Related papers: The All-Pairs Vitality-Maximization (VIMAX) Proble…
For an optimization problem $\Pi$ on graphs whose solutions are vertex sets, a vertex $v$ is called $c$-essential for $\Pi$ if all solutions of size at most $c \cdot OPT$ contain $v$. Recent work showed that polynomial-time algorithms to…
Pairwise network comparison is essential for various applications, including neuroscience, disease research, and dynamic network analysis. While existing literature primarily focuses on comparing entire network structures, we address a…
Edge connectivity and vertex connectivity are two fundamental concepts in graph theory. Although by now there is a good understanding of the structure of graphs based on their edge connectivity, our knowledge in the case of vertex…
A vertex partition $\pi = \{V_1, V_2, \ldots, V_k\}$ of $G$ is called a \emph{transitive partition} of size $k$ if $V_i$ dominates $V_j$ for all $1\leq i<j\leq k$. For two disjoint subsets $A$ and $B$ of $V$, we say $A$ \emph{strongly…
Enumerating maximal $k$-biplexes (MBPs) of a bipartite graph has been used for applications such as fraud detection. Nevertheless, there usually exists an exponential number of MBPs, which brings up two issues when enumerating MBPs, namely…
We are motivated by the fact that multiple representations of the environment are required to stand for the changes in appearance with time and for changes that appear in a cyclic manner. These changes are, for example, from day to night…
As graph data becomes more ubiquitous, the need for robust inferential graph algorithms to operate in these complex data domains is crucial. In many cases of interest, inference is further complicated by the presence of adversarial data…
This paper considers dynamic networks where vertices and edges represent manifest signals and causal dependencies among the signals, respectively. We address the problem of how to determine if the dynamics of a network can be identified…
We introduce a class of budgeted prize-collecting covering subgraph problems. For an input graph with prizes on the vertices and costs on the edges, the aim of these problems is to find a connected subgraph such that the cost of its edges…
Network sparsification aims to reduce the number of edges of a network while maintaining its structural properties; such properties include shortest paths, cuts, spectral measures, or network modularity. Sparsification has multiple…
The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, information retrieval and many other areas related to the World Wide Web. There exist several algorithms for the problem with…
We investigate the time-complexity of the All-Pairs Max-Flow problem: Given a graph with $n$ nodes and $m$ edges, compute for all pairs of nodes the maximum-flow value between them. If Max-Flow (the version with a given source-sink pair…
Can we efficiently compute optimal solutions to instances of a hard problem from optimal solutions to neighboring (i.e., locally modified) instances? For example, can we efficiently compute an optimal coloring for a graph from optimal…
Complex networks are made up of vertices and edges. The edges, which may be directed or undirected, are equipped with positive weights. Modeling complex systems that consist of different types of objects leads to multilayer networks, in…
A problem that arises in drawings of transportation networks is to minimize the number of crossings between different transportation lines. While this can be done efficiently under specific constraints, not all solutions are visually…
The maximum clique (MC) problem is a challenging graph mining problem which, due to its NP-hard nature, can take a substantial amount of execution time. The MC problem is dominated by set intersection operations similar to Maximal Clique…
In a bipartite graph, a subgraph is an $s$-biplex if each vertex of the subgraph is adjacent to all but at most $s$ vertices on the opposite set. The enumeration of $s$-biplexes from a given graph is a fundamental problem in bipartite graph…
Modularity maximization is one of the state-of-the-art methods for community detection that has gained popularity in the last decade. Yet it suffers from the resolution limit problem by preferring under certain conditions large communities…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
A permutation graph can be defined as an intersection graph of segments whose endpoints lie on two parallel lines $l_1$ and $l_2$, one on each. A bipartite permutation graph is a permutation graph which is bipartite. In this paper we study…