相关论文: Efficient reversal of transductions of sparse grap…

We prove several negative results about first-order transducibility for classes of sparse graphs: - for every $t \in \mathbb{N}$, the class of graphs of treewidth at most $t+1$ is not transducible from the class of graphs of treewidth at…

We give new decomposition theorems for classes of graphs that can be transduced in first-order logic from classes of sparse graphs -- more precisely, from classes of bounded expansion and from nowhere dense classes. In both cases, the…

We construct a fixed parameter algorithm parameterized by d and k that takes as an input a graph G' obtained from a d-degenerate graph G by complementing on at most k arbitrary subsets of the vertex set of G and outputs a graph H such that…

The concept of bounded expansion provides a robust way to capture sparse graph classes with interesting algorithmic properties. Most notably, every problem definable in first-order logic can be solved in linear time on bounded expansion…

Graph classes of bounded tree rank were introduced recently in the context of the model checking problem for first-order logic of graphs. These graph classes are a common generalization of graph classes of bounded degree and bounded…

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…

Transductions are a general formalism for expressing transformations of graphs (and more generally, of relational structures) in logic. We prove that a graph class $\mathscr{C}$ can be $\mathsf{FO}$-transduced from a class of bounded-height…

A class of graphs is structurally nowhere dense if it can be constructed from a nowhere dense class by a first-order transduction. Structurally nowhere dense classes vastly generalize nowhere dense classes and constitute important examples…

We study the first-order (FO) model checking problem of dense graphs, namely those which have FO interpretations in (or are FO transductions of) some sparse graph classes. We give a structural characterization of the graph classes which are…

We study various aspects of the first-order transduction quasi-order on graph classes, which provides a way of measuring the relative complexity of graph classes based on whether one can encode the other using a formula of first-order (FO)…

Graph-based representations underlie a wide range of scientific problems. Graph connectivity is typically represented as a sparse matrix in the Compressed Sparse Row format. Large-scale graphs rely on distributed storage, allocating…

Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…

We present an algorithm to count the number of occurrences of a pattern graph $H$ as an induced subgraph in a host graph $G$. If $G$ belongs to a bounded expansion class, the algorithm runs in linear time. Our design choices are motivated…

In the Network Inference problem, one seeks to recover the edges of an unknown graph from the observations of cascades propagating over this graph. In this paper, we approach this problem from the sparse recovery perspective. We introduce a…

In a quest to thoroughly understand the first-order transduction hierarchy of hereditary graph classes, some questions in particular stand out; such as, what properties hold for graph classes that are first-order transductions of planar…

We introduce the computational problem of graphlet transform of a sparse large graph. Graphlets are fundamental topology elements of all graphs/networks. They can be used as coding elements to encode graph-topological information at…

Classes with bounded rankwidth are MSO-transductions of trees and classes with bounded linear rankwidth are MSO-transductions of paths -- a result that shows a strong link between the properties of these graph classes considered from the…

In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications. Different from existing research…

We give $\operatorname{CMSO}$-transductions that, given a graph $G$, output its modular decomposition, its split decomposition and its bi-join decomposition. This improves results by Courcelle [Logical Methods in Computer Science, 2006] who…

Given a $k$-node pattern graph $H$ and an $n$-node host graph $G$, the subgraph counting problem asks to compute the number of copies of $H$ in $G$. In this work we address the following question: can we count the copies of $H$ faster if…