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Graph Isomorphism (GI) is a fundamental algorithmic problem. Amongst graph classes for which the computational complexity of GI has been resolved, trees are arguably the most fundamental. Tree Isomorphism is complete for deterministic…
We extend the notion of canonical ordering (initially developed for planar triangulations and 3-connected planar maps) to cylindric (essentially simple) triangulations and more generally to cylindric (essentially internally) $3$-connected…
We show that the class of chordal claw-free graphs admits LREC$_=$-definable canonization. LREC$_=$ is a logic that extends first-order logic with counting by an operator that allows it to formalize a limited form of recursion. This…
In the past decades for more and more graph classes the Graph Isomorphism Problem was shown to be solvable in polynomial time. An interesting family of graph classes arises from intersection graphs of geometric objects. In this work we show…
We consider all compatible topologies of an arbitrary finite-dimensional vector space over a non-trivial valuation field whose metric completion is a locally compact space. We construct the canonical lattice isomorphism between the lattice…
IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$…
We obtain a canonical representation for block matrices. The representation facilitates simple computation of the determinant, the matrix inverse, and other powers of a block matrix, as well as the matrix logarithm and the matrix…
The process of identifying stars is integral toward stellar based orientation determination in spacecraft. Star identification involves matching points in an image of the sky with stars in an astronomical catalog. A unified framework for…
We consider the class univalent log-harmonic mappings on the unit disk. Firstly, we obtain necessary and sufficient conditions for a complex-valued continuous function to be starlike or convex in the unit disk. Then we present a general…
Graph alignment in two correlated random graphs refers to the task of identifying the correspondence between vertex sets of the graphs. Recent results have characterized the exact information-theoretic threshold for graph alignment in…
Let $\C$ be a sequence of multisets of subspaces of a vector space $\F_q^k$. We describe a practical algorithm which computes a canonical form and the stabilizer of $\C$ under the group action of the general semilinear group. It allows us…
Generating realistic images of complex visual scenes becomes challenging when one wishes to control the structure of the generated images. Previous approaches showed that scenes with few entities can be controlled using scene graphs, but…
In this paper, we reduce the logspace shortest path problem to biconnected graphs; in particular, we present a logspace shortest path algorithm for general graphs which uses a logspace shortest path oracle for biconnected graphs. We also…
In 1969, Alan Tucker characterized proper circular-arc graphs as those graphs whose augmented adjacency matrices have the circularly compatible ones property. Moreover, he also found a polynomial-time algorithm for deciding whether any…
We investigate the space complexity of certain perfect matching problems over bipartite graphs embedded on surfaces of constant genus (orientable or non-orientable). We show that the problems of deciding whether such graphs have (1) a…
We present an algebraic characterization of the complexity classes Logspace and Nlogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is rooted in proof theory…
This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space…
The individualization-refinement paradigm for computing a canonical labeling and the automorphism group of a graph is investigated. A new algorithmic design aimed at reducing the size of the associated search space is introduced, and a new…
We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.
We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…