Related papers: A practical algorithm for 3-admissibility
The Fibonacci dimension fdim(G) of a graph G is introduced as the smallest integer f such that G admits an isometric embedding into Gamma_f, the f-dimensional Fibonacci cube. We give bounds on the Fibonacci dimension of a graph in terms of…
We study the problem of learning the structure of an optimal Bayesian network when additional constraints are posed on the network or on its moralized graph. More precisely, we consider the constraint that the network or its moralized graph…
Moving an autonomous agent through an unknown environment is one of the crucial problems for robotics and network analysis. Therefore, it received a lot of attention in the last decades and was analyzed in many different settings. The graph…
Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of efforts have been devoted to calculating graphlet statistics where random walk based approaches are…
Artificial intelligence is essential to succeed in challenging activities that involve dynamic environments, such as object manipulation tasks in indoor scenes. Most of the state-of-the-art literature explores robotic grasping methods by…
In the Partially Embedded Planarity problem, we are given a graph $G$ together with a topological drawing of a subgraph $H$ of $G$. The task is to decide whether the drawing can be extended to a drawing of the whole graph such that no two…
We present practical linear and almost linear-time algorithms to compute a chain decomposition of a directed acyclic graph (DAG), $G=(V,E)$. The number of vertex-disjoint chains computed is very close to the minimum. The time complexity of…
We present a certifying algorithm that tests graphs for 3-edge-connectivity; the algorithm works in linear time. If the input graph is not 3-edge-connected, the algorithm returns a 2-edge-cut. If it is 3-edge-connected, it returns a…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
Several modern applications involve huge graphs and require fast answers to reachability queries. In more than two decades since first proposals, several approaches have been presented adopting on-line searches, hop labelling or transitive…
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 contractible in M. Our algorithm runs in space polynomial in…
We consider the embeddability problem of a graph G into a two-dimensional simplicial complex C: Given G and C, decide whether G admits a topological embedding into C. The problem is NP-hard, even in the restricted case where C is…
Let \pi(G) denote the set of prime divisors of the order of a finite group G. The prime graph of G is the graph with vertex set \pi(G) with edges {p,q} if and only if there exists an element of order pq in G. In this paper, we prove that a…
This paper focuses on finding a spanning tree of a graph to maximize the number of its internal vertices. We present an approximation algorithm for this problem which can achieve a performance ratio $\frac{4}{3}$ on undirected simple…
Understanding what graph neural networks can learn, especially their ability to learn to execute algorithms, remains a central theoretical challenge. In this work, we prove exact learnability results for graph algorithms under…
Computing classical centrality measures such as betweenness and closeness is computationally expensive on large-scale graphs. In this work, we introduce an efficient force layout algorithm that embeds a graph into a low-dimensional space,…
We consider the problem of graph generation guided by network statistics, i.e., the generation of graphs which have given values of various numerical measures that characterize networks, such as the clustering coefficient and the number of…
In the graph stream model of computation, an algorithm processes the edges of an input graph in one or more sequential passes while using a memory sublinear in the input size. This model poses significant challenges for constructing long…
Generation of realistic topologies plays an important role in determining the accuracy and validity of simulation studies. This study presents a discussion to justify why, and how often randomly generated adjacency matrices may not not…
We study the $P_3$-convexity, the path convexity generated by all three-vertex paths, and focus on the problem of counting the $P_3$-convex vertex sets of a graph $G$, denoted by $\noc(G)$. First, we settle the associated extremal question:…