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In Bayesian structure learning, we are interested in inferring a distribution over the directed acyclic graph (DAG) structure of Bayesian networks, from data. Defining such a distribution is very challenging, due to the combinatorially large sample space, and approximations based on MCMC are often required. Recently, a novel class of probabilistic models, called Generative Flow Networks (GFlowNets), have been introduced as a general framework for generative modeling of discrete and composite objects, such as graphs. In this work, we propose to use a GFlowNet as an alternative to MCMC for approximating the posterior distribution over the structure of Bayesian networks, given a dataset of observations. Generating a sample DAG from this approximate distribution is viewed as a sequential decision problem, where the graph is constructed one edge at a time, based on learned transition probabilities. Through evaluation on both simulated and real data, we show that our approach, called DAG-GFlowNet, provides an accurate approximation of the posterior over DAGs, and it compares favorably against other methods based on MCMC or variational inference., QC 20230523

The increasing popularity of SAT and BDD techniques in verification and synthesis encourages the search for additional speed-ups. Since typical SAT and BDD algorithms are exponential in the worst-case, the structure of real-world instances is a natural source of improvements. While SAT and BDD techniques are often presented as mutually exclusive alternatives, our work points out that both can be improved via the use of the same structural properties of instances. Our proposed methods are based on efficient problem partitioning and can be easily applied as pre-processing with arbitrary SAT solvers and BDD packages without source code modifications. Finding a better variable-ordering is a well recognized problem for both SAT solvers and BDD packages. Currently, all leading edge variable-ordering algorithms are dynamic, in the sense that they are invoked many times in the course of the host algorithm that solves SAT or manipulates BDDs. Examples include the DLCS ordering for SAT solvers and variable-sifting during BDD manipulations. In this work we propose a universal variable-ordering MINCE (MIN Cut Etc.) that pre-processes a given Boolean formula in CNF. MINCE is completely independent from target algorithms and outperforms both DLCS for SAT and variable sifting for BDDs. We argue that MINCE tends to capture structural properties of Boolean functions arising from real-world applications. Our contribution is validated on the ISCAS circuits and the DIMACS benchmarks. Empirically, our technique often outperforms existing techniques by a factor of two or more. Our results motivate search for stronger dynamic ordering heuristics and combined static/dynamic techniques., Presented at the International Conference on Computer Aided Design (ICCAD), held in San Jose, CA on 4-8 November, 2001. Pub. in the Proceedings of the International Conference on Computer Aided Design (ICCAD), 2001. The original document contains color images.

Labelled acyclic graphs with some restrictions on the labelling function can be used to describe concurrent processes. In this paper, we show how the restrictions on the labelling functions can be related with the assumptions made on the properties of the dependence and independence relations between actions. Furthermore, we compare two different recognizing devices for a particular class of labelled acyclic graphs, i.e. finite state automata on a free partially commutative monoid and finite state asynchronous automata, and give some results on the existence of minimal automata recognizing a given language.

Fast parallel algorithms are presented for updating the distance matrix, shortest paths for all pairs and biconnected components for an undirected graph and the topological ordering of vertices of a directed acyclic graph when an incremental change has been made to the graph. The kinds of changes that are considered here include insertion of a vertex of insertion and deletion of an edge or a change in the weight of an edge. The machine model used is a parallel random access machine which allows simultaneous reads but prohibits simultaneous writes into the same memory location. The algorithms described in this paper require O(log n) time and use 0(N-cubed) processors. These algorithms are efficient when compared to previously known 0(log-squared of n) time start-over algorithms for initial computation of the above mentioned properties of graphs. The previous solution is maintained in mulple inverted trees (a rooted tree where a child node points toward its parent) and after a minor change the new solution is rapidly recomputed from these trees, Sponsored in part by Contract F49620-83-C-0082.

The author shows that the problem of computing source-sink reliability is NP-hard, in fact P-complete, even for undirected and acyclic directed source-sink planar graphs having vertex degree at most three. Thus the source-sink reliability problem is unlikely to have an efficient algorithm, even when the graph can be laid out on a rectilinear grid. Keywords include: Reliability; complexity; planar graph; acyclic graph; NP-hard; P-complete.

We assume a multiple granularity database locking scheme similar to that of Gray, et al. in which a rooted directed acyclic graph is used to represent the levels of granularity. We prove that even if it is known in advance exactly what database references the transaction will make, it is NP-complete to find the optimal locking strategy for the transaction.

Cílem této práce je vytvořit aplikaci pro automatické rozmísťování uzlů v acyklických orientovaných grafech. Práce se především zaměřuje na pokročilé možnosti při tvorbě umístění uzlů, z kterých za zmínku stojí výběr polohy vybraných uzlů, rozdělení grafu na podgrafy či podporu polygonálních uzlů. V řešení jsou popsány vybrané algoritmy, které jsou použity ve výsledné aplikaci, a to konkrétně Fruchterman-Reingoldův silou orientovaný algoritmus, algoritmus Kamada-Kawai a algoritmus založený na Meyerových metodách samo-organizujících se grafů., The goal of this work is to create an application for automatic node placement of acyclic oriented graphs. The work is mainly focusing on advanced possibilities of graph layout, for example selection of location of selected nodes, division of a graph into sub-graphs or support of polygonal nodes. The solution describes chosen algorithms, which are being used in the resulting application. Specifically, Fruchterman-Reingold force oriented algorithm, algorithm Kamada-Kawai and an algorithm based on Meyer's self-organizing graphs.

Cílem této práce je vytvořit aplikaci pro automatické rozmísťování uzlů v acyklických orientovaných grafech. Práce se především zaměřuje na pokročilé možnosti při tvorbě umístění uzlů, z kterých za zmínku stojí výběr polohy vybraných uzlů, rozdělení grafu na podgrafy či podporu polygonálních uzlů. V řešení jsou popsány vybrané algoritmy, které jsou použity ve výsledné aplikaci, a to konkrétně Fruchterman-Reingoldův silou orientovaný algoritmus, algoritmus Kamada-Kawai a algoritmus založený na Meyerových metodách samo-organizujících se grafů., The goal of this work is to create an application for automatic node placement of acyclic oriented graphs. The work is mainly focusing on advanced possibilities of graph layout, for example selection of location of selected nodes, division of a graph into sub-graphs or support of polygonal nodes. The solution describes chosen algorithms, which are being used in the resulting application. Specifically, Fruchterman-Reingold force oriented algorithm, algorithm Kamada-Kawai and an algorithm based on Meyer's self-organizing graphs.

Cílem této práce je vytvořit aplikaci pro automatické rozmísťování uzlů v acyklických orientovaných grafech. Práce se především zaměřuje na pokročilé možnosti při tvorbě umístění uzlů, z kterých za zmínku stojí výběr polohy vybraných uzlů, rozdělení grafu na podgrafy či podporu polygonálních uzlů. V řešení jsou popsány vybrané algoritmy, které jsou použity ve výsledné aplikaci, a to konkrétně Fruchterman-Reingoldův silou orientovaný algoritmus, algoritmus Kamada-Kawai a algoritmus založený na Meyerových metodách samo-organizujících se grafů., The goal of this work is to create an application for automatic node placement of acyclic oriented graphs. The work is mainly focusing on advanced possibilities of graph layout, for example selection of location of selected nodes, division of a graph into sub-graphs or support of polygonal nodes. The solution describes chosen algorithms, which are being used in the resulting application. Specifically, Fruchterman-Reingold force oriented algorithm, algorithm Kamada-Kawai and an algorithm based on Meyer's self-organizing graphs.

Cílem této práce je vytvořit aplikaci pro automatické rozmísťování uzlů v acyklických orientovaných grafech. Práce se především zaměřuje na pokročilé možnosti při tvorbě umístění uzlů, z kterých za zmínku stojí výběr polohy vybraných uzlů, rozdělení grafu na podgrafy či podporu polygonálních uzlů. V řešení jsou popsány vybrané algoritmy, které jsou použity ve výsledné aplikaci, a to konkrétně Fruchterman-Reingoldův silou orientovaný algoritmus, algoritmus Kamada-Kawai a algoritmus založený na Meyerových metodách samo-organizujících se grafů., The goal of this work is to create an application for automatic node placement of acyclic oriented graphs. The work is mainly focusing on advanced possibilities of graph layout, for example selection of location of selected nodes, division of a graph into sub-graphs or support of polygonal nodes. The solution describes chosen algorithms, which are being used in the resulting application. Specifically, Fruchterman-Reingold force oriented algorithm, algorithm Kamada-Kawai and an algorithm based on Meyer's self-organizing graphs.

Cílem této práce je vytvořit aplikaci pro automatické rozmísťování uzlů v acyklických orientovaných grafech. Práce se především zaměřuje na pokročilé možnosti při tvorbě umístění uzlů, z kterých za zmínku stojí výběr polohy vybraných uzlů, rozdělení grafu na podgrafy či podporu polygonálních uzlů. V řešení jsou popsány vybrané algoritmy, které jsou použity ve výsledné aplikaci, a to konkrétně Fruchterman-Reingoldův silou orientovaný algoritmus, algoritmus Kamada-Kawai a algoritmus založený na Meyerových metodách samo-organizujících se grafů., The goal of this work is to create an application for automatic node placement of acyclic oriented graphs. The work is mainly focusing on advanced possibilities of graph layout, for example selection of location of selected nodes, division of a graph into sub-graphs or support of polygonal nodes. The solution describes chosen algorithms, which are being used in the resulting application. Specifically, Fruchterman-Reingold force oriented algorithm, algorithm Kamada-Kawai and an algorithm based on Meyer's self-organizing graphs.