Related papers: Code Equivalence, Point Set Equivalence, and Polyn…
An inverse problem of identifying inhomogeneity or crack in the workpiece made of nonlinear magnetic material is investigated. To recover the shape from the local measurements, a piecewise constant level set algorithm is proposed. By means…
We show that the sequence of dimensions of the linear spaces, generated by a given rank-metric code together with itself under several applications of a field automorphism, is an invariant for the whole equivalence class of the code. The…
Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This…
Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave…
While the use of programming problems on exams is a common form of summative assessment in CS courses, grading such exam problems can be a difficult and inconsistent process. Through an analysis of historical grading patterns we show that…
In this paper, we study the question of classifying self-similar sets under bi-Lipschitz mappings and obtain an important bi-Lipschitz invariant, which is an ideal of a ring related to IFS. Roughly speaking, different Lipschitz equivalence…
In this paper we study a natural generalization of both {\sc $k$-Path} and {\sc $k$-Tree} problems, namely, the {\sc Subgraph Isomorphism} problem. In the {\sc Subgraph Isomorphism} problem we are given two graphs $F$ and $G$ on $k$ and $n$…
Nonlinear multi-scale problems are ubiquitous in materials science and biology. Complicated interactions between nonlinearities and (nonseparable) multiple scales pose a major challenge for analysis and simulation. In this paper, we study…
Given a graph $G$ and two independent sets of $G$, the independent set reconfiguration problem asks whether one independent set can be transformed into the other by moving a single vertex at a time, such that at each intermediate step we…
We describe the package "IncidenceCorrespondenceCohomology" for the computer algebra system Macaulay2. The main feature concerns the computation of characters and dimensions for the cohomology groups of line bundles on the incidence…
The intersection of a linear code with its dual is called the hull of the code. It is known that, for classical linear codes under the Hamming-metric, the dimension of the hull can be reduced up to equivalence. This phenomenon leads to the…
Perfect Matching-Cut is the problem of deciding whether a graph has a perfect matching that contains an edge-cut. We show that this problem is NP-complete for planar graphs with maximum degree four, for planar graphs with girth five, for…
We prove that the art gallery problem is equivalent under polynomial time reductions to deciding whether a system of polynomial equations over the real numbers has a solution. The art gallery problem is a classical problem in computational…
The problem of searching a polygonal region for an unpredictably moving intruder by a set of stationary guards, each carrying an orientable laser, is known as the Searchlight Scheduling Problem. Determining the computational complexity of…
We study the problem of similarity learning and its application to image retrieval with large-scale data. The similarity between pairs of images can be measured by the distances between their high dimensional representations, and the…
This paper studies the computational complexity of the Edge Packing problem and the Vertex Packing problem. The edge packing problem (denoted by $\bar{EDS}$) and the vertex packing problem (denoted by $\bar{DS} $) are linear programming…
The complexity of the graph isomorphism problem for trapezoid graphs has been open over a decade. This paper shows that the problem is GI-complete. More precisely, we show that the graph isomorphism problem is GI-complete for comparability…
In the Exact Matching Problem (EM), we are given a graph equipped with a fixed coloring of its edges with two colors (red and blue), as well as a positive integer $k$. The task is then to decide whether the given graph contains a perfect…
We consider multivariable polynomials over a fixed number field, linear in some of the variables. For a system of such polynomials satisfying certain technical conditions we prove the existence of search bounds for simultaneous zeros with…
Circular-arc graphs are intersection graphs of arcs on the circle. The aim of our work is to present a polynomial time algorithm testing whether two circular-arc graphs are isomorphic. To accomplish our task we construct decomposition…