相关论文: Dynamic complexity of Reachability: How many chang…

Motion planning is a fundamental problem of robotics with applications in many areas of computer science and beyond. Its restriction to graphs has been investigated in the literature for it allows to concentrate on the combinatorial problem…

A temporal graph $\mathcal{G}=(G,\lambda)$ can be represented by an underlying graph $G=(V,E)$ together with a function $\lambda$ that assigns to each edge $e\in E$ the set of time steps during which $e$ is present. The reachability graph…

The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…

The dynamic complexity of the reachability query is studied in the dynamic complexity framework of Patnaik and Immerman, restricted to quantifier-free update formulas. It is shown that, with this restriction, the reachability query cannot…

The dynamic shortest paths problem on planar graphs asks us to preprocess a planar graph $G$ such that we may support insertions and deletions of edges in $G$ as well as distance queries between any two nodes $u,v$ subject to the constraint…

We study graph ordering problems with a min-max objective. A classical problem of this type is cutwidth, where given a graph we want to order its vertices such that the number of edges crossing any point is minimized. We give a $…

In this paper we introduce a general framework for casting fully dynamic transitive closure into the problem of reevaluating polynomials over matrices. With this technique, we improve the best known bounds for fully dynamic transitive…

We study the automorphism groups of countable homogeneous directed graphs (and some additional homogeneous structures) from the point of view of topological dynamics. We determine precisely which of these automorphism groups are amenable…

A digraph $G$ is weightable if its edges can be weighted with real numbers such that the total weight in each directed cycle equals 1. There are several equivalent conditions: that $G$ admits a 0/1-weighting with the same property, or that…

In this work we introduce the graph-theoretic notion of mendability: for each locally checkable graph problem we can define its mending radius, which captures the idea of how far one needs to modify a partial solution in order to "patch a…

We study the model-checking problem for first- and monadic second-order logic on finite relational structures. The problem of verifying whether a formula of these logics is true on a given structure is considered intractable in general, but…

Covariate adjustment is a widely used approach to estimate total causal effects from observational data. Several graphical criteria have been developed in recent years to identify valid covariates for adjustment from graphical causal…

Important data mining problems such as nearest-neighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in…

Reachability queries ask whether there exists a path from the source vertex to the target vertex on a graph. Recently, several powerful reachability queries, such as Label-Constrained Reachability (LCR) queries and Regular Path Queries…

Emerging networked systems become increasingly flexible and reconfigurable. This introduces an opportunity to adjust networked systems in a demand-aware manner, leveraging spatial and temporal locality in the workload for online…

We consider the problem of estimating the graph size, where one is given only local access to the graph. We formally define a query model in which one starts with a \emph{seed} node and is allowed to make queries about neighbours of nodes…

We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…

We characterize the reachability probabilities in stochastic directed graphs by means of reinforcement learning methods. In particular, we show that the dynamics of the transition probabilities in a stochastic digraph can be modeled via a…

We show a fully dynamic algorithm for maintaining $(1+\epsilon)$-approximate \emph{size} of maximum matching of the graph with $n$ vertices and $m$ edges using $m^{0.5-\Omega_{\epsilon}(1)}$ update time. This is the first polynomial…

Given a graph $G$ and two independent sets of same size, the Independent Set Reconfiguration Problem under token sliding ask whether one can, in a step by step manner, transform the first independent set into the second one. In each step we…