oltean, M. (eds) Optical Supercomputing. OSC 2010. Lecture Notes in Computer Science, vol 6748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22494-2_11
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DOI: https://doi.org/10.1007/978-3-642-22494-2_11
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