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In observational studies, the true causal model is typically unknown and needs to be estimated from available observational and limited experimental data. In such cases, the learned causal model is commonly represented as a partially…
We present a dynamic algorithm for the recognition of proper circular-arc (PCA) graphs, that supports the insertion and removal of vertices (together with its incident edges). The main feature of the algorithm is that it outputs a minimally…
Most of real-world graphs are dynamic, i.e., they change over time by a sequence of update operations. While the regression problem has been studied for static graphs and temporal graphs, it is not investigated for general dynamic graphs.…
Modern graphs are both large and dynamic, presenting significant challenges for fundamental queries, such as the Single-Source Shortest Path (SSSP) problem. Naively recomputing the SSSP tree after each topology change is prohibitively…
Answering connectivity queries is fundamental to fully dynamic graphs where edges and vertices are inserted and deleted frequently. Existing work proposes data structures and algorithms with worst-case guarantees. We propose a new data…
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…
Let $G$ be an undirected graph. An edge of $G$ dominates itself and all edges adjacent to it. A subset $E'$ of edges of $G$ is an edge dominating set of $G$, if every edge of the graph is dominated by some edge of $E'$. We say that $E'$ is…
Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Since an exact computation is prohibitive in large networks, several approximation algorithms have been…
Motivated by recent applications of dominator computations, we consider the problem of dynamically maintaining the dominators of flow graphs through a sequence of insertions and deletions of edges. Our main theoretical contribution is a…
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…
We give the first fully dynamic algorithm which maintains a $(1-\epsilon)$-approximate densest subgraph in worst-case time $\text{poly}(\log n, \epsilon^{-1})$ per update. Dense subgraph discovery is an important primitive for many…
We study the problem of dynamically maintaining the connected components of an undirected graph subject to edge insertions and deletions. We give the first parallel algorithm for the problem which is work-efficient, supports batches of…
Depth first search (DFS) tree is a fundamental data structure for solving graph problems. The classical algorithm [SiComp74] for building a DFS tree requires $O(m+n)$ time for a given graph $G$ having $n$ vertices and $m$ edges. Recently,…
This paper initiates the studies of parallel algorithms for core maintenance in dynamic graphs. The core number is a fundamental index reflecting the cohesiveness of a graph, which are widely used in large-scale graph analytics. The core…
Over the years, there has been extensive work on fully dynamic algorithms for classic graph problems that admit greedy solutions. Examples include $(\Delta+1)$ vertex coloring, maximal independent set, and maximal matching. For all three…
Most graphs in real life keep changing with time. These changes can be in the form of insertion or deletion of edges or vertices. Such rapidly changing graphs motivate us to study dynamic graph algorithms. However, three important graph…
Dynamic connectivity is a well-studied problem, but so far the most compelling progress has been confined to the edge-update model: maintain an understanding of connectivity in an undirected graph, subject to edge insertions and deletions.…
With few exceptions (namely, algorithms for maximal matching, $2$-approximate vertex cover, and certain constant-stretch spanners), all known fully dynamic algorithms in general graphs require (amortized) $\Omega(\log n)$ update/query time.…
A celebrated result of Johansson in graph theory states that every triangle-free graph of maximum degree $\Delta$ can be properly colored with $O(\Delta/\ln\Delta)$ colors, improving upon the "greedy bound" of $\Delta+1$ coloring in general…
In the \emph{dynamic edge coloring} problem, one has to maintain a graph of maximum degree $\Delta$ with at most $\Delta+c$ colors, given updates to the edges of the graph. An important objective is to minimize the \emph{recourse}, which is…