Efficient Algorithms for the Problems of Enumerating Cuts by Non-decreasing Weights

Yeh, Li-Pu; Wang, Biing-Feng; Su, Hsin-Hao

doi:10.1007/s00453-009-9284-5

Cited by 19 publications

(20 citation statements)

References 29 publications

(46 reference statements)

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“…Within graph theory, the problem of determining the minimal cuts (see next section for formal definition) arises in many varieties and has been an active area of research for decades 44 − 50 with importance in a large number of applications. 51 − 55 We will combine previous graph theory work on minimal cuts 42 in a novel application: the automatic determination of minimum or near-minimum cut surface terminations for any given Miller face of any given zeolite.…”

Section: Methods: Theory Of Minimal Cuts In Graphsmentioning

confidence: 99%

Cutting Materials in Half: A Graph Theory Approach for Generating Crystal Surfaces and Its Prediction of 2D Zeolites

et al. 2018

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Scientific interest in two-dimensional (2D) materials, ranging from graphene and other single layer materials to atomically thin crystals, is quickly increasing for a large variety of technological applications. While in silico design approaches have made a large impact in the study of 3D crystals, algorithms designed to discover atomically thin 2D materials from their parent 3D materials are by comparison more sparse. We hypothesize that determining how to cut a 3D material in half (i.e., which Miller surface is formed) by severing a minimal number of bonds or a minimal amount of total bond energy per unit area can yield insight into preferred crystal faces. We answer this question by implementing a graph theory technique to mathematically formalize the enumeration of minimum cut surfaces of crystals. While the algorithm is generally applicable to different classes of materials, we focus on zeolitic materials due to their diverse structural topology and because 2D zeolites have promising catalytic and separation performance compared to their 3D counterparts. We report here a simple descriptor based only on structural information that predicts whether a zeolite is likely to be synthesizable in the 2D form and correctly identifies the expressed surface in known layered 2D zeolites. The discovery of this descriptor allows us to highlight other zeolites that may also be synthesized in the 2D form that have not been experimentally realized yet. Finally, our method is general since the mathematical formalism can be applied to find the minimum cut surfaces of other crystallographic materials such as metal–organic frameworks, covalent-organic frameworks, zeolitic-imidazolate frameworks, metal oxides, etc.

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Section: Methods: Theory Of Minimal Cuts In Graphsmentioning

confidence: 99%

Cutting Materials in Half: A Graph Theory Approach for Generating Crystal Surfaces and Its Prediction of 2D Zeolites

et al. 2018

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“…• The complexity of the algorithms of k-cutset increases with k because they are enumeration algorithms [14].…”

Section: Examplementioning

confidence: 99%

Integration of Structural Constraints into TSP Models

Isoart

Régin

2019

Lecture Notes in Computer Science

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Several models based on constraint programming have been proposed to solve the traveling salesman problem (TSP). The most efficient ones, such as the weighted circuit constraint (WCC), mainly rely on the Lagrangian relaxation of the TSP, based on the search for spanning tree or more precisely "1-tree". The weakness of these approaches is that they do not include enough structural constraints and are based almost exclusively on edge costs. The purpose of this paper is to correct this drawback by introducing the Hamiltonian cycle constraint associated with propagators. We propose some properties preventing the existence of a Hamiltonian cycle in a graph or, conversely, properties requiring that certain edges be in the TSP solution set. Notably, we design a propagator based on the research of k-cutsets. The combination of this constraint with the WCC constraint allows us to obtain, for the resolution of the TSP, gains of an order of magnitude for the number of backtracks as well as a strong reduction of the computation time.

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“…To feed non-crossing cuts to PM-Tree, we can use method in [32] to generate all minimal cuts. But, the minimal cut size is so large that the index has a large cost.…”

Section: Property 1 the Structure Of Probabilistic Matching Tree Is mentioning

confidence: 99%

“…Thus we assign a weight ln(1 − P r(e)) to each edge e in g c . There are many efficient algorithms that can compute a minimum cut in a deterministic graph [32].…”

Section: Property 1 the Structure Of Probabilistic Matching Tree Is mentioning

confidence: 99%

Pattern Match Query in a Large Uncertain Graph

Yuan

Wang

Chen

2014

Proceedings of the 23rd ACM International Conference on Conference on Information and Knowledge Management

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Many studies have been conducted on seeking an efficient solution for pattern matching over graphs. This interest is largely due to large number of applications in many fields, which require efficient solutions for pattern matching, including protein complex prediction, social network analysis and structural pattern recognition. However, in many real applications, the graph data are often noisy, incomplete, and inaccurate. In other words, there exist many uncertain graphs. Therefore, in this paper, we study pattern matching in a large uncertain graph. Specifically, we want to retrieve all qualified matches of a query pattern in the uncertain graph. Though pattern matching over an uncertain graph is NP-hard, we employ a filtering-and-verification framework to speed up the search. In the filtering phase, we propose a probabilistic matching tree, PM-tree, based on match cuts obtained by a cut selection process. Based on PM-tree, we devise a collective pruning strategy to prune a large number of unqualified matches. During the verification phase, we develop an efficient sampling algorithm to validate the remaining candidates. Extensive experimental results demonstrate the effectiveness and efficiency of the proposed algorithms.

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Efficient Algorithms for the Problems of Enumerating Cuts by Non-decreasing Weights

Cited by 19 publications

References 29 publications

Cutting Materials in Half: A Graph Theory Approach for Generating Crystal Surfaces and Its Prediction of 2D Zeolites

Cutting Materials in Half: A Graph Theory Approach for Generating Crystal Surfaces and Its Prediction of 2D Zeolites

Integration of Structural Constraints into TSP Models

Pattern Match Query in a Large Uncertain Graph

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