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We present the first algorithm for maintaining a maximal independent set (MIS) of a fully dynamic graph---which undergoes both edge insertions and deletions---in polylogarithmic time. Our algorithm is randomized and, per update, takes…
While orthogonal drawings have a long history, smooth orthogonal drawings have been introduced only recently. So far, only planar drawings or drawings with an arbitrary number of crossings per edge have been studied. Recently, a lot of…
Several recent results from dynamic and sublinear graph coloring are surveyed. This problem is widely studied and has motivating applications like network topology control, constraint satisfaction, and real-time resource scheduling. Graph…
In the dynamic set cover problem, the input is a dynamic universe of elements and a fixed collection of sets. As elements are inserted or deleted, the goal is to efficiently maintain an approximate minimum set cover. While the past decade…
Orienting the edges of an undirected graph such that the resulting digraph satisfies some given constraints is a classical problem in graph theory, with multiple algorithmic applications. In particular, an $st$-orientation orients each edge…
The field of dynamic graph algorithms aims at achieving a thorough understanding of real-world networks whose topology evolves with time. Traditionally, the focus has been on the classic sequential, centralized setting where the main…
In this paper we introduce a general framework for casting fully dynamic transitive closure into the problem of reevaluating polynomials over matrices. With this technique, we improve the best known bounds for fully dynamic transitive…
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…
Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…
Robotic motion-planning problems, such as a UAV flying fast in a partially-known environment or a robot arm moving around cluttered objects, require finding collision-free paths quickly. Typically, this is solved by constructing a graph,…
The dynamic matrix inverse problem is to maintain the inverse of a matrix undergoing element and column updates. It is the main subroutine behind the best algorithms for many dynamic problems whose complexity is not yet well-understood,…
The aim of edge editing or modification problems is to change a given graph by adding and deleting of a small number of edges in order to satisfy a certain property. We consider the Edge Editing to a Connected Graph of Given Degrees problem…
A stable cutset is a set of vertices $S$ of a connected graph, that is pairwise non-adjacent and when deleting $S$, the graph becomes disconnected. Determining the existence of a stable cutset in a graph is known to be NP-complete. In this…
An $\alpha$-spanner of a graph $ G $ is a subgraph $ H $ such that $ H $ preserves all distances of $ G $ within a factor of $ \alpha $. In this paper, we give fully dynamic algorithms for maintaining a spanner $ H $ of a graph $ G $…
Triangle listing is an important topic significant in many practical applications. Efficient algorithms exist for the task of triangle listing. Recent algorithms leverage an orientation framework, which can be thought of as mapping an…
Dynamic Connectivity is a fundamental algorithmic graph problem, motivated by a wide range of applications to social and communication networks and used as a building block in various other algorithms, such as the bi-connectivity and the…
The dynamic scaling of distributed computations plays an important role in the utilization of elastic computational resources, such as the cloud. It enables the provisioning and de-provisioning of resources to match dynamic resource…
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…
Suppose we are given a bipartite graph that admits a perfect matching and an adversary may delete any edge from the graph with the intention of destroying all perfect matchings. We consider the task of adding a minimum cost edge-set to the…
We study the problem of finding and monitoring fixed-size subgraphs in a continually changing large-scale graph. We present the first approach that (i) performs worst-case optimal computation and communication, (ii) maintains a total memory…