Related papers: Computing Minimal Persistent Cycles: Polynomial an…
The circuits of a polyhedron are a superset of its edge directions. Circuit walks, a sequence of steps along circuits, generalize edge walks and are "short" if they have few steps or small total length. Both interpretations of short are…
We study the problems of finding a minimum cycle basis (a minimum weight set of cycles that form a basis for the cycle space) and a minimum homology basis (a minimum weight set of cycles that generates the $1$-dimensional…
Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…
In a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be NP-complete even when restricted to bipartite graphs. It has been…
Graphs and hypergraphs are foundational structures in discrete mathematics. They have many practical applications, including the rapidly developing field of bioinformatics, and more generally, biomathematics. They are also a source of…
Minimum cost homomorphism problems can be viewed as a generalization of list homomorphism problems. They also extend two well-known graph colouring problems: the minimum colour sum problem and the optimum cost chromatic partition problem.…
Cycles in graphs often signify interesting processes. For example, cyclic trading patterns can indicate inefficiencies or economic dependencies in trade networks, cycles in food webs can identify fragile dependencies in ecosystems, and…
We consider high dimensional variants of the maximum flow and minimum cut problems in the setting of simplicial complexes and provide both algorithmic and hardness results. By viewing flows and cuts topologically in terms of the simplicial…
The aim of applied topology is to use and develop topological methods for applied mathematics, science and engineering. One of the main tools is persistent homology, an adaptation of classical homology, which assigns a barcode, i.e. a…
We study circle valued maps and consider the persistence of the homology of their fibers. The outcome is a finite collection of computable invariants which answer the basic questions on persistence and in addition encode the topology of the…
Probabilistic circuits (PCs) are a unifying representation for probabilistic models that support tractable inference. Numerous applications of PCs like controllable text generation depend on the ability to efficiently multiply two circuits.…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
The dicycle transversal number t(D) of a digraph D is the minimum size of a dicycle transversal of D, i. e. a set T of vertices of D such that D-T is acyclic. We study the following problem: Given a digraph D, decide if there is a dicycle B…
Graphs model real-world circumstances in many applications where they may constantly change to capture the dynamic behavior of the phenomena. Topological persistence which provides a set of birth and death pairs for the topological features…
We introduce a new bilevel version of the classic shortest path problem and completely characterize its computational complexity with respect to several problem variants. In our problem, the leader and the follower each control a subset of…
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…
In the Survivable Network Design Problem (SNDP), the input is an edge-weighted (di)graph $G$ and an integer $r_{uv}$ for every pair of vertices $u,v\in V(G)$. The objective is to construct a subgraph $H$ of minimum weight which contains…
A general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure is presented. The obtained simplicial complex preserves all pertinent topological…
This paper revisits the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph $G$ and a set of terminal pairs $P$ and asks whether $G$ contains a set of pairwise edge-disjoint paths connecting every terminal…
Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much…