Related papers: Connectivity Algorithm
We construct a new quantum algorithm for the graph collision problem; that is, the problem of deciding whether the set of marked vertices contains a pair of adjacent vertices in a known graph G. The query complexity of our algorithm is…
The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…
A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various…
We consider problems to make a given bidirected graph strongly connected with minimum cardinality of additional signs or additional arcs. For the former problem, we show the minimum number of additional signs and give a linear-time…
This paper is a short introduction to the theory of tangles, both in graphs and general connectivity systems. An emphasis is put on the correspondence between tangles of order k and k-connected components. In particular, we prove that there…
The Mapper algorithm is a popular tool for visualization and data exploration in topological data analysis. We investigate an inverse problem for the Mapper algorithm: Given a dataset $X$ and a graph $G$, does there exist a set of Mapper…
Many distributed learning techniques have been motivated by the increasing size of datasets and their inability to fit into main memory on a single machine. We propose an algorithm that finds the nearest neighbor in a graph locally without…
We present an algorithm for computation of cell adjacencies for well-based cylindrical algebraic decomposition. Cell adjacency information can be used to compute topological operations e.g. closure, boundary, connected components, and…
A linear-time algorithm for generating auxiliary subgraphs for the 3-edge-connected components of a connected multigraph is presented. The algorithm uses an innovative graph contraction operation and makes only one pass over the graph. By…
This paper presents a graph signal processing algorithm to uncover the intrinsic low-rank components and the underlying graph of a high-dimensional, graph-smooth and grossly-corrupted dataset. In our problem formulation, we assume that the…
Relations between discrete quantities such as people, genes, or streets can be described by networks, which consist of nodes that are connected by edges. Network analysis aims to identify important nodes in a network and to uncover…
We employ the mathematical programming approach in conjunction with the graph theory to study the structure of correspondent banking networks. Optimizing the network requires decisions to be made to onboard, terminate or restrict the bank…
Short cycles connectivity is a generalization of ordinary connectivity. Instead by a path (sequence of edges), two vertices have to be connected by a sequence of short cycles, in which two adjacent cycles have at least one common vertex. If…
A new algorithm to obtain the chromatic number of a finite, connected graph is proposed in this paper. The algorithm is based on contraction of non adjacent vertices.
The adjacency operator of a graph has a spectrum and a class of scalar-valued spectral measures which have been systematically analyzed; it also has a spectral multiplicity function which has been less studied. The first purpose of this…
In this paper, we use a partition of the links of a network in order to uncover its community structure. This approach allows for communities to overlap at nodes, so that nodes may be in more than one community. We do this by making a node…
We investigate sublinear-time algorithms that take partially erased graphs represented by adjacency lists as input. Our algorithms make degree and neighbor queries to the input graph and work with a specified fraction of adversarial…
Mutually connected components (MCCs) play an important role as a measure of resilience in the study of interdependent networks. Despite their importance, an efficient algorithm to obtain the statistics of all MCCs during the removal of…
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
Fiber graphs of Gr\"obner bases from contingency tables are important in statistical hypothesis testing, where one studies random walks on these graphs using the Metropolis-Hastings algorithm. The connectivity of the graphs has implications…