相关论文: \~{O}ptimal Dual Vertex Failure Connectivity Label…

Given a graph $G=(V,E)$ and a positive integer $t\geq2$, the task in the vertex cover $P_t$ ($VCP_t$) problem is to find a minimum subset of vertices $F\subseteq V$ such that every path of order $t$ in $G$ contains at least one vertex from…

Vertical federated learning (VFL) enables multiple parties with disjoint features to collaboratively train models without sharing raw data. While privacy vulnerabilities of VFL are extensively-studied, its security threats-particularly…

In this study, we address the complex issue of graph clustering in signed graphs, which are characterized by positive and negative weighted edges representing attraction and repulsion among nodes, respectively. The primary objective is to…

How to utilize the pseudo labels has always been a research hotspot in machine learning. However, most methods use pseudo labels as supervised training, and lack of valid assessing for their accuracy. Moreover, applications of pseudo labels…

In the graph clustering problem with a planted solution, the input is a graph on $n$ vertices partitioned into $k$ clusters, and the task is to infer the clusters from graph structure. A standard assumption is that clusters induce…

For a simple graph $G$, the $2$-distance graph, $D_2(G)$, is a graph with the vertex set $V(G)$ and two vertices are adjacent if and only if their distance is $2$ in the graph $G$. In this paper, we characterize all graphs with connected…

A vertex $v$ is called an AR-vertex, if $v$ has distinct edge weight sums for each distinct subset of edges incident on $v$. i.e., if $\{x_1,x_2,\dots,x_k\}$ are the edge labels of the edges incident on $v$, then the $2^k$ subset sums are…

We present near-optimal algorithms for detecting small vertex cuts in the CONGEST model of distributed computing. Despite extensive research in this area, our understanding of the vertex connectivity of a graph is still incomplete,…

Robust network design, which aims to guarantee network availability under various failure scenarios while optimizing performance/cost objectives, has received significant attention. Existing approaches often rely on model-based…

Hub labeling schemes are popular methods for computing distances on road networks and other large complex networks, often answering to a query within a few microseconds for graphs with millions of edges. In this work, we study their…

Structured prediction tasks in machine learning involve the simultaneous prediction of multiple labels. This is typically done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise elements, each…

A distributed proof (also known as local certification, or proof-labeling scheme) is a mechanism to certify that the solution to a graph problem is correct. It takes the form of an assignment of labels to the nodes, that can be checked…

Given a simple weighted directed graph $G = (V, E, \omega)$ on $n$ vertices as well as two designated terminals $s, t\in V$, our goal is to compute the shortest path from $s$ to $t$ avoiding any pair of presumably failed edges $f_1, f_2\in…

Graph Neural Networks (GNNs) have been widely employed for semi-supervised node classification tasks on graphs. However, the performance of GNNs is significantly affected by label noise, that is, a small amount of incorrectly labeled nodes…

The problem of labeled graph generation is gaining attention in the Deep Learning community. The task is challenging due to the sparse and discrete nature of graph spaces. Several approaches have been proposed in the literature, most of…

Let $G$ be a directed graph with $n$ vertices and $m$ edges, and let $s \in V(G)$ be a designated source vertex. We consider the problem of single source reachability (SSR) from $s$ in presence of failures of edges (or vertices). Formally,…

We revisit the vertex-failure connectivity oracle problem. This is one of the most basic graph data structure problems under vertex updates, yet its complexity is still not well-understood. We essentially settle the complexity of this…

We consider space efficient implementations of some classical applications of DFS including the problem of testing biconnectivity and $2$-edge connectivity, finding cut vertices and cut edges, computing chain decomposition and…

This paper considers a natural fault-tolerant shortest paths problem: for some constant integer $f$, given a directed weighted graph with no negative cycles and two fixed vertices $s$ and $t$, compute (either explicitly or implicitly) for…

A set of vertices in a graph is a dominating set if every vertex outside the set has a neighbor in the set. A dominating set is connected if the subgraph induced by its vertices is connected. The connected domatic partition problem asks for…