Related papers: Fully Dynamic MIS in Uniformly Sparse Graphs
We revisit the recent polynomial-time algorithm for the MAX WEIGHT INDEPENDENT SET (MWIS) problem in bounded-degree graphs that do not contain a fixed graph whose every component is a subdivided claw as an induced subgraph [Abrishami,…
We consider the problems of maintaining an approximate maximum matching and an approximate minimum vertex cover in a dynamic graph undergoing a sequence of edge insertions/deletions. Starting with the seminal work of Onak and Rubinfeld…
We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…
We consider the directed minimum weight cycle problem in the fully dynamic setting. To the best of our knowledge, so far no fully dynamic algorithms have been designed specifically for the minimum weight cycle problem in general digraphs.…
Conditional lower bounds for dynamic graph problems has received a great deal of attention in recent years. While many results are now known for the fully-dynamic case and such bounds often imply worst-case bounds for the partially dynamic…
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…
Designing dynamic graph algorithms against an adaptive adversary is a major goal in the field of dynamic graph algorithms. While a few such algorithms are known for spanning trees, matchings, and single-source shortest paths, very little…
We present two algorithms for dynamically maintaining a spanning forest of a graph undergoing edge insertions and deletions. Our algorithms guarantee {\em worst-case update time} and work against an adaptive adversary, meaning that an edge…
We give an algorithm that, with high probability, maintains a $(1-\epsilon)$-approximate $s$-$t$ maximum flow in undirected, uncapacitated $n$-vertex graphs undergoing $m$ edge insertions in $\tilde{O}(m+ n F^*/\epsilon)$ total update time,…
We consider dynamic algorithms for maintaining Single-Source Reachability (SSR) and approximate Single-Source Shortest Paths (SSSP) on $n$-node $m$-edge directed graphs under edge deletions (decremental algorithms). The previous fastest…
We describe algorithms, based on Avis and Fukuda's reverse search paradigm, for listing all maximal independent sets in a sparse graph in polynomial time and delay per output. For bounded degree graphs, our algorithms take constant time per…
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…
There has been a surge of interest in spectral hypergraph sparsification, a natural generalization of spectral sparsification for graphs. In this paper, we present a simple fully dynamic algorithm for maintaining spectral hypergraph…
We propose a fully dynamic algorithm for maintaining reachability information in directed graphs. The proposed deterministic dynamic algorithm has an update time of $O((ins*n^{2}) + (del * (m+n*log(n))))$ where $m$ is the current number of…
This paper presents a comprehensive study of algorithms for maintaining the number of all connected four-vertex subgraphs in a dynamic graph. Specifically, our algorithms maintain the number of paths of length three in deterministic…
We present the first data structures that maintain near optimal maximum cardinality and maximum weighted matchings on sparse graphs in sublinear time per update. Our main result is a data structure that maintains a $(1+\epsilon)$…
We show a fully dynamic algorithm for maintaining $(1+\epsilon)$-approximate \emph{size} of maximum matching of the graph with $n$ vertices and $m$ edges using $m^{0.5-\Omega_{\epsilon}(1)}$ update time. This is the first polynomial…
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…
In a very recent breakthrough, Behnezhad and Ghafari [FOCS'24] developed a novel fully dynamic randomized algorithm for maintaining a $(1-\epsilon)$-approximation of maximum matching with amortized update time potentially much better than…
Given a dynamic graph subject to insertions and deletions of edges, a natural question is whether the graph presently admits a planar embedding. We give a deterministic fully-dynamic algorithm for general graphs, running in amortized…