Related papers: A Change-Sensitive Algorithm for Maintaining Maxim…
Complex systems which can be represented in the form of static and dynamic graphs arise in different fields, e.g. communication, engineering and industry. One of the interesting problems in analysing dynamic network structures is to monitor…
Given a directed graph $G$, a transitive reduction $G^t$ of $G$ (first studied by Aho, Garey, Ullman [SICOMP `72]) is a minimal subgraph of $G$ that preserves the reachability relation between every two vertices in $G$. In this paper, we…
The availability of large scale event data with time stamps has given rise to dynamically evolving knowledge graphs that contain temporal information for each edge. Reasoning over time in such dynamic knowledge graphs is not yet well…
In this paper a greedy algorithm to detect conflict cliques in interval graphs and circular-arc graphs is analyzed. In a graph, a stable set requires that at most one vertex is chosen for each edge. It is equivalent to requiring that at…
Motivated by the problem of maintaining data structures for a large sets of points that are evolving over the course of time, we consider the problem of maintaining a set of labels assigned to the vertices of a tree, where the locations of…
This work introduces a novel algorithm for finding the connected components of a graph where the vertices and edges are grouped into sets defining a Set--Based Graph. The algorithm, under certain restrictions on those sets, has the…
In this paper, we propose a characterization of chordal bipartite graphs and an efficient enumeration algorithm for chordal bipartite induced subgraphs. A chordal bipartite graph is a bipartite graph without induced cycles with length six…
Estimating the number of triangles in graph streams using a limited amount of memory has become a popular topic in the last decade. Different variations of the problem have been studied, depending on whether the graph edges are provided in…
A maximum weighted matching for bipartite graphs $G=(A \cup B,E)$ can be found by using the algorithm of Edmonds and Karp with a Fibonacci Heap and a modified Dijkstra in $O(nm + n^2 \log{n})$ time where n is the number of nodes and m the…
We consider the problem of constructing a bipartite graph whose degrees lie in prescribed intervals. Necessary and sufficient conditions for the existence of such graphs are well-known. However, existing realization algorithms suffer from…
The main topic considered is maximizing the number of cycles in a graph with given number of edges. In 2009, Kir\'aly conjectured that there is constant $c$ such that any graph with $m$ edges has at most $(1.4)^m$ cycles. In this paper, it…
Given a bipartite graph, where the two sets of vertices are applicants and posts and ranks on the edges represent preferences of applicants over posts, a {\em rank-maximal} matching is one in which the maximum number of applicants is…
Evolving trees arise in many real-life scenarios from computer file systems and dynamic call graphs, to fake news propagation and disease spread. Most layout algorithms for static trees do not work well in an evolving setting (e.g., they…
We consider systems made of autonomous mobile robots evolving in highly dynamic discrete environment i.e., graphs where edges may appear and disappear unpredictably without any recurrence, stability, nor periodicity assumption. Robots are…
Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructible if they do get disrupted. These desirable properties of networks can be measured…
Graph embedding, aiming to learn low-dimensional representations (aka. embeddings) of nodes, has received significant attention recently. Recent years have witnessed a surge of efforts made on static graphs, among which Graph Convolutional…
A set of vertices in a graph forms a potential maximal clique if there exists a minimal chordal completion in which it is a maximal clique. Potential maximal cliques were first introduced as a key tool to obtain an efficient, though…
We study the fundamental problem of butterfly (i.e. (2,2)-bicliques) counting in bipartite streaming graphs. Similar to triangles in unipartite graphs, enumerating butterflies is crucial in understanding the structure of bipartite graphs.…
We develop the first theoretically-efficient algorithm for maintaining the maximal independent set (MIS) of a graph in the parallel batch-dynamic setting. In this setting, a graph is updated with batches of edge insertions/deletions, and…
We develop an experimental algorithm for the exact solving of the maximum independent set problem. The algorithm consecutively finds the maximal independent sets of vertices in an arbitrary undirected graph such that the next such set…