相关论文: Multiple Source Dual Fault Tolerant BFS Trees

We present a general toolbox, based on new vertex sparsifiers, for designing data structures to maintain shortest paths in dynamic graphs. In an $m$-edge graph undergoing edge insertions and deletions, our data structures give the first…

Given a class of graphs $\mathcal{H}$, the problem $\oplus\mathsf{Sub}(\mathcal{H})$ is defined as follows. The input is a graph $H\in \mathcal{H}$ together with an arbitrary graph $G$. The problem is to compute, modulo $2$, the number of…

Search is a central problem in artificial intelligence, and breadth-first search (BFS) and depth-first search (DFS) are the two most fundamental ways to search. In this paper we derive estimates for average BFS and DFS runtime. The average…

For a finite set $\mathcal{F}$ of graphs, the $\mathcal{F}$-Hitting problem aims to compute, for a given graph $G$ (taken from some graph class $\mathcal{G}$) of $n$ vertices (and $m$ edges) and a parameter $k\in\mathbb{N}$, a set $S$ of…

We study graph partitioning problems from a min-max perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main…

In this paper we reassess the parameterized complexity and approximability of the well-studied Steiner Forest problem in several graph classes of bounded width. The problem takes an edge-weighted graph and pairs of vertices as input, and…

Dijkstra's algorithm for the Single-Source Shortest Path (SSSP) problem is notoriously hard to parallelize in $o(n)$ depth, $n$ being the number of vertices in the input graph, without increasing the required parallel work unreasonably.…

In this paper we design {\sf FPT}-algorithms for two parameterized problems. The first is \textsc{List Digraph Homomorphism}: given two digraphs $G$ and $H$ and a list of allowed vertices of $H$ for every vertex of $G$, the question is…

This paper introduces a design method for densergraph-frequency graph Fourier frames (DGFFs) to enhance graph signal processing and analysis. The graph Fourier transform (GFT) enables us to analyze graph signals in the graph spectral domain…

Preservers and additive spanners are sparse (hence cheap to store) subgraphs that preserve the distances between given pairs of nodes exactly or with some small additive error, respectively. Since real-world networks are prone to failures,…

Breadth First Search (BFS) and other graph traversal techniques are widely used for measuring large unknown graphs, such as online social networks. It has been empirically observed that an incomplete BFS is biased toward high degree nodes.…

One of the simplest problems on directed graphs is that of identifying the set of vertices reachable from a designated source vertex. This problem can be solved easily sequentially by performing a graph search, but efficient parallel…

Graph Sparsification aims at compressing large graphs into smaller ones while preserving important characteristics of the input graph. In this work we study Vertex Sparsifiers, i.e., sparsifiers whose goal is to reduce the number of…

We present the first parallel depth-first search algorithm for undirected graphs that has near-linear work and sublinear depth. Concretely, in any $n$-node $m$-edge undirected graph, our algorithm computes a DFS in $\tilde{O}(\sqrt{n})$…

Recent work has established that, for every positive integer $k$, every $n$-node graph has a $(2k-1)$-spanner on $O(f^{1-1/k} n^{1+1/k})$ edges that is resilient to $f$ edge or vertex faults. For vertex faults, this bound is tight. However,…

We consider the problem of finding small distance-preserving subgraphs of undirected, unweighted interval graphs with $k$ terminal vertices. To start with, we show that finding an optimal distance-preserving subgraph is $\mathsf{NP}$-hard…

Subgraph matching is a basic operation widely used in many applications. However, due to its NP-hardness and the explosive growth of graph data, it is challenging to compute subgraph matching, especially in large graphs. In this paper, we…

The problem of Subgraph Isomorphism is defined as follows: Given a pattern H and a host graph G on n vertices, does G contain a subgraph that is isomorphic to H? Eppstein [SODA 95, J'GAA 99] gives the first linear time algorithm for…

In 1999, Brodal and Fagerberg (BF) gave an algorithm for maintaining a low outdegree orientation of a dynamic uniformly sparse graph. Specifically, for a dynamic graph on $n$-vertices, with arboricity bounded by $\alpha$ at all times, the…

Finding small vertex covers in a graph has applications in numerous domains. Two common formulations of the problem include: Minimum Vertex Cover, which finds the smallest vertex cover in a graph, and Parameterized Vertex Cover, which finds…