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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…
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…
We study reachability and shortest paths problems in dynamic directed graphs. Whereas algebraic dynamic data structures supporting edge updates and reachability/distance queries have been known for quite a long time, they do not, in…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained…
Dynamically maintaining the minimum cut in a graph $G$ under edge insertions and deletions is a fundamental problem in dynamic graph algorithms for which no conditional lower bound on the time per operation exists. In an $n$-node graph the…
Graphlet counting is an important problem as it has numerous applications in several fields, including social network analysis, biological network analysis, transaction network analysis, etc. Most of the practical networks are dynamic. A…
We study the edge-colouring problem, and give efficient algorithms where the number of colours is parameterised by the graph's arboricity, $\alpha$. In a dynamic graph, subject to insertions and deletions, we give a deterministic algorithm…
This paper considers a general data-fitting problem over a networked system, in which many computing nodes are connected by an undirected graph. This kind of problem can find many real-world applications and has been studied extensively in…
In this paper, we present a new exact algorithm for counting perfect matchings, which relies on neither inclusion-exclusion principle nor tree-decompositions. For any bipartite graph of $2n$ nodes and $\Delta n$ edges such that $\Delta \geq…
The links between optimal control of dynamical systems and neural networks have proved beneficial both from a theoretical and from a practical point of view. Several researchers have exploited these links to investigate the stability of…
We give the first non-trivial decremental dynamic embedding of a weighted, undirected graph $G$ into $\ell_p$ space. Given a weighted graph $G$ undergoing a sequence of edge weight increases, the goal of this problem is to maintain a…
Graph analytics attract much attention from both research and industry communities. Due to the linear time complexity, the $k$-core decomposition is widely used in many real-world applications such as biology, social networks, community…
In this paper we study the problem of fully dynamic maximal matching with lookahead. In a fully dynamic $n$-vertex graph setting, we have to handle updates (insertions and removals of edges), and answer queries regarding the current graph,…
We initiate the study of approximate maximum matching in the vertex partition model, for graphs subject to dynamic changes. We assume that the $n$ vertices of the graph are partitioned among $k$ players, who execute a distributed algorithm…
Logic optimization constitutes a critical phase within the Electronic Design Automation (EDA) flow, essential for achieving desired circuit power, performance, and area (PPA) targets. These logic circuits are typically represented as…
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…
Say that an edge of a graph G dominates itself and every other edge adjacent to it. An edge dominating set of a graph G = (V,E) is a subset of edges E' of E which dominates all edges of G. In particular, if every edge of G is dominated by…
The core number of a vertex is a basic index depicting cohesiveness of a graph, and has been widely used in large-scale graph analytics. In this paper, we study the update of core numbers of vertices in dynamic graphs with edge…
While operating communication networks adaptively may improve utilization and performance, frequent adjustments also introduce an algorithmic challenge: the re-optimization of traffic engineering solutions is time-consuming and may limit…