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Graph algorithms enormously contribute to the domains such as blockchains, social networks, biological networks, telecommunication networks, and several others. The ever-increasing demand of data-volume, as well as speed of such…
In this paper we consider the \emph{fully-dynamic} All-Pairs Effective Resistance problem, where the goal is to maintain effective resistances on a graph $G$ among any pair of query vertices under an intermixed sequence of edge insertions…
Computing a maximum independent set (MaxIS) is a fundamental NP-hard problem in graph theory, which has important applications in a wide spectrum of fields. Since graphs in many applications are changing frequently over time, the problem of…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
Near ubiquitous mobile computing has led to intense interest in dynamic graph theory. This provides a new and challenging setting for algorithmics and complexity theory. For any graph-based problem, the rapid evolution of a (possibly…
There is an extensive literature on dynamic algorithms for a large number of graph theoretic problems, particularly for all varieties of shortest path problems. Germane to this paper are a number fully dynamic algorithms that are known for…
We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster…
Graph algorithms are central to large-scale applications such as navigation systems, social networks, and data analysis platforms. This thesis studies two important challenges in such systems: robustness to failures and fairness in…
A dynamic graph algorithm is a data structure that supports edge insertions, deletions, and specific problem queries. While extensive research exists on dynamic algorithms for graph problems solvable in polynomial time, most of these…
We study solution discovery, where the goal is to obtain a feasible solution to a problem from an initial configuration by a bounded sequence of local moves. In many applications, however, the graph that defines which vertex sets are…
In the fully dynamic edge connectivity problem, the input is a simple graph $G$ undergoing edge insertions and deletions, and the goal is to maintain its edge connectivity, denoted $\lambda_G$. We present two simple randomized algorithms…
Dynamically changing graphs are used in many applications of graph algorithms. The scope of these graphs are in graphics, communication networks and in VLSI designs where graphs are subjected to change, such as addition and deletion of…
We study the computability and complexity of the exploration problem in a class of highly dynamic graphs: periodically varying (PV) graphs, where the edges exist only at some (unknown) times defined by the periodic movements of carriers.…
The graph-navigability problem concerns how one can find as short paths as possible between a pair of vertices, given an incomplete picture of a graph. We study the navigability of graphs where the vertices are tagged by a number (between 1…
Given a simple $n$-vertex, $m$-edge graph $G$ undergoing edge insertions and deletions, we give two new fully dynamic algorithms for exactly maintaining the edge connectivity of $G$ in $\tilde{O}(n)$ worst-case update time and…
Recently, Li et al. [2022] presented a dynamic Dyck-reachability algorithm for bidirected graphs. The basic idea is based on updating edge weights in a data structure called the merged graph $G_m$. As noted in Krishna et al. [2023], the…
During the last 10 years it has become popular to study dynamic graph problems in a emergency planning or sensitivity setting: Instead of considering the general fully dynamic problem, we only have to process a single batch update of size…
On an evolving graph that is continuously updated by a high-velocity stream of edges, how can one efficiently maintain if two vertices are connected? This is the connectivity problem, a fundamental and widely studied problem on graphs. We…
Dynamic graph research is an essential subject in Computer Science. The shortest path problem is still the central in this field; moreover there is a variety of applications in practical projects. In this paper, we select the transportation…
Connectivity query processing is a fundamental problem in graph processing. Given an undirected graph and two query vertices, the problem aims to identify whether they are connected via a path. Given frequent edge updates in real graph…