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Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…
We present a practically efficient algorithm for maintaining a global minimum cut in large dynamic graphs under both edge insertions and deletions. While there has been theoretical work on this problem, our algorithm is the first…
Graph clustering or community detection constitutes an important task for investigating the internal structure of graphs, with a plethora of applications in several domains. Traditional techniques for graph clustering, such as spectral…
We present an on-line algorithm for maintaining a topological order of a directed acyclic graph as arcs are added, and detecting a cycle when one is created. Our algorithm takes O(m^{1/2}) amortized time per arc, where m is the total number…
Consider the problem of maintaining source sink reachability($st$-Reachability), single source reachability(SSR) and strongly connected component(SCC) in an edge decremental directed graph. In particular, we design a randomized algorithm…
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…
The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is…
Partial orders and directed acyclic graphs are commonly recurring data structures that arise naturally in numerous domains and applications and are used to represent ordered relations between entities in the domains. Examples are task…
Graph pattern matching algorithms to handle million-scale dynamic graphs are widely used in many applications such as social network analytics and suspicious transaction detections from financial networks. On the other hand, the computation…
Detecting and visualizing what are the most relevant changes in an evolving network is an open challenge in several domains. We present a fast algorithm that filters subsets of the strongest nodes and edges representing an evolving weighted…
We study dynamic algorithms in the model of algorithms with predictions. We assume the algorithm is given imperfect predictions regarding future updates, and we ask how such predictions can be used to improve the running time. This can be…
Maximum cardinality matching in bipartite graphs is an important and well-studied problem. The fully dynamic version, in which edges are inserted and deleted over time has also been the subject of much attention. Existing algorithms for…
Motivated by the problem of routing reliably and scalably in a graph, we introduce the notion of a splicer, the union of spanning trees of a graph. We prove that for any bounded-degree n-vertex graph, the union of two random spanning trees…
We present a data structure that in a dynamic graph of treedepth at most $d$, which is modified over time by edge insertions and deletions, maintains an optimum-height elimination forest. The data structure achieves worst-case update time…
Depth first search (DFS) tree is one of the most well-known data structures for designing efficient graph algorithms. Given an undirected graph $G=(V,E)$ with $n$ vertices and $m$ edges, the textbook algorithm takes $O(n+m)$ time to…
A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…
In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an $n$-vertex graph $G=(V,E,w)$ with positive real edge weights, and our goal is to maintain a tree which is a good…
We give improved algorithms for maintaining edge-orientations of a fully-dynamic graph, such that the out-degree of each vertex is bounded. On one hand, we show how to orient the edges such that the out-degree of each vertex is proportional…
In this paper, we propose Continuous Graph Flow, a generative continuous flow based method that aims to model complex distributions of graph-structured data. Once learned, the model can be applied to an arbitrary graph, defining a…
In this thesis, we present new techniques to deal with fundamental algorithmic graph problems where graphs are directed and partially dynamic, i.e. undergo either a sequence of edge insertions or deletions: - Single-Source Reachability…