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♯P-completeness Of 01-permanent
The #P-completeness of 01-permanent, sometimes known as Valiant's theorem,Christos Papadimitriou, Christos H. Papadimitriou. ''Computational Complexity.'' Addison-Wesley, 1994. . Page 443 is a mathematical proof about the permanent (mathematics), permanent of matrix (mathematics), matrices, considered a seminal result in computational complexity theory. In a 1979 scholarly paper, Leslie Valiant proved that the computational problem of computing the permanent of a matrix is Sharp-P-complete, #P-hard, even if the matrix is restricted to have entries that are all 0 or 1. In this restricted case, computing the permanent is even Sharp-P-complete, #P-complete, because it corresponds to the Sharp-P, #P problem of counting the number of permutation matrices one can get by changing ones into zeroes. Valiant's 1979 paper also introduced Sharp-P, #P as a complexity class. Valiant's definition of completeness, and his proof of completeness of 01-permanent, both used Polynomial-time reduct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christos Papadimitriou
Christos Charilaos Papadimitriou (; born August 16, 1949) is a Greek-American theoretical computer scientist and the Donovan Family Professor of Computer Science at Columbia University. Education Papadimitriou studied at the National Technical University of Athens, where in 1972 he received his Bachelor of Arts degree in electrical engineering. He then pursued graduate studies at Princeton University, where he received his Ph.D. in electrical engineering and computer science in 1976 after completing a doctoral dissertation titled "The complexity of combinatorial optimization problems." Career Papadimitriou has taught at Harvard, MIT, the National Technical University of Athens, Stanford, UCSD, University of California, Berkeley and is currently the Donovan Family Professor of Computer Science at Columbia University. Papadimitriou co-authored a paper on pancake sorting with Bill Gates, then a Harvard undergraduate. Papadimitriou recalled "Two years later, I called to tell him ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |