Related papers: Explicit Solution Equation for Every Combinatorial…
We study here several variants of the covariates fine balance problem where we generalize some of these problems and introduce a number of others. We present here a comprehensive complexity study of the covariates problems providing…
We consider optimization problems that are formulated and solved in the framework of tropical mathematics. The problems consist in minimizing or maximizing functionals defined on vectors of finite-dimensional semimodules over idempotent…
Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…
The success of machine learning solutions for reasoning about discrete structures has brought attention to its adoption within combinatorial optimization algorithms. Such approaches generally rely on supervised learning by leveraging…
This paper introduces a discrete relaxation for the class of combinatorial optimization problems which can be described by a set partitioning formulation under packing constraints. We present two combinatorial relaxations based on computing…
Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…
Advancements in mathematical programming have made it possible to efficiently tackle large-scale real-world problems that were deemed intractable just a few decades ago. However, provably optimal solutions may not be accepted due to the…
Finding the sparsest solutions to a tensor complementarity problem is generally NP-hard due to the nonconvexity and noncontinuity of the involved $\ell_0$ norm. In this paper, a special type of tensor complementarity problems with…
Finding a Z-eigenpair of a symmetric tensor is equivalent to finding a KKT point of a sphere constrained minimization problem. Based on this equivalency, in this paper, we first propose a class of iterative methods to get a Z-eigenpair of a…
Memcomputing is a novel paradigm of computation that utilizes dynamical elements with memory to both store and process information on the same physical location. Its building blocks can be fabricated in hardware with standard electronic…
This paper aims to find efficient solutions to a multi-objective optimization problem (MP) with convex polynomial data. To this end, a hybrid method, which allows us to transform problem (MP) into a scalar convex polynomial optimization…
Given a directed graph $G$ on $n$ vertices with a special vertex $s$, the directed minimum degree spanning tree problem requires computing a incoming spanning tree rooted at $s$ whose maximum tree in-degree is the smallest among all such…
Automated mathematical reasoning is a challenging problem that requires an agent to learn algebraic patterns that contain long-range dependencies. Two particular tasks that test this type of reasoning are (1) mathematical equation…
We study output-sensitive algorithms and complexity for multiobjective combinatorial optimization problems. In this computational complexity framework, an algorithm for a general enumeration problem is regarded efficient if it is…
Relevant combinatorial optimization problems (COPs) are often NP-hard. While they have been tackled mainly via handcrafted heuristics in the past, advances in neural networks have motivated the development of general methods to learn…
We consider apictorial edge-matching puzzles, in which the goal is to arrange a collection of puzzle pieces with colored edges so that the colors match along the edges of adjacent pieces. We devise an algebraic representation for this…
We give a method to determine an explicit solution to a system of two inhomogeneous linear recursive sequences of higher order. Our approach can be used efficiently in solving certain combinatorial problems. We finish the paper by…
We study a natural generalization of stable matching to the maximum weight stable matching problem and we obtain a combinatorial polynomial time algorithm for it by reducing it to the problem of finding a maximum weight ideal cut in a DAG.…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…
This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…