Related papers: Explicit Solution Equation for Every Combinatorial…
We propose a general solution approach for min-max-robust counterparts of combinatorial optimization problems with uncertain linear objectives. We focus on the discrete scenario case, but our approach can be extended to other types of…
This article presents a methodology that automatically derives a combinatorial specification for a permutation class C, given its basis B of excluded patterns and the set of simple permutations in C, when these sets are both finite. This is…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
A combinatorial optimization problem (COP) has a finite groundset $E(\left|E\right|=N$), a weight vector $c=\left(c^e:e\in E\right)$ and a family $T\in E$ of feasible subsets with objective to find $t\in T$ with maximal weight:…
We study the problem of finding elements in the intersection of an arbitrary conic variety in $\mathbb{F}^n$ with a given linear subspace (where $\mathbb{F}$ can be the real or complex field). This problem captures a rich family of…
Monte Carlo Search gives excellent results in multiple difficult combinatorial problems. Using a prior to perform non uniform playouts during the search improves a lot the results compared to uniform playouts. Handmade heuristics tailored…
Efficient computability is an important property of solution concepts in matching markets. We consider the computational complexity of finding and verifying various solution concepts in trading networks-multi-sided matching markets with…
In this paper we studied combinatorial problems with parameterized locally budgeted uncertainty. We are looking for a solutions set such that for any parameters vector there exists a solution in the set with robustness near optimal. The…
In this paper, we present a new formalism, the Field Tensor Network Integral Logical Operator (FTNILO), to obtain the explicit equation that returns the minimum, maximum, and zeros of a multivariable injective function, and an algorithm for…
Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in combinatorial analysis, with critical applications in cryptography, bioinformatics, and statistical modeling. This…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
It is well known that rather general mutation-recombination models can be solved algorithmically (though not in closed form) by means of Haldane linearization. The price to be paid is that one has to work with a multiple tensor product of…
A real symmetric matrix (resp., tensor) is said to be copositive if the associated quadratic (resp., homogeneous) form is greater than or equal to zero over the nonnegative orthant. The problem of detecting their copositivity is NP-hard.…
We introduce a numerical strategy to efficiently solve the out-of-equilibrium Dyson equation in the transient regime. By discretizing the equation into a compact matrix form and applying state-of-the-art matrix compression techniques, we…
Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The tensor ring (TR) decomposition is invariant under the permutation of tensors with different mode…
In this paper, we introduce a novel approach to solve the many-body Schrodinger equation by the tensor neural network. Based on the tensor product structure, we can do the direct numerical integration by using fixed quadrature points for…
Polynomial optimization problems represent a wide class of optimization problems, with a large number of real-world applications. Current approaches for polynomial optimization, such as the sum of squares (SOS) method, rely on large-scale…
Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances. The practical side of theoretical computer…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
We consider the problem of solving mixed random linear equations with $k$ components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels…