Add to ORKGWe revisit the fundamental Boolean Matrix Multiplication (BMM) problem. With the invention of algebraic fast matrix multiplication over 50 years ago, it also became known that BMM can be solved in truly subcubic $O(n^\omega)$ time, where $\omega<3$; much work has gone into bringing $\omega$ closer to $2$. Since then, a parallel line of work has sought comparably fast combinatorial algorithms but with limited success. The naive $O(n^3)$-time algorithm was initially improved by a $\log^2{n}$ factor [Arlazarov et al.; RAS'70], then by $\log^{2.25}{n}$ [Bansal and Williams; FOCS'09], then by $\log^3{n}$ [Chan; SODA'15], and finally by $\log^4{n}$ [Yu; ICALP'15]. We design a combinatorial algorithm for BMM running in time $n^3 / 2^{\Omega(\sqr...
Motivated by studying the power of randomness, certifying algorithms and barriers for fine-grained r...
The most studied linear algebraic operation, matrix multiplication, has surprisingly fast O(n^ω) tim...
Let M(n) denote the bit complexity of multiplying n-bit integers, let ω ∈ (2, 3] be an exponent for ...
In this paper we propose models of combinatorial algorithms for the Boolean Matrix Multiplication (B...
We present new combinatorial algorithms for Boolean matrix multiplication (BMM) and preprocessing a ...
Karppa & Kaski (2019) proposed a novel type of ``broken" or ``opportunistic" multiplication algorith...
AbstractWe present several bilinear algorithms for the acceleration of multiplication of n X n matri...
A probabilistic algorithm is presented to calculate the Boolean product of two n × n Boolean matrice...
In 2003 Cohn and Umans introduced a new group-theoretic framework for doing fast matrix multiplicati...
We further develop the group-theoretic approach to fast matrix multiplication introduced by Cohn and...
© 2018 ACM. We say an algorithm on n × n matrices with integer entries in [-M,M] (or n-node graphs w...
AbstractAn N × N matrix product can be evaluated with precision E > 0 in O(Ns+ϵ log (M/E) log log (M...
In this work, we use algebraic methods for studying distance computation and subgraph detection task...
For vertices $u$ and $v$ of an $n$-vertex graph $G$, a $uv$-trail of $G$ is an induced $uv$-path of ...
Matrix multiplication (hereafter we use the acronym MM) is among the most fundamental operations of ...
Motivated by studying the power of randomness, certifying algorithms and barriers for fine-grained r...
The most studied linear algebraic operation, matrix multiplication, has surprisingly fast O(n^ω) tim...
Let M(n) denote the bit complexity of multiplying n-bit integers, let ω ∈ (2, 3] be an exponent for ...
In this paper we propose models of combinatorial algorithms for the Boolean Matrix Multiplication (B...
We present new combinatorial algorithms for Boolean matrix multiplication (BMM) and preprocessing a ...
Karppa & Kaski (2019) proposed a novel type of ``broken" or ``opportunistic" multiplication algorith...
AbstractWe present several bilinear algorithms for the acceleration of multiplication of n X n matri...
A probabilistic algorithm is presented to calculate the Boolean product of two n × n Boolean matrice...
In 2003 Cohn and Umans introduced a new group-theoretic framework for doing fast matrix multiplicati...
We further develop the group-theoretic approach to fast matrix multiplication introduced by Cohn and...
© 2018 ACM. We say an algorithm on n × n matrices with integer entries in [-M,M] (or n-node graphs w...
AbstractAn N × N matrix product can be evaluated with precision E > 0 in O(Ns+ϵ log (M/E) log log (M...
In this work, we use algebraic methods for studying distance computation and subgraph detection task...
For vertices $u$ and $v$ of an $n$-vertex graph $G$, a $uv$-trail of $G$ is an induced $uv$-path of ...
Matrix multiplication (hereafter we use the acronym MM) is among the most fundamental operations of ...
Motivated by studying the power of randomness, certifying algorithms and barriers for fine-grained r...
The most studied linear algebraic operation, matrix multiplication, has surprisingly fast O(n^ω) tim...
Let M(n) denote the bit complexity of multiplying n-bit integers, let ω ∈ (2, 3] be an exponent for ...