Related papers: Fully Dynamic MIS in Uniformly Sparse Graphs
The core numbers of vertices in a graph are one of the most well-studied cohesive subgraph models because of the linear running time. In practice, many data graphs are dynamic graphs that are continuously changing by inserting or removing…
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 approximability of the maximum size independent set (MIS) problem in bounded degree graphs. This is one of the most classic and widely studied NP-hard optimization problems. We focus on the well known minimum degree greedy…
We introduce a notion for hierarchical graph clustering which we call the expander hierarchy and show a fully dynamic algorithm for maintaining such a hierarchy on a graph with $n$ vertices undergoing edge insertions and deletions using…
We present a deterministic dynamic algorithm for maintaining a $(1+\epsilon)f$-approximate minimum cost set cover with $O(f\log(Cn)/\epsilon^2)$ amortized update time, when the input set system is undergoing element insertions and…
This work presents inGRASS, a novel algorithm designed for incremental spectral sparsification of large undirected graphs. The proposed inGRASS algorithm is highly scalable and parallel-friendly, having a nearly-linear time complexity for…
Truss decomposition is a method used to analyze large sparse graphs in order to identify successively better connected subgraphs. Since in many domains the underlying graph changes over time, its associated truss decomposition needs to be…
In this paper we show a new algorithm for the decremental single-source reachability problem in directed planar graphs. It processes any sequence of edge deletions in $O(n\log^2{n}\log\log{n})$ total time and explicitly maintains the set of…
We study maximum matchings in fully dynamic graphs, which are graphs that undergo both edge insertions and deletions. Our focus is on algorithms that estimate the size of maximum matching after each update while spending a small time. An…
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…
We study geometric set cover problems in dynamic settings, allowing insertions and deletions of points and objects. We present the first dynamic data structure that can maintain an $O(1)$-approximation in sublinear update time for set cover…
The maximum independent set problem is a classic optimization problem that has also been studied quite intensively in the distributed setting. While the problem is hard to approximate in general, there are good approximation algorithms…
In the dynamic minimum set cover problem, a challenge is to minimize the update time while guaranteeing close to the optimal $\min(O(\log n), f)$ approximation factor. (Throughout, $m$, $n$, $f$, and $C$ are parameters denoting the maximum…
We refine upper bounds on the permanent saturation time of metric graphs using interval exchange transformations (IETs). Earlier results gave bounds under incommensurable edge lengths, we improve and generalize them by using the ergodic and…
In this paper, we present a fully-dynamic distributed algorithm for maintaining a minimum spanning tree on general graphs with positive real edge weights. The goal of a dynamic MST algorithm is to update efficiently the minimum spanning…
The greedy sequential algorithm for maximal independent set (MIS) loops over the vertices in arbitrary order adding a vertex to the resulting set if and only if no previous neighboring vertex has been added. In this loop, as in many…
Depth first search (DFS) tree is a fundamental data structure for solving various problems in graphs. It is well known that it takes $O(m+n)$ time to build a DFS tree for a given undirected graph $G=(V,E)$ on $n$ vertices and $m$ edges. We…
The Maximum Independent Set problem is fundamental for extracting conflict-free structure from large graphs, with applications in scheduling, recommendation, and network analysis. However, existing heuristics can stagnate when search…
An algorithm on weighted graphs is called universally optimal if it is optimal for every input graph, in the worst case taken over all weight assignments. Informally, this means the algorithm is competitive even with algorithms that are…
In this work, we propose, analyze and empirically validate a lazy-update approach to maintain accurate approximations of the $2$-hop neighborhoods of dynamic graphs resulting from sequences of edge insertions. We first show that under…