69 research outputs found
Parallel Model Counting with CUDA: Algorithm Engineering for Efficient Hardware Utilization
Propositional model counting (MC) and its extensions as well as applications in the area of probabilistic reasoning have received renewed attention in recent years. As a result, also the need for quickly solving counting-based problems with automated solvers is critical for certain areas. In this paper, we present experiments evaluating various techniques in order to improve the performance of parallel model counting on general purpose graphics processing units (GPGPUs). Thereby, we mainly consider engineering efficient algorithms for model counting on GPGPUs that utilize the treewidth of a propositional formula by means of dynamic programming. The combination of our techniques results in the solver GPUSAT3, which is based on the programming framework Cuda that -compared to other frameworks- shows superior extensibility and driver support. When combining all findings of this work, we show that GPUSAT3 not only solves more instances of the recent Model Counting Competition 2020 (MCC 2020) than existing GPGPU-based systems, but also solves those significantly faster. A portfolio with one of the best solvers of MCC 2020 and GPUSAT3 solves 19% more instances than the former alone in less than half of the runtime
Counting Complexity for Reasoning in Abstract Argumentation
In this paper, we consider counting and projected model counting of
extensions in abstract argumentation for various semantics. When asking for
projected counts we are interested in counting the number of extensions of a
given argumentation framework while multiple extensions that are identical when
restricted to the projected arguments count as only one projected extension. We
establish classical complexity results and parameterized complexity results
when the problems are parameterized by treewidth of the undirected
argumentation graph. To obtain upper bounds for counting projected extensions,
we introduce novel algorithms that exploit small treewidth of the undirected
argumentation graph of the input instance by dynamic programming (DP). Our
algorithms run in time double or triple exponential in the treewidth depending
on the considered semantics. Finally, we take the exponential time hypothesis
(ETH) into account and establish lower bounds of bounded treewidth algorithms
for counting extensions and projected extension.Comment: Extended version of a paper published at AAAI-1
Structural Node Embeddings with Homomorphism Counts
Graph homomorphism counts, first explored by Lov\'asz in 1967, have recently
garnered interest as a powerful tool in graph-based machine learning. Grohe
(PODS 2020) proposed the theoretical foundations for using homomorphism counts
in machine learning on graph level as well as node level tasks. By their very
nature, these capture local structural information, which enables the creation
of robust structural embeddings. While a first approach for graph level tasks
has been made by Nguyen and Maehara (ICML 2020), we experimentally show the
effectiveness of homomorphism count based node embeddings. Enriched with node
labels, node weights, and edge weights, these offer an interpretable
representation of graph data, allowing for enhanced explainability of machine
learning models.
We propose a theoretical framework for isomorphism-invariant homomorphism
count based embeddings which lend themselves to a wide variety of downstream
tasks. Our approach capitalises on the efficient computability of graph
homomorphism counts for bounded treewidth graph classes, rendering it a
practical solution for real-world applications. We demonstrate their
expressivity through experiments on benchmark datasets. Although our results do
not match the accuracy of state-of-the-art neural architectures, they are
comparable to other advanced graph learning models. Remarkably, our approach
demarcates itself by ensuring explainability for each individual feature. By
integrating interpretable machine learning algorithms like SVMs or Random
Forests, we establish a seamless, end-to-end explainable pipeline. Our study
contributes to the advancement of graph-based techniques that offer both
performance and interpretability
Energy flow polynomials: A complete linear basis for jet substructure
We introduce the energy flow polynomials: a complete set of jet substructure
observables which form a discrete linear basis for all infrared- and
collinear-safe observables. Energy flow polynomials are multiparticle energy
correlators with specific angular structures that are a direct consequence of
infrared and collinear safety. We establish a powerful graph-theoretic
representation of the energy flow polynomials which allows us to design
efficient algorithms for their computation. Many common jet observables are
exact linear combinations of energy flow polynomials, and we demonstrate the
linear spanning nature of the energy flow basis by performing regression for
several common jet observables. Using linear classification with energy flow
polynomials, we achieve excellent performance on three representative jet
tagging problems: quark/gluon discrimination, boosted W tagging, and boosted
top tagging. The energy flow basis provides a systematic framework for complete
investigations of jet substructure using linear methods.Comment: 41+15 pages, 13 figures, 5 tables; v2: updated to match JHEP versio
Treewidth-aware Reductions of Normal ASP to SAT -- Is Normal ASP Harder than SAT after All?
Answer Set Programming (ASP) is a paradigm for modeling and solving problems
for knowledge representation and reasoning. There are plenty of results
dedicated to studying the hardness of (fragments of) ASP. So far, these studies
resulted in characterizations in terms of computational complexity as well as
in fine-grained insights presented in form of dichotomy-style results, lower
bounds when translating to other formalisms like propositional satisfiability
(SAT), and even detailed parameterized complexity landscapes. A generic
parameter in parameterized complexity originating from graph theory is the
so-called treewidth, which in a sense captures structural density of a program.
Recently, there was an increase in the number of treewidth-based solvers
related to SAT. While there are translations from (normal) ASP to SAT, no
reduction that preserves treewidth or at least keeps track of the treewidth
increase is known. In this paper we propose a novel reduction from normal ASP
to SAT that is aware of the treewidth, and guarantees that a slight increase of
treewidth is indeed sufficient. Further, we show a new result establishing
that, when considering treewidth, already the fragment of normal ASP is
slightly harder than SAT (under reasonable assumptions in computational
complexity). This also confirms that our reduction probably cannot be
significantly improved and that the slight increase of treewidth is
unavoidable. Finally, we present an empirical study of our novel reduction from
normal ASP to SAT, where we compare treewidth upper bounds that are obtained
via known decomposition heuristics. Overall, our reduction works better with
these heuristics than existing translations
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