88 research outputs found
Improved Bounds for Sampling Solutions of Random CNF Formulas
Let be a random -CNF formula on variables and clauses,
where each clause is a disjunction of literals chosen independently and
uniformly. Our goal is to sample an approximately uniform solution of
(or equivalently, approximate the partition function of ).
Let be the density. The previous best algorithm runs in time
for any [Galanis,
Goldberg, Guo, and Yang, SIAM J. Comput.'21]. Our result significantly improves
both bounds by providing an almost-linear time sampler for any
.
The density captures the \emph{average degree} in the random
formula. In the worst-case model with bounded \emph{maximum degree}, current
best efficient sampler works up to degree bound [He, Wang, and Yin,
FOCS'22 and SODA'23], which is, for the first time, superseded by its
average-case counterpart due to our bound. Our result is the first
progress towards establishing the intuition that the solvability of the
average-case model (random -CNF formula with bounded average degree) is
better than the worst-case model (standard -CNF formula with bounded maximal
degree) in terms of sampling solutions.Comment: 51 pages, all proofs added, and bounds slightly improve
Unveiling the Limits of Learned Local Search Heuristics: Are You the Mightiest of the Meek?
In recent years, combining neural networks with local search heuristics has
become popular in the field of combinatorial optimization. Despite its
considerable computational demands, this approach has exhibited promising
outcomes with minimal manual engineering. However, we have identified three
critical limitations in the empirical evaluation of these integration attempts.
Firstly, instances with moderate complexity and weak baselines pose a challenge
in accurately evaluating the effectiveness of learning-based approaches.
Secondly, the absence of an ablation study makes it difficult to quantify and
attribute improvements accurately to the deep learning architecture. Lastly,
the generalization of learned heuristics across diverse distributions remains
underexplored. In this study, we conduct a comprehensive investigation into
these identified limitations. Surprisingly, we demonstrate that a simple
learned heuristic based on Tabu Search surpasses state-of-the-art (SOTA)
learned heuristics in terms of performance and generalizability. Our findings
challenge prevailing assumptions and open up exciting avenues for future
research and innovation in combinatorial optimization
Computer Aided Verification
This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book
From algorithms to connectivity and back: finding a giant component in random k-SAT
We take an algorithmic approach to studying the solution space geometry of
relatively sparse random and bounded degree -CNFs for large . In the
course of doing so, we establish that with high probability, a random -CNF
with variables and clause density
has a giant component of solutions that are connected in a graph where
solutions are adjacent if they have Hamming distance and that a
similar result holds for bounded degree -CNFs at similar densities. We are
also able to deduce looseness results for random and bounded degree -CNFs in
a similar regime.
Although our main motivation was understanding the geometry of the solution
space, our methods have algorithmic implications. Towards that end, we
construct an idealized block dynamics that samples solutions from a random
-CNF with density . We show this
Markov chain can with high probability be implemented in polynomial time and by
leveraging spectral independence, we also observe that it mixes relatively
fast, giving a polynomial time algorithm to with high probability sample a
uniformly random solution to a random -CNF. Our work suggests that the
natural route to pinning down when a giant component exists is to develop
sharper algorithms for sampling solutions in random -CNFs.Comment: 41 pages, 1 figur
Tools and Algorithms for the Construction and Analysis of Systems
This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems
Fast sampling of satisfying assignments from random -SAT
We give a nearly linear-time algorithm to approximately sample satisfying
assignments in the random -SAT model when the density of the formula scales
exponentially with . The best previously known sampling algorithm for the
random -SAT model applies when the density of the formula is
less than and runs in time (Galanis,
Goldberg, Guo and Yang, SIAM J. Comput., 2021). Here is the number of
variables and is the number of clauses. Our algorithm achieves a
significantly faster running time of and samples satisfying
assignments up to density .
The main challenge in our setting is the presence of many variables with
unbounded degree, which causes significant correlations within the formula and
impedes the application of relevant Markov chain methods from the
bounded-degree setting (Feng, Guo, Yin and Zhang, J. ACM, 2021; Jain, Pham and
Vuong, 2021). Our main technical contribution is a bound of the
sum of influences in the -SAT model which turns out to be robust against the
presence of high-degree variables. This allows us to apply the spectral
independence framework and obtain fast mixing results of a uniform-block
Glauber dynamics on a carefully selected subset of the variables. The final key
ingredient in our method is to take advantage of the sparsity of
logarithmic-sized connected sets and the expansion properties of the random
formula, and establish relevant properties of the set of satisfying assignments
that enable the fast simulation of this Glauber dynamics.Comment: 47 page
Approximate Solutions to Abstract Argumentation Problems Using Graph Neural Networks
This thesis explores a new approach to approximating decision problems in abstract argumentation using Graph Convolutional Networks (GCN). It demonstrates that such an approach can reach well-balanced accuracy levels above 90 \% across a range of different decision problems, argumentation semantics, and benchmarks.
This thesis develops a new Deep Neural Network (DNN) architecture adapted from the classic GCN that better addresses the specific issues found in abstract argumentation. Likewise, it develops a training approach that produces superior results for abstract argumentation data sets by introducing structured randomness and dynamic adaptation to the training data.
Then, the thesis systematically applies this architecture to a large argumentation dataset across the main argumentation semantics used in the biannual ICCMA competition. It evaluates the performance of the model in a variety of different settings and across benchmarks, size bands, and model variants. The main models show good performance in the majority of cases, although there is some variation.
Having created the core model, the thesis goes on to explore additional extensions of the core work. This first focuses on combining the approximate approach with exact approaches using a deterministic algorithm and a SAT solver, showing an improvement by solving six additional hard instances relative to existing solvers.
Second, we explore a visualisation approach that can give new insights into argumentation graphs by applying a dimensionality reduction technique to weights from the trained GCN models, showing new insights in explaining benchmark performance.
Finally, we explore using the same basic architecture to address another problem that can be structured using abstract argumentation. In this case, we apply the approach to the prediction of misinformation in tweets and achieve good performance on a key dataset
Stochastic local search: a state-of-the-art review
The main objective of this paper is to provide a state-of-the-art review, analyze and discuss stochastic local search techniques used for solving hard combinatorial problems. It begins with a short introduction, motivation and some basic notation on combinatorial problems, search paradigms and other relevant features of searching techniques as needed for background. In the following a brief overview of the stochastic local search methods along with an analysis of the state-of-the-art stochastic local search algorithms is given. Finally, the last part of the paper present and discuss some of the most latest trends in application of stochastic local search algorithms in machine learning, data mining and some other areas of science and engineering. We conclude with a discussion on capabilities and limitations of stochastic local search algorithms
VLSI Design
This book provides some recent advances in design nanometer VLSI chips. The selected topics try to present some open problems and challenges with important topics ranging from design tools, new post-silicon devices, GPU-based parallel computing, emerging 3D integration, and antenna design. The book consists of two parts, with chapters such as: VLSI design for multi-sensor smart systems on a chip, Three-dimensional integrated circuits design for thousand-core processors, Parallel symbolic analysis of large analog circuits on GPU platforms, Algorithms for CAD tools VLSI design, A multilevel memetic algorithm for large SAT-encoded problems, etc
Automated Heuristic Generation By Intelligent Search
This thesis presents research that examines the effectiveness of several different program synthesis techniques when used to automate the creation of heuristics for a local search-based Boolean Satisfiability solver.
Previous research focused on the automated creation of heuristics has almost exclusively relied on evolutionary computation techniques such as genetic programming to achieve its goal. In wider program synthesis research, there are many other techniques which can automate the creation of programs. However, little effort has been expended on utilising these alternate techniques in automated heuristic creation.
In this thesis we analyse how three different program synthesis techniques perform when used to automatically create heuristics for our problem domain. These are genetic programming, exhaustive enumeration and a new technique called local search program synthesis. We show how genetic programming can create effective heuristics for our domain. By generating millions of heuristics, we demonstrate how exhaustive enumeration can create small, easily understandable and effective heuristics. Through an analysis of the memoized results from the exhaustive enumeration experiments, we then describe local search program synthesis, a program synthesis technique based on the minimum tree edit distance metric. Using the memoized results, we simulate local search program synthesis on our domain, and present evidence that suggests it is a viable technique for automatically creating heuristics.
We then define the necessary algorithms required to use local search program synthesis without any reliance on memoized data. Through experimentation, we show how local search program synthesis can be used to create effective heuristics for our domain. We then identify examples of heuristics created that are of higher quality than those produced from other program synthesis methods. At certain points in this thesis, we perform a more detailed analysis on some of the heuristics created. Through this analysis, we show that, on certain problem instances, several of the heuristics have better performance than some state-of-the-art, hand-crafted heuristics
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