Related papers: Better Decremental and Fully Dynamic Sensitivity O…

In the decremental $(1+\epsilon)$-approximate Single-Source Shortest Path (SSSP) problem, we are given a graph $G=(V,E)$ with $n = |V|, m = |E|$, undergoing edge deletions, and a distinguished source $s \in V$, and we are asked to process…

We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…

Let G be a directed weighted graph (DiGraph) on n vertices and m edges with source s and sink t. An edge in G is vital if its removal reduces the capacity of (s,t)-mincut. Since the seminal work of Ford and Fulkerson, a long line of work…

We consider exact distance oracles for directed weighted planar graphs in the presence of failing vertices. Given a source vertex $u$, a target vertex $v$ and a set $X$ of $k$ failed vertices, such an oracle returns the length of a shortest…

We consider the problem of maintaining an approximate maximum integral matching in a dynamic graph $G$, while the adversary makes changes to the edges of the graph. The goal is to maintain a $(1+\epsilon)$-approximate maximum matching for…

Given an undirected graph $G=(V,E)$ of $n$ vertices and $m$ edges with weights in $[1,W]$, we construct vertex sensitive distance oracles (VSDO), which are data structures that preprocess the graph, and answer the following kind of queries:…

We consider the problem of maintaining an (approximately) minimum vertex cover in an $n$-node graph $G = (V, E)$ that is getting updated dynamically via a sequence of edge insertions/deletions. We show how to maintain a…

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…

We study the multi-agent Smoothed Online Convex Optimization (SOCO) problem, where $N$ agents interact through a communication graph. In each round, each agent $i$ receives a strongly convex hitting cost function $f^i_t$ in an online…

Let $G=(V,E)$ be an undirected weighted graph on $n=|V|$ vertices and $S\subseteq V$ be a Steiner set. Steiner mincut is a well-studied concept, which provides a generalization to both (s,t)-mincut (when $|S|=2$) and global mincut (when…

Distributed optimization has a rich history. It has demonstrated its effectiveness in many machine learning applications, etc. In this paper we study a subclass of distributed optimization, namely decentralized optimization in a non-smooth…

An \emph{$\alpha$-approximate vertex fault-tolerant distance sensitivity oracle} (\emph{$\alpha$-VSDO}) for a weighted input graph $G=(V, E, w)$ and a source vertex $s \in V$ is the data structure answering an $\alpha$-approximate distance…

We study deterministic algorithms for computing graph cuts, with focus on two fundamental problems: balanced sparse cut and $k$-vertex connectivity for small $k$ ($k=O(\polylog n)$). Both problems can be solved in near-linear time with…

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 study the succinct representations of vertex cuts by centralized oracles and labeling schemes. For an undirected $n$-vertex graph $G = (V,E)$ and integer parameter $f \geq 1$, the goal is supporting vertex cut queries: Given $F \subseteq…

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…

An $f$-edge fault-tolerant distance sensitive oracle ($f$-DSO) with stretch $\sigma \geq 1$ is a data structure that preprocesses an input graph $G$. When queried with the triple $(s,t,F)$, where $s, t \in V$ and $F \subseteq E$ contains at…

We present the first deterministic data structures for maintaining approximate minimum vertex cover and maximum matching in a fully dynamic graph $G = (V,E)$, with $|V| = n$ and $|E| =m$, in $o(\sqrt{m}\,)$ time per update. In particular,…

We study two fundamental decremental dynamic graph problems. In both problems, we need to maintain a vertex-weighted forest of size $n$ under edge deletions, weight updates, and a certain information-retrieval query. Both problems can be…

Let $s$ denote a distinguished source vertex of a non-negatively real weighted and undirected graph $G$ with $n$ vertices and $m$ edges. In this paper we present two efficient \emph{single-source approximate-distance sensitivity oracles},…