Related papers: CMSO-transducing tree-like graph decompositions

This article establishes that the split decomposition of graphs introduced by Cunnigham, is definable in Monadic Second-Order Logic.This result is actually an instance of a more general result covering canonical graph decompositions like…

In this paper we describe an approach to constraint-based syntactic theories in terms of finite tree automata. The solutions to constraints expressed in weak monadic second order (MSO) logic are represented by tree automata recognizing the…

Modular Decomposition focuses on repeatedly identifying a module M (a collection of vertices that shares exactly the same neighbourhood outside of M) and collapsing it into a single vertex. This notion of exactitude of neighbourhood is very…

The Pathwidth Theorem states that if a class of graphs has unbounded pathwidth, then it contains all trees as graph minors. We prove a similar result for dense graphs. More precisely, we give a finite family of tree-like patterns and prove…

In this paper the chordal graph structures of polynomial sets appearing in triangular decomposition in top-down style are studied when the input polynomial set to decompose has a chordal associated graph. In particular, we prove that the…

Logical transductions provide a very useful tool to encode classes of structures inside other classes of structures. In this paper we study first-order (FO) transductions and the quasiorder they induce on infinite classes of finite graphs.…

We present a new graph compressor that works by recursively detecting repeated substructures and representing them through grammar rules. We show that for a large number of graphs the compressor obtains smaller representations than other…

Possibly the most famous algorithmic meta-theorem is Courcelle's theorem, which states that all MSO-expressible graph properties are decidable in linear time for graphs of bounded treewidth. Unfortunately, the running time's dependence on…

Among the novel metrics used to study the relative importance of nodes in complex networks, k-core decomposition has found a number of applications in areas as diverse as sociology, proteinomics, graph visualization, and distributed system…

The notions of weakly bipartitive and bipartitive families were introduced by Montgolfier (2003) as a general tool for studying some decomposition of graphs and other combinatorial structures. In this paper, we give a matrix description of…

We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived categories and even marked filtrations, where one descends not…

Graph encoders in AMR-to-text generation models often rely on neighborhood convolutions or global vertex attention. While these approaches apply to general graphs, AMRs may be amenable to encoders that target their tree-like structure. By…

Can we use machine learning to compress graph data? The absence of ordering in graphs poses a significant challenge to conventional compression algorithms, limiting their attainable gains as well as their ability to discover relevant…

In order to manage massive graphs in practice, it is often necessary to resort to graph compression, which aims at reducing the memory used when storing and processing the graph. Efficient compression methods have been proposed in the…

We consider dataflow architecture for two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We improve the earlier technique of almost continuous program…

This article describes lossless compression algorithms for multisets of sequences, taking advantage of the multiset's unordered structure. Multisets are a generalisation of sets where members are allowed to occur multiple times. A multiset…

We introduce a denotational semantic framework for shared-memory concurrent programs in a C11-style memory model. This denotational approach is an alternative to techniques based on "execution graphs" and axiomatizations, and it allows for…

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…

One of the most famous algorithmic meta-theorems states that every graph property that can be defined by a sentence in counting monadic second order logic (CMSOL) can be checked in linear time for graphs of bounded treewidth, which is known…

Graph autoencoders have gained attention in nonlinear reduced-order modeling of parameterized partial differential equations defined on unstructured grids. Despite they provide a geometrically consistent way of treating complex domains,…