TY - GEN
T1 - Holographic computation of balanced succinct permanent instances (Extended abstract)
AU - Dolev, Shlomi
AU - Fandina, Nova
AU - Rosen, Joseph
N1 - Funding Information: 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.
PY - 2011/7/29
Y1 - 2011/7/29
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=79960708780&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-642-22494-2_11
DO - https://doi.org/10.1007/978-3-642-22494-2_11
M3 - Conference contribution
SN - 9783642224935
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 100
EP - 112
BT - Optical Supercomputing - Third International Workshop, OSC 2010, Revised Selected Papers
T2 - 3rd International Workshop on Optical Supercomputing, OSC 2010
Y2 - 17 November 2010 through 19 November 2010
ER -