Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
.879-approximation algorithms for MAX CUT and MAX 2SAT
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
The Complexity of Planar Counting Problems
SIAM Journal on Computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Complexity of Counting in Sparse, Regular, and Planar Graphs
SIAM Journal on Computing
Quantum Circuits That Can Be Simulated Classically in Polynomial Time
SIAM Journal on Computing
Theoretical Computer Science
A Combinatorial Proof of Kneser’s Conjecture
Combinatorica
Holographic Algorithms (Extended Abstract)
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Holographic algorithms: from art to science
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Bases Collapse in Holographic Algorithms
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
On the Theory of Matchgate Computations
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Proof verification and hardness of approximation problems
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
On symmetric signatures in holographic algorithms
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Matrices and Matroids for Systems Analysis
Matrices and Matroids for Systems Analysis
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Completeness for parity problems
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Valiant’s holant theorem and matchgate tensors
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Some results on matchgates and holographic algorithms
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Holographic algorithms: the power of dimensionality resolved
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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Leslie Valiant recently proposed a theory of holographic algorithms. These novel algorithms achieve exponential speed-ups for certain computational problems compared to naive algorithms for the same problems. The methodology uses Pfaffians and (planar) perfect matchings as basic computational primitives, and attempts to create exponential cancellations in computation. In this article we survey this new theory of matchgate computations and holographic algorithms.