Related papers: Optimal Dyck Reachability for Data-Dependence and …
Proximity graph-based methods have emerged as a leading paradigm for approximate nearest neighbor (ANN) search in the system community. This paper presents fresh insights into the theoretical foundation of these methods. We describe an…
In this work, we study the maximum matching problem from the perspective of sensitivity. The sensitivity of an algorithm $A$ on a graph $G$ is defined as the maximum Wasserstein distance between the output distributions of $A$ on $G$ and on…
We revisit the classic problem of dynamically maintaining shortest paths between all pairs of nodes of a directed weighted graph. The allowed updates are insertions and deletions of nodes and their incident edges. We give worst-case…
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…
For any $\varepsilon > 0$, we give a polynomial-time $n^\varepsilon$-approximation algorithm for Max Independent Set in graphs of bounded twin-width given with an $O(1)$-sequence. This result is derived from the following time-approximation…
In this paper, we initiate the study of the dynamic maintenance of $2$-edge-connectivity relationships in directed graphs. We present an algorithm that can update the $2$-edge-connected blocks of a directed graph with $n$ vertices through a…
Assuming a directed acyclic graph (DAG) that represents prior knowledge of causal relationships between variables is a common starting point for cause-effect estimation. Existing literature typically invokes hypothetical domain expert…
We study the $k$-edge connectivity problem on undirected graphs in the distributed sketching model, where we have $n$ nodes and a referee. Each node sends a single message to the referee based on its 1-hop neighborhood in the graph, and the…
Reachability queries checking the existence of a path from a source node to a target node are fundamental operators for querying and processing graph data. Current approaches for index-based evaluation of reachability queries either focus…
The Minimum Path Cover (MPC) problem consists of finding a minimum-cardinality set of node-disjoint paths that cover all nodes in a given graph. We explore a variant of the MPC problem on acyclic digraphs (DAGs) where, given a subset of…
{\em Algorithms with predictions} incorporate machine learning predictions into algorithm design. A plethora of recent works incorporated predictions to improve on worst-case optimal bounds for online problems. In this paper, we initiate…
A unit disk graph is the intersection graph of n congruent disks in the plane. Dominating sets in unit disk graphs are widely studied due to their application in wireless ad-hoc networks. Because the minimum dominating set problem for unit…
Effective resistances are ubiquitous in graph algorithms and network analysis. In this work, we study sublinear time algorithms to approximate the effective resistance of an adjacent pair $s$ and $t$. We consider the classical adjacency…
Despite the possibility to quickly compute reachable sets of large-scale linear systems, current methods are not yet widely applied by practitioners. The main reason for this is probably that current approaches are not push-button-capable…
We show how to find and efficiently maintain maximal k-edge-connected subgraphs in undirected graphs. In particular, we provide the following results. (1) A general framework for maintaining the maximal k-edge-connected subgraphs upon…
Inquiries such as whether a task A depends on a task B, whether an author A has been influenced by a paper B, whether a certain protein is associated with a specific biological process or molecular function, or whether class A inherits from…
The MEG (minimum equivalent graph) problem is, given a directed graph, to find a small subset of the edges that maintains all reachability relations between nodes. The problem is NP-hard. This paper gives a proof that, for graphs where each…
We propose a simple and natural approximation algorithm for the problem of finding a 2-edge-connected spanning subgraph of minimum total edge cost in a graph. The algorithm maintains a spanning forest starting with an empty edge set. In…
Given a data graph G, a source vertex u and a target vertex v of a reachability query, the reachability query is used to answer whether there exists a path from u to v in G. Reachability query processing is one of the fundamental operations…
Approximate Nearest Neighbor Search (ANNS) has become a fundamental component in many real-world applications. Among various ANNS algorithms, graph-based methods are state-of-the-art. However, ANNS often suffers from a significant drop in…