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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…
Acting on time-critical events by processing ever growing social media or news streams is a major technical challenge. Many of these data sources can be modeled as multi-relational graphs. Continuous queries or techniques to search for rare…
We study the problem of dynamically maintaining the connected components of an undirected graph subject to edge insertions and deletions. We give the first parallel algorithm for the problem which is work-efficient, supports batches of…
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…
This paper considers fully dynamic graph algorithms with both faster worst case update time and sublinear space. The fully dynamic graph connectivity problem is the following: given a graph on a fixed set of n nodes, process an online…
We study the problem of maintaining a breadth-first spanning tree and the induced BFS ordering in a directed graph under edge updates. While semi-dynamic algorithms are known, maintaining the spanning tree, level information, and numbering…
In this paper we study the problem of dynamically maintaining graph properties under batches of edge insertions and deletions in the massively parallel model of computation. In this setting, the graph is stored on a number of machines, each…
Vertex connectivity and edge connectivity are fundamental concepts in graph theory that have been widely studied from both structural and algorithmic perspectives. The focus of this paper is on computing these two parameters for graphs…
In many real datasets such as social media streams and cyber data sources, graphs change over time through a graph update stream of edge insertions and deletions. Detecting critical patterns in such dynamic graphs plays an important role in…
In this paper, we present an on-line fully dynamic algorithm for maintaining strongly connected component of a directed graph in a shared memory architecture. The edges and vertices are added or deleted concurrently by fixed number of…
We present a deterministic fully-dynamic data structure for maintaining information about the cut-vertices in a graph; i.e. the vertices whose removal would disconnect the graph. Our data structure supports insertion and deletion of edges,…
Truss was proposed to study social network data represented by graphs. A k-truss of a graph is a cohesive subgraph, in which each edge is contained in at least k-2 triangles within the subgraph. While truss has been demonstrated as superior…
We present a data structure that can maintain a simple planar graph under edge contractions in linear total time. The data structure supports adjacency queries and provides access to neighbor lists in $O(1)$ time. Moreover, it can report…
Today's communication networks have stringent availability requirements and hence need to rapidly restore connectivity after failures. Modern networks thus implement various forms of fast reroute mechanisms in the data plane, to bridge the…
We show an algorithm for dynamic maintenance of connectivity information in an undirected planar graph subject to edge deletions. Our algorithm may answer connectivity queries of the form `Are vertices $u$ and $v$ connected with a path?' in…
We study the problem of connecting the parts of a multipartite graph using a minimum number of edges under a matching constraint. We introduce interconnection trees, defined as matchings whose projections onto the quotient graph form a…
We study dynamic planar graphs with $n$ vertices, subject to edge deletion, edge contraction, edge insertion across a face, and the splitting of a vertex in specified corners. We dynamically maintain a combinatorial embedding of such a…
Finding $k$-cores in graphs is a valuable and effective strategy for extracting dense regions of otherwise sparse graphs. We focus on the important problem of maintaining cores on rapidly changing dynamic graphs, where batches of edge…
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…
The dynamic trees problem is to maintain a forest subject to edge insertions and deletions while facilitating queries such as connectivity, path weights, and subtree weights. Dynamic trees are a fundamental building block of a large number…