Information Processing Letters
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Note on a Lower Bound on the Linear Complexity of the Fast Fourier Transform
Journal of the ACM (JACM)
Optimality of the Fast Fourier transform
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
EUROCAM '82 Proceedings of the European Computer Algebra Conference on Computer Algebra
AN IMPROVED OVERLAP ARGUMENT FOR ON-LINE MULTIPLICATION
AN IMPROVED OVERLAP ARGUMENT FOR ON-LINE MULTIPLICATION
Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Fast integer multiplication using modular arithmetic
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
A note on the size of OBDDs for the graph of integer multiplication
Information Processing Letters
Complexity of Comparing Monomials and Two Improvements of the Buchberger-Möller Algorithm
Mathematical Methods in Computer Science
Approximability and Parameterized Complexity of Minmax Values
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Regularity of the Euclid Algorithm; application to the analysis of fast GCD Algorithms
Journal of Symbolic Computation
Information Processing Letters
Optimal tree structures for group key tree management considering insertion and deletion cost
Theoretical Computer Science
Interpolation of polynomials given by straight-line programs
Theoretical Computer Science
Space- and time-efficient polynomial multiplication
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
The number of decomposable univariate polynomials. extended abstract
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
An exact algorithm for subgraph homeomorphism
Journal of Discrete Algorithms
Algorithms for propositional model counting
Journal of Discrete Algorithms
Recursive n-gram hashing is pairwise independent, at best
Computer Speech and Language
Algorithms for propositional model counting
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
On the OBDD complexity of the most significant bit of integer multiplication
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Speeding up dynamic programming for some NP-hard graph recoloring problems
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Saving space by algebraization
Proceedings of the forty-second ACM symposium on Theory of computing
A low complexity probabilistic test for integer multiplication
Journal of Complexity
An in-place truncated fourier transform and applications to polynomial multiplication
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Controlled non-uniform random generation of decomposable structures
Theoretical Computer Science
Faster algorithms on branch and clique decompositions
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Randomized OBDDs for the most significant bit of multiplication need exponential size
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
On the OBDD complexity of the most significant bit of integer multiplication
Theoretical Computer Science
Fast fourier transforms over poor fields
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Faster polynomial multiplication via discrete fourier transforms
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Homotopy techniques for multiplication modulo triangular sets
Journal of Symbolic Computation
The universality of iterated hashing over variable-length strings
Discrete Applied Mathematics
A larger lower bound on the OBDD complexity of the most significant bit of multiplication
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Schönhage-Strassen algorithm with MapReduce for multiplying terabit integers
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Algorithms for monitoring real-time properties
RV'11 Proceedings of the Second international conference on Runtime verification
On the bit-complexity of sparse polynomial and series multiplication
Journal of Symbolic Computation
A new algorithm for long integer cube computation with some insight into higher powers
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Relaxed p-adic Hensel lifting for algebraic systems
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Most Tensor Problems Are NP-Hard
Journal of the ACM (JACM)
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For more than 35 years, the fastest known method for integer multiplication has been the Schönhage-Strassen algorithm running in time O(n log n log log n). Under certain restrictive conditions there is a corresponding Ω(n log n) lower bound. The prevailing conjecture has always been that the complexity of an optimal algorithm is Θ(n log n). We present a major step towards closing the gap from above by presenting an algorithm running in time n log n, 2O(log* n). The main result is for boolean circuits as well as for multitape Turing machines, but it has consequences to other models of computation as well.