Holographic computation of balanced succinct permanent instances

Authors:
Shlomi Dolev;Nova Fandina;Joseph Rosen
Affiliations:
Department of Computer Science, Ben Gurion University of the Negev, Israel;Department of Computer Science, Ben Gurion University of the Negev, Israel;Department of Electrical and Computer Engineering, Ben Gurion University of the Negev, Israel
Venue:
OSC'10 Proceedings of the Third international conference on Optical supercomputing
Year:
2010

Citing 4
Cited 0

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Natural Computing: an international journal

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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).