Related papers: Decomposing Petri nets
In weighted graphs the shortest path between two nodes is often reached through an indirect path, out of all possible connections, leading to structural redundancies which play key roles in the dynamics and evolution of complex networks. We…
Truss decomposition is a method used to analyze large sparse graphs in order to identify successively better connected subgraphs. Since in many domains the underlying graph changes over time, its associated truss decomposition needs to be…
In this paper, we revisit the split decomposition of graphs and give new combinatorial and algorithmic results for the class of totally decomposable graphs, also known as the distance hereditary graphs, and for two non-trivial subclasses,…
We show that every connected graph $G$ has a tree decomposition indexed by a tree $T$ such that $T$ is a subgraph of $G$ and the width of the tree decomposition is bounded from above by a function of the pathwidth of $G$. This answers a…
Several problems that are NP-hard on general graphs are efficiently solvable on graphs with bounded treewidth. Efforts have been made to generalize treewidth and the related notion of pathwidth to digraphs. Directed treewidth, DAG-width and…
Numerous fundamental database and reasoning problems are known to be NP-hard in general but tractable on instances where the underlying hypergraph structure is $\beta$-acyclic. Despite the importance of many of these problems, there has…
In this paper we introduce a new network reachability problem where the goal is to find the most reliable path between two nodes in a network, represented as a directed acyclic graph. Individual edges within this network may fail according…
We study connectivity problems from a fine-grained parameterized perspective. Cygan et al. (TALG 2022) obtained algorithms with single-exponential running time $\alpha^{tw} n^{O(1)}$ for connectivity problems parameterized by treewidth…
Complex molecules and mesoscopic structures are naturally described by general networks of elementary building blocks and tight-binding is one of the simplest quantum model suitable for studying the physical properties arising from the…
The iterative absorption method has recently led to major progress in the area of (hyper-)graph decompositions. Amongst other results, a new proof of the Existence conjecture for combinatorial designs, and some generalizations, was…
The heterogeneous structure implies that a very few nodes may play the critical role in maintaining structural and functional properties of a large-scale network. Identifying these vital nodes is one of the most important tasks in network…
We show an algorithm that, given an $n$-vertex graph $G$ and a parameter $k$, in time $2^{O(k \log k)} n^{O(1)}$ finds a tree decomposition of $G$ with the following properties: * every adhesion of the tree decomposition is of size at most…
We explore the robustness of complex networks against physical damage. We focus on spatially embedded network models and datasets where links are physical objects or physically transfer some quantity, which can be disrupted at any point…
A connected graph is 4-connected if it contains at least five vertices and removing any three of them does not disconnect it. A frequent preprocessing step in graph drawing is to decompose a plane graph into its 4-connected components and…
We consider two covering variants of the network design problem. We are given a set of origin/destination pairs, called O/D pairs, and each such O/D pair is covered if there exists a path in the network from the origin to the destination…
We study the correspondence between Bayesian Networks and graphical representation of proofs in linear logic. The goal of this paper is threefold: to develop a proof-theoretical account of Bayesian inference (in the spirit of the…
Concurrent programming is used in all large and complex computer systems. However, concurrency errors and system failures (ex: crashes and deadlocks) are common. We find that Petri nets can be used to model concurrent systems and find and…
Constraint Satisfaction Problems (CSPs) play a central role in many applications in Artificial Intelligence and Operations Research. In general, solving CSPs is NP-complete. The structure of CSPs is best described by hypergraphs. Therefore,…
In this note we describe an application of low-high orders in fault-tolerant network design. Baswana et al. [DISC 2015] study the following reachability problem. We are given a flow graph $G = (V, A)$ with start vertex $s$, and a spanning…
We consider a variant of treewidth that we call clique-partitioned treewidth in which each bag is partitioned into cliques. This is motivated by the recent development of FPT-algorithms based on similar parameters for various problems. With…