Zobrazeno 1 - 10
of 270
pro vyhledávání: '"Kaski, Petteri"'
Autor:
Kaski, Petteri, Michałek, Mateusz
The exponent $\sigma(T)$ of a tensor $T\in\mathbb{F}^d\otimes\mathbb{F}^d\otimes\mathbb{F}^d$ over a field $\mathbb{F}$ captures the base of the exponential growth rate of the tensor rank of $T$ under Kronecker powers. Tensor exponents are fundamenta
Externí odkaz:
http://arxiv.org/abs/2404.06427
In this paper we further explore the recently discovered connection by Bj\"{o}rklund and Kaski [STOC 2024] and Pratt [STOC 2024] between the asymptotic rank conjecture of Strassen [Progr. Math. 1994] and the three-way partitioning problem. We show th
Externí odkaz:
http://arxiv.org/abs/2404.04987
Autor:
Björklund, Andreas, Kaski, Petteri
Strassen's asymptotic rank conjecture [Progr. Math. 120 (1994)] claims a strong submultiplicative upper bound on the rank of a three-tensor obtained as an iterated Kronecker product of a constant-size base tensor. The conjecture, if true, most notabl
Externí odkaz:
http://arxiv.org/abs/2310.11926
Finding a Hamiltonian cycle in a given graph is computationally challenging, and in general remains so even when one is further given one Hamiltonian cycle in the graph and asked to find another. In fact, no significantly faster algorithms are known
Externí odkaz:
http://arxiv.org/abs/2308.01574
Given a directed graph, we show how to efficiently find a shortest (directed, simple) cycle on an even number of vertices. As far as we know, no polynomial-time algorithm was previously known for this problem. In fact, finding any even cycle in a dir
Externí odkaz:
http://arxiv.org/abs/2111.02992
Autor:
Björklund, Andreas, Kaski, Petteri
Given as input two $n$-element sets $\mathcal A,\mathcal B\subseteq\{0,1\}^d$ with $d=c\log n\leq(\log n)^2/(\log\log n)^4$ and a target $t\in \{0,1,\ldots,d\}$, we show how to count the number of pairs $(x,y)\in \mathcal A\times \mathcal B$ with int
Externí odkaz:
http://arxiv.org/abs/2007.14092
Autor:
Björklund, Andreas, Kaski, Petteri
We show that computing the Tutte polynomial of a linear matroid of dimension $k$ on $k^{O(1)}$ points over a field of $k^{O(1)}$ elements requires $k^{\Omega(k)}$ time unless the \#ETH---a counting extension of the Exponential Time Hypothesis of Impa
Externí odkaz:
http://arxiv.org/abs/2003.03595
Autor:
Karppa, Matti, Kaski, Petteri
We study the problem of multiplying two bit matrices with entries either over the Boolean algebra $(0,1,\vee,\wedge)$ or over the binary field $(0,1,+,\cdot)$. We engineer high-performance open-source algorithm implementations for contemporary multip
Externí odkaz:
http://arxiv.org/abs/1909.01554
We study tensor networks as a model of arithmetic computation for evaluating multilinear maps. These capture any algorithm based on low border rank tensor decompositions, such as $O(n^{\omega+\epsilon})$ time matrix multiplication, and in addition ma
Externí odkaz:
http://arxiv.org/abs/1712.09630