Related papers: On a logical model of combinatorial problems
We use a combinatorial approach to compute the number of non-isomorphic choices on four elements that can be explained by models of bounded rationality.
Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model…
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
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 study several consequences of the packing problem, a conjecture from combinatorial optimization, using algebraic invariants of square-free monomial ideals. While the packing problem is currently unresolved, we successfully settle the…
We investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation (PLDE). Two kinds of polynomials are to be distinguished, we call them /periodic/ and…
The recently introduced polynomial time integration framework proposes a novel way to construct time integrators for solving systems of first-order ordinary differential equation by using interpolating polynomials in the complex time plane.…
The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higher-dimensional polyhedron has recently received increasing attention. In this paper (written for the…
The problem of solving tropical linear systems, a natural problem of tropical mathematics, has already proven to be very interesting from the algorithmic point of view: it is known to be in $NP\cap coNP$ but no polynomial time algorithm is…
We provide a logical characterization of non-deterministic polynomial time defined by BSS machines over semirings via existential second-order logic interpreted in the semiring semantics developed by Gr\"adel and Tannen. Furthermore, we…
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
Reducing the NP-problems to the convex/linear analysis on the Birkhoff polytope.
A partial complement of the graph $G$ is a graph obtained from $G$ by complementing all the edges in one of its induced subgraphs. We study the following algorithmic question: for a given graph $G$ and graph class $\mathcal{G}$, is there a…
We introduce a new concept of approximation applicable to decision problems and functions, inspired by Bayesian probability. From the perspective of a Bayesian reasoner with limited computational resources, the answer to a problem that…
For a given set of intervals on the real line, we consider the problem of ordering the intervals with the goal of minimizing an objective function that depends on the exposed interval pieces (that is, the pieces that are not covered by…
The planar Kepler problem is complexified and we show that this holomorphic completely integrable Hamiltonian system has nontrivial monodromy.
Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of…
We are often interested in decomposing complex, structured data into simple components that explain the data. The linear version of this problem is well-studied as dictionary learning and factor analysis. In this work, we propose a…
We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization…