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Graph isomorphism, subgraph isomorphism, and maximum common subgraphs are classical well-investigated objects. Their (parameterized) complexity and efficiently tractable cases have been studied. In the present paper, for a given set of…
We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number $k$ of nodes are required to be connected in the solution. A prototypical example is…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…
We study the concept of the continuous mean distance of a weighted graph. For connected unweighted graphs, the mean distance can be defined as the arithmetic mean of the distances between all pairs of vertices. This parameter provides a…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…
Given a network represented by a weighted directed graph G, we consider the problem of finding a bounded cost set of nodes S such that the influence spreading from S in G, within a given time bound, is as large as possible. The dynamic that…
Monitoring edge-geodetic sets in a graph are subsets of vertices such that every edge of the graph must lie on all the shortest paths between two vertices of the monitoring set. These objects were introduced in a work by Foucaud, Krishna…
Given a road network modelled as a planar straight-line graph $G=(V,E)$ with $|V|=n$, let $(u,v)\in V\times V$, the shortest path (distance) between $u,v$ is denoted as $\delta_G(u,v)$. Let $\delta(G)=\max_{(u,v)}\delta_G(u,v)$, for…
In graph theory, a tree is one of the more popular families of graphs with a wide range of applications in computer science as well as many other related fields. While there are several distance measures over the set of all trees, we…
Phylogenetic networks generalize phylogenetic trees by allowing reticulate evolutionary events such as horizontal gene transfer and hybridization. Among the many subclasses of phylogenetic networks, orchard networks have attracted…
The topic is the average order $A(G)$ of a connected induced subgraph of a graph $G$. This generalizes, to graphs in general, the average order of a subtree of a tree. In 1984, Jamison proved that the average order, over all trees of order…
Let $G = (V,E,\ell)$ be a $n$-node $m$-edge weighted undirected graph, where $\ell: E \rightarrow (0,\infty)$ is a real \emph{length} function defined on its edges, and let $g$ denote the girth of $G$, i.e., the length of its shortest…
We consider the classical tree edit distance between ordered labeled trees, which is defined as the minimum-cost sequence of node edit operations that transform one tree into another. The state-of-the-art solutions for the tree edit…
Say that an edge of a graph G dominates itself and every other edge adjacent to it. An edge dominating set of a graph G = (V,E) is a subset of edges E' of E which dominates all edges of G. In particular, if every edge of G is dominated by…
We introduce a new graph-theoretic concept in the area of network monitoring. In this area, one wishes to monitor the vertices and/or the edges of a network (viewed as a graph) in order to detect and prevent failures. Inspired by two…
Motivated by applications in network epidemiology, we consider the problem of determining whether it is possible to delete at most $k$ edges from a given input graph (of small treewidth) so that the resulting graph avoids a set…
Computing the similarity between two data points plays a vital role in many machine learning algorithms. Metric learning has the aim of learning a good metric automatically from data. Most existing studies on metric learning for…
The random intersection graph model $\mathcal G(n,m,p)$ is considered. Due to substantial edge dependencies, studying even fundamental statistics such as the subgraph count is significantly more challenging than in the classical binomial…
We give the first non-trivial fully dynamic probabilistic tree embedding algorithm for weighted graphs undergoing edge insertions and deletions. We obtain a trade-off between amortized update time and expected stretch against an oblivious…