Related papers: Reducing the size and number of linear programs in…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
The aim of this research is twofold: Firstly, to model and solve a complex nurse scheduling problem with an integer programming formulation and evolutionary algorithms. Secondly, to detail a novel statistical method of comparing and hence…
Deep learning's success has been attributed to the training of large, overparameterized models on massive amounts of data. As this trend continues, model training has become prohibitively costly, requiring access to powerful computing…
In this work, two algorithms are developed related to lattice codes. In the first one, an extended complete Gr\"obner basis is computed for the label code of a lattice. This basis supports all term orderings associated with a total degree…
We describe a dynamic programming algorithm for computing the marginal distribution of discrete probabilistic programs. This algorithm takes a functional interpreter for an arbitrary probabilistic programming language and turns it into an…
We consider N-fold 4-block decomposable integer programs, which simultaneously generalize N-fold integer programs and two-stage stochastic integer programs with N scenarios. In previous work [R. Hemmecke, M. Koeppe, R. Weismantel, A…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing…
We consider the problem of controlling a Markov decision process (MDP) with a large state space, so as to minimize average cost. Since it is intractable to compete with the optimal policy for large scale problems, we pursue the more modest…
When applying Grover's algorithm to an unordered database, the probability of obtaining correct results usually decreases as the quantity of target increases. To amend the limitation, numbers of improved schemes are proposed. In this paper,…
Inspired by rational canonical forms, we introduce and analyze two decompositions of dynamic programming (DP) problems for systems with linear dynamics. Specifically, we consider both finite and infinite horizon DP problems in which the…
It is known that for binary codes one can use Gr\"obner bases to obtain a subset of codewords of minimal support that can be used to determine the second generalized Hamming weight of the code. In this paper we establish conditions on a…
Analyzing the computational complexity of evolutionary algorithms for binary search spaces has significantly increased their theoretical understanding. With this paper, we start the computational complexity analysis of genetic programming.…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…
There are two gradient descent decoding procedures for binary codes proposed independently by Liebler and by Ashikhmin and Barg. Liebler in his paper mentions that both algorithms have the same philosophy but in fact they are rather…
This paper argues that continued AI scaling requires repeated efficiency doublings. Classical AI scaling laws remain useful because they make progress predictable despite diminishing returns, but the compute variable in those laws is best…
This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear…
In this paper we present two algorithms for the computation of a diagonal form of a matrix over non-commutative Euclidean domain over a field with the help of Gr\"obner bases. This can be viewed as the pre-processing for the computation of…
We consider the number of linear extensions of an N-free order P. We give upper and lower bounds on this number in terms of parameters of the corresponding arc diagram. We propose a dynamic programming algorithm to calculate the number. The…