4 citations · 11 across the 11 of their papers we have counts for
13 papers
Labeled Interleaving Distance for Reeb Graphs
Fangfei Lan, Salman Parsa, Bei Wang
Merge trees, contour trees, and Reeb graphs are graph-based topological descriptors that capture topological changes of (sub)level sets of scalar fields. Comparing scalar fields us…
Minimum Height Drawings of Ordered Trees in Polynomial Time: Homotopy Height of Tree Duals
Salman Parsa, Tim Ophelders
We consider drawings of graphs in the plane in which vertices are assigned distinct points in the plane and edges are drawn as simple curves connecting the vertices and such that t…
On Complexity of Computing Bottleneck and Lexicographic Optimal Cycles in a Homology Class
Erin Wolf Chambers, Salman Parsa, Hannah Schreiber
Homology features of spaces which appear in applications, for instance 3D meshes, are among the most important topological properties of these objects. Given a non-trivial cycle in…
Instability of the Smith Index Under Joins and Applications to Embeddability
Salman Parsa
We say a -dimensional simplicial complex embeds into double dimension if it embeds into the Euclidean space of dimension . For instance, a graph is planar iff it embeds into…
Algorithms for Contractibility of Compressed Curves on 3-Manifold Boundaries
Erin Wolf Chambers, Francis Lazarus, Arnaud de Mesmay +1
In this paper we prove that the problem of deciding contractibility of an arbitrary closed curve on the boundary of a 3-manifold is in NP. We emphasize that the manifold and the cu…
How to Morph Graphs on the Torus
Erin Wolf Chambers, Jeff Erickson, Patrick Lin +1
We present the first algorithm to morph graphs on the torus. Given two isotopic essentially 3-connected embeddings of the same graph on the Euclidean flat torus, where the edges in…
On embeddability of joins and their `factors'
S. Parsa, A. Skopenkov
We present a short and clear proof of the following particular case of a 2006 result of Melikhov-Schepin: Let be a -dimensional simplicial complex and the union of t…
On the Smith classes, the van Kampen obstruction and embeddability of
Salman Parsa
In this survey-research paper, we first introduce the theory of Smith classes of complexes with fixed-point free, periodic maps on them. These classes, when defined for the deleted…
Deciding contractibility of a non-simple curve on the boundary of a 3-manifold: A computational Loop Theorem
Éric Colin de Verdière, Salman Parsa
We present an algorithm for the following problem. Given a triangulated 3-manifold M and a (possibly non-simple) closed curve on the boundary of M, decide whether this curve is con…
On the embeddability of
Salman Parsa
We relate the embeddability of the simplicial complex into to that of into . In brief, the embeddability of into , in…
Hardness of Segment Cover, Contiguous SAT and Visibility with Uncertain Obstacles
Sharareh Alipour, Salman Parsa
We define the problem segment cover as follows. We are given a set of pairs of sub-intervals of the unit interval. The problem asks if there is a choice of a single interval from e…
Small Model -Complexes in -space and Applications
Salman Parsa
We consider computational complexity of problems related to the fundamental group and the first homology group of (embeddable) -complexes. We show, as an extension of an earlier…
Algorithms for Dynamic Reeb Graphs
Salman Parsa
We present an algorithm for updating the Reeb graph under fully dynamic changes of the function values. The basic event is the interchange of two consecutive vertex values. The alg…