Pub Date : 2021-03-18DOI: 10.4230/LIPIcs.SEA.2021.18
V. Buchhold, D. Wagner
Customizable contraction hierarchies are one of the most popular route planning frameworks in practice, due to their simplicity and versatility. In this work, we present a novel algorithm for finding k-nearest neighbors in customizable contraction hierarchies by systematically exploring the associated separator decomposition tree. Compared to previous bucket-based approaches, our algorithm requires much less target-dependent preprocessing effort. Moreover, we use our novel approach in two concrete applications. The first application are online k-closest point-of-interest queries, where the points of interest are only revealed at query time. We achieve query times of about 25 milliseconds on a continental road network, which is fast enough for interactive systems. The second application is travel demand generation. We show how to accelerate a recently introduced travel demand generator by a factor of more than 50 using our novel nearest-neighbor algorithm.
{"title":"Nearest-Neighbor Queries in Customizable Contraction Hierarchies and Applications","authors":"V. Buchhold, D. Wagner","doi":"10.4230/LIPIcs.SEA.2021.18","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2021.18","url":null,"abstract":"Customizable contraction hierarchies are one of the most popular route planning frameworks in practice, due to their simplicity and versatility. In this work, we present a novel algorithm for finding k-nearest neighbors in customizable contraction hierarchies by systematically exploring the associated separator decomposition tree. Compared to previous bucket-based approaches, our algorithm requires much less target-dependent preprocessing effort. Moreover, we use our novel approach in two concrete applications. The first application are online k-closest point-of-interest queries, where the points of interest are only revealed at query time. We achieve query times of about 25 milliseconds on a continental road network, which is fast enough for interactive systems. The second application is travel demand generation. We show how to accelerate a recently introduced travel demand generator by a factor of more than 50 using our novel nearest-neighbor algorithm.","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"145 1","pages":"18:1-18:18"},"PeriodicalIF":0.0,"publicationDate":"2021-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76671208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-02DOI: 10.4230/LIPIcs.SEA.2021.17
Demian Hespe, S. Lamm, C. Schorr
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. In recent years, some of the most successful algorithms for solving this problem are based on the branch-and-bound or branch-and-reduce paradigms. In particular, branch-and-reduce algorithms, which combine branch-and-bound with reduction rules, have been able to achieve substantial results, solving many previously infeasible real-world instances. These results were to a large part achieved by developing new, more practical reduction rules. However, other components that have been shown to have a significant impact on the performance of these algorithms have not received as much attention. One of these is the branching strategy, which determines what vertex is included or excluded in a potential solution. Even now, the most commonly used strategy selects vertices solely based on their degree and does not take into account other factors that contribute to the performance of the algorithm. In this work, we develop and evaluate several novel branching strategies for both branch-andbound and branch-and-reduce algorithms. Our strategies are based on one of two approaches which are motivated by existing research. They either (1) aim to decompose the graph into two or more connected components which can then be solved independently, or (2) try to remove vertices that hinder the application of a reduction rule which can lead to smaller graphs. Our experimental evaluation on a large set of real-world instances indicates that our strategies are able to improve the performance of the state-of-the-art branch-and-reduce algorithm by Akiba and Iwata. To be more specific, our reduction-based packing branching rule is able to outperform the default branching strategy of selecting a vertex of highest degree on 65% of all instances tested. Furthermore, our decomposition-based strategy based on edge cuts is able to achieve a speedup of 2.29 on sparse networks (1.22 on all instances). 2012 ACM Subject Classification Mathematics of computing → Graph algorithms; Theory of computation → Branch-and-bound; Mathematics of computing → Combinatorial optimization
{"title":"Targeted Branching for the Maximum Independent Set Problem","authors":"Demian Hespe, S. Lamm, C. Schorr","doi":"10.4230/LIPIcs.SEA.2021.17","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2021.17","url":null,"abstract":"Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. In recent years, some of the most successful algorithms for solving this problem are based on the branch-and-bound or branch-and-reduce paradigms. In particular, branch-and-reduce algorithms, which combine branch-and-bound with reduction rules, have been able to achieve substantial results, solving many previously infeasible real-world instances. These results were to a large part achieved by developing new, more practical reduction rules. However, other components that have been shown to have a significant impact on the performance of these algorithms have not received as much attention. One of these is the branching strategy, which determines what vertex is included or excluded in a potential solution. Even now, the most commonly used strategy selects vertices solely based on their degree and does not take into account other factors that contribute to the performance of the algorithm. In this work, we develop and evaluate several novel branching strategies for both branch-andbound and branch-and-reduce algorithms. Our strategies are based on one of two approaches which are motivated by existing research. They either (1) aim to decompose the graph into two or more connected components which can then be solved independently, or (2) try to remove vertices that hinder the application of a reduction rule which can lead to smaller graphs. Our experimental evaluation on a large set of real-world instances indicates that our strategies are able to improve the performance of the state-of-the-art branch-and-reduce algorithm by Akiba and Iwata. To be more specific, our reduction-based packing branching rule is able to outperform the default branching strategy of selecting a vertex of highest degree on 65% of all instances tested. Furthermore, our decomposition-based strategy based on edge cuts is able to achieve a speedup of 2.29 on sparse networks (1.22 on all instances). 2012 ACM Subject Classification Mathematics of computing → Graph algorithms; Theory of computation → Branch-and-bound; Mathematics of computing → Combinatorial optimization","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"2 1","pages":"17:1-17:21"},"PeriodicalIF":0.0,"publicationDate":"2021-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89573755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-02DOI: 10.4230/LIPIcs.SEA.2021.8
Tobias Heuer, Nikolai Maas, Sebastian Schlag
The balanced hypergraph partitioning problem (HGP) is to partition the vertex set of a hypergraph into k disjoint blocks of bounded weight, while minimizing an objective function defined on the hyperedges. Whereas real-world applications often use vertex and edge weights to accurately model the underlying problem, the HGP research community commonly works with unweighted instances. In this paper, we argue that, in the presence of vertex weights, current balance constraint definitions either yield infeasible partitioning problems or allow unnecessarily large imbalances and propose a new definition that overcomes these problems. We show that state-of-the-art hypergraph partitioners often struggle considerably with weighted instances and tight balance constraints (even with our new balance definition). Thus, we present a recursive-bipartitioning technique that is able to reliably compute balanced (and hence feasible) solutions. The proposed method balances the partition by pre-assigning a small subset of the heaviest vertices to the two blocks of each bipartition (using an algorithm originally developed for the job scheduling problem) and optimizes the actual partitioning objective on the remaining vertices. We integrate our algorithm into the multilevel hypergraph partitioner KaHyPar and show that our approach is able to compute balanced partitions of high quality on a diverse set of benchmark instances.
{"title":"Multilevel Hypergraph Partitioning with Vertex Weights Revisited","authors":"Tobias Heuer, Nikolai Maas, Sebastian Schlag","doi":"10.4230/LIPIcs.SEA.2021.8","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2021.8","url":null,"abstract":"The balanced hypergraph partitioning problem (HGP) is to partition the vertex set of a hypergraph into k disjoint blocks of bounded weight, while minimizing an objective function defined on the hyperedges. Whereas real-world applications often use vertex and edge weights to accurately model the underlying problem, the HGP research community commonly works with unweighted instances. In this paper, we argue that, in the presence of vertex weights, current balance constraint definitions either yield infeasible partitioning problems or allow unnecessarily large imbalances and propose a new definition that overcomes these problems. We show that state-of-the-art hypergraph partitioners often struggle considerably with weighted instances and tight balance constraints (even with our new balance definition). Thus, we present a recursive-bipartitioning technique that is able to reliably compute balanced (and hence feasible) solutions. The proposed method balances the partition by pre-assigning a small subset of the heaviest vertices to the two blocks of each bipartition (using an algorithm originally developed for the job scheduling problem) and optimizes the actual partitioning objective on the remaining vertices. We integrate our algorithm into the multilevel hypergraph partitioner KaHyPar and show that our approach is able to compute balanced partitions of high quality on a diverse set of benchmark instances.","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"11 1","pages":"8:1-8:20"},"PeriodicalIF":0.0,"publicationDate":"2021-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81537579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4230/LIPIcs.SEA.2021.22
Thomas Bläsius, T. Friedrich, Maximilian Katzmann
Force-directed drawing algorithms are the most commonly used approach to visualize networks. While they are usually very robust, the performance of Euclidean spring embedders decreases if the graph exhibits the high level of heterogeneity that typically occurs in scale-free real-world networks. As heterogeneity naturally emerges from hyperbolic geometry (in fact, scale-free networks are often perceived to have an underlying hyperbolic geometry), it is natural to embed them into the hyperbolic plane instead. Previous techniques that produce hyperbolic embeddings usually make assumptions about the given network, which (if not met) impairs the quality of the embedding. It is still an open problem to adapt force-directed embedding algorithms to make use of the heterogeneity of the hyperbolic plane, while also preserving their robustness. We identify fundamental differences between the behavior of spring embedders in Euclidean and hyperbolic space, and adapt the technique to take advantage of the heterogeneity of the hyperbolic plane. 2012 ACM Subject Classification Theory of computation → Random projections and metric embeddings
{"title":"Force-Directed Embedding of Scale-Free Networks in the Hyperbolic Plane","authors":"Thomas Bläsius, T. Friedrich, Maximilian Katzmann","doi":"10.4230/LIPIcs.SEA.2021.22","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2021.22","url":null,"abstract":"Force-directed drawing algorithms are the most commonly used approach to visualize networks. While they are usually very robust, the performance of Euclidean spring embedders decreases if the graph exhibits the high level of heterogeneity that typically occurs in scale-free real-world networks. As heterogeneity naturally emerges from hyperbolic geometry (in fact, scale-free networks are often perceived to have an underlying hyperbolic geometry), it is natural to embed them into the hyperbolic plane instead. Previous techniques that produce hyperbolic embeddings usually make assumptions about the given network, which (if not met) impairs the quality of the embedding. It is still an open problem to adapt force-directed embedding algorithms to make use of the heterogeneity of the hyperbolic plane, while also preserving their robustness. We identify fundamental differences between the behavior of spring embedders in Euclidean and hyperbolic space, and adapt the technique to take advantage of the heterogeneity of the hyperbolic plane. 2012 ACM Subject Classification Theory of computation → Random projections and metric embeddings","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"57 1","pages":"22:1-22:18"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90996138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4230/LIPIcs.SEA.2021.20
L. Georgiadis, K. Giannis, G. Italiano, E. Kosinas
We consider two problems regarding the computation of connectivity cuts in undirected graphs, namely identifying vertex-edge cut-pairs and identifying 2-edge cuts, and present an experimental study of efficient algorithms for their computation. In the first problem, we are given a biconnected graph G and our goal is to find all vertices v such that G v is not 2-edge-connected, while in the second problem, we are given a 2-edge-connected graph G and our goal is to find all edges e such that G e is not 2-edge-connected. These problems are motivated by the notion of twinless strong connectivity in directed graphs but are also of independent interest. Moreover, the computation of 2-edge cuts is a main step in algorithms that compute the 3-edge-connected components of a graph. In this paper, we present streamlined versions of two recent linear-time algorithms of Georgiadis and Kosinas that compute all vertex-edge cut-pairs and all 2-edge cuts, respectively. We compare the empirical performance of our vertex-edge cut-pairs algorithm with an alternative linear-time method that exploits the structure of the triconnected components of G . Also, we compare the empirical performance of our 2-edge cuts algorithm with the algorithm of Tsin, which was reported to be the fastest one among the previously existing for this problem. To that end, we conduct a thorough experimental study to highlight the merits and weaknesses of each technique.
{"title":"Computing Vertex-Edge Cut-Pairs and 2-Edge Cuts in Practice","authors":"L. Georgiadis, K. Giannis, G. Italiano, E. Kosinas","doi":"10.4230/LIPIcs.SEA.2021.20","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2021.20","url":null,"abstract":"We consider two problems regarding the computation of connectivity cuts in undirected graphs, namely identifying vertex-edge cut-pairs and identifying 2-edge cuts, and present an experimental study of efficient algorithms for their computation. In the first problem, we are given a biconnected graph G and our goal is to find all vertices v such that G v is not 2-edge-connected, while in the second problem, we are given a 2-edge-connected graph G and our goal is to find all edges e such that G e is not 2-edge-connected. These problems are motivated by the notion of twinless strong connectivity in directed graphs but are also of independent interest. Moreover, the computation of 2-edge cuts is a main step in algorithms that compute the 3-edge-connected components of a graph. In this paper, we present streamlined versions of two recent linear-time algorithms of Georgiadis and Kosinas that compute all vertex-edge cut-pairs and all 2-edge cuts, respectively. We compare the empirical performance of our vertex-edge cut-pairs algorithm with an alternative linear-time method that exploits the structure of the triconnected components of G . Also, we compare the empirical performance of our 2-edge cuts algorithm with the algorithm of Tsin, which was reported to be the fastest one among the previously existing for this problem. To that end, we conduct a thorough experimental study to highlight the merits and weaknesses of each technique.","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"277 1","pages":"20:1-20:19"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77715234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4230/LIPIcs.SEA.2021.3
Mark Blacher, Joachim Giesen, L. Kuehne
Modern CPUs provide single instruction-multiple data (SIMD) instructions. SIMD instructions process several elements of a primitive data type simultaneously in fixed-size vectors. Classical sorting algorithms are not directly expressible in SIMD instructions. Accelerating sorting algorithms with SIMD instruction is therefore a creative endeavor. A promising approach for sorting with SIMD instructions is to use sorting networks for small arrays and Quicksort for large arrays. In this paper we improve vectorization techniques for sorting networks and Quicksort. In particular, we show how to use the full capacity of vector registers in sorting networks and how to make vectorized Quicksort robust with respect to different key distributions. To demonstrate the performance of our techniques we implement an in-place hybrid sorting algorithm for the data type int with AVX2 intrinsics. Our implementation is at least 30% faster than state-of-the-art high-performance sorting alternatives. 2012 ACM Subject Classification Theory of computation → Sorting and searching
{"title":"Fast and Robust Vectorized In-Place Sorting of Primitive Types","authors":"Mark Blacher, Joachim Giesen, L. Kuehne","doi":"10.4230/LIPIcs.SEA.2021.3","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2021.3","url":null,"abstract":"Modern CPUs provide single instruction-multiple data (SIMD) instructions. SIMD instructions process several elements of a primitive data type simultaneously in fixed-size vectors. Classical sorting algorithms are not directly expressible in SIMD instructions. Accelerating sorting algorithms with SIMD instruction is therefore a creative endeavor. A promising approach for sorting with SIMD instructions is to use sorting networks for small arrays and Quicksort for large arrays. In this paper we improve vectorization techniques for sorting networks and Quicksort. In particular, we show how to use the full capacity of vector registers in sorting networks and how to make vectorized Quicksort robust with respect to different key distributions. To demonstrate the performance of our techniques we implement an in-place hybrid sorting algorithm for the data type int with AVX2 intrinsics. Our implementation is at least 30% faster than state-of-the-art high-performance sorting alternatives. 2012 ACM Subject Classification Theory of computation → Sorting and searching","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"1 1","pages":"3:1-3:16"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91314983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4230/LIPIcs.SEA.2021.5
Emmanuel Arrighi, Mateus de Oliveira Oliveira
In the Steiner tree problem, the input consists of an edge-weighted graph G together with a set S of terminal vertices. The goal is to find a minimum weight tree in G that spans all terminals. This fundamental NP-hard problem has direct applications in many subfields of combinatorial optimization, such as planning, scheduling, etc. In this work we introduce a new heuristic for the Steiner tree problem, based on a simple routine for improving the cost of sub-optimal Steiner trees: first, the sub-optimal tree is split into three connected components, and then these components are reconnected by using an algorithm that computes an optimal Steiner tree with 3-terminals (the roots of the three components). We have implemented our heuristic into a solver and compared it with several state-of-the-art solvers on well-known data sets. Our solver performs very well across all the data sets, and outperforms most of the other benchmarked solvers on very large graphs, which have been either obtained from real-world applications or from randomly generated data sets. 2012 ACM Subject Classification Theory of computation → Theory of randomized search heuristics
{"title":"Three Is Enough for Steiner Trees","authors":"Emmanuel Arrighi, Mateus de Oliveira Oliveira","doi":"10.4230/LIPIcs.SEA.2021.5","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2021.5","url":null,"abstract":"In the Steiner tree problem, the input consists of an edge-weighted graph G together with a set S of terminal vertices. The goal is to find a minimum weight tree in G that spans all terminals. This fundamental NP-hard problem has direct applications in many subfields of combinatorial optimization, such as planning, scheduling, etc. In this work we introduce a new heuristic for the Steiner tree problem, based on a simple routine for improving the cost of sub-optimal Steiner trees: first, the sub-optimal tree is split into three connected components, and then these components are reconnected by using an algorithm that computes an optimal Steiner tree with 3-terminals (the roots of the three components). We have implemented our heuristic into a solver and compared it with several state-of-the-art solvers on well-known data sets. Our solver performs very well across all the data sets, and outperforms most of the other benchmarked solvers on very large graphs, which have been either obtained from real-world applications or from randomly generated data sets. 2012 ACM Subject Classification Theory of computation → Theory of randomized search heuristics","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"16 1","pages":"5:1-5:15"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84815244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4230/LIPIcs.SEA.2021.9
Ernst Althaus, Dan Schnurbusch, Julian Wüschner, Sarah Ziegler
We revisit the exact algorithm to compute the treewidth of a graph of Tamaki and present it in a way that facilitates improvements. The so-called I-blocks and O-blocks enumerated by the algorithm are interpreted as subtrees of a tree-decomposition that is constructed. This simplifies the proof of correctness and allows to discard subtrees from the enumeration by some simple observations. In our experiments, we show that one of these modifications in particular reduces the number of enumerated objects considerably. 2012 ACM Subject Classification Theory of computation → Fixed parameter tractability
{"title":"On Tamaki's Algorithm to Compute Treewidths","authors":"Ernst Althaus, Dan Schnurbusch, Julian Wüschner, Sarah Ziegler","doi":"10.4230/LIPIcs.SEA.2021.9","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2021.9","url":null,"abstract":"We revisit the exact algorithm to compute the treewidth of a graph of Tamaki and present it in a way that facilitates improvements. The so-called I-blocks and O-blocks enumerated by the algorithm are interpreted as subtrees of a tree-decomposition that is constructed. This simplifies the proof of correctness and allows to discard subtrees from the enumeration by some simple observations. In our experiments, we show that one of these modifications in particular reduces the number of enumerated objects considerably. 2012 ACM Subject Classification Theory of computation → Fixed parameter tractability","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"1 1","pages":"9:1-9:18"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81295074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4230/LIPIcs.SEA.2021.19
Coline Gianfrotta, Vladimir Reinharz, D. Barth, A. Denise
This article proposes to use an RNA graph similarity metric, based on the MCES resolution problem, to compare the occurrences of specific complex motifs in RNA graphs, according to their context represented as subgraph. We rely on a new modeling by graphs of these contexts, at two different levels of granularity, and obtain a classification of these graphs, which is consistent with the RNA 3D structure. RNA many non-translational functions, as a ribozyme, riboswitch, or ribosome, require complex structures. Those are composed of a rigid skeleton, a set of canonical interactions called the secondary structure. Decades of experimental and theoretical work have produced precise thermodynamic parameters and efficient algorithms to predict, from sequence, the secondary structure of RNA molecules. On top of the skeleton, the nucleotides form an intricate network of interactions that are not captured by present thermodynamic models. This network has been shown to be composed of modular motifs, that are linked to function, and have been leveraged for better prediction and design. A peculiar subclass of complex structural motifs are those connecting RNA regions far away in the secondary structure. They are crucial to predict since they determine the global shape of the molecule, therefore important for the function. In this paper, we show by using our graph approach that the context is important for the formation of conserved complex structural motifs. We furthermore show that a natural classification of structural variants of the motifs emerges from their context. We explore the cases of three known motif families and we exhibit their experimentally emerging classification. 2012 ACM Subject Classification Applied computing → Molecular structural biology
{"title":"A Graph-Based Similarity Approach to Classify Recurrent Complex Motifs from Their Context in RNA Structures","authors":"Coline Gianfrotta, Vladimir Reinharz, D. Barth, A. Denise","doi":"10.4230/LIPIcs.SEA.2021.19","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2021.19","url":null,"abstract":"This article proposes to use an RNA graph similarity metric, based on the MCES resolution problem, to compare the occurrences of specific complex motifs in RNA graphs, according to their context represented as subgraph. We rely on a new modeling by graphs of these contexts, at two different levels of granularity, and obtain a classification of these graphs, which is consistent with the RNA 3D structure. RNA many non-translational functions, as a ribozyme, riboswitch, or ribosome, require complex structures. Those are composed of a rigid skeleton, a set of canonical interactions called the secondary structure. Decades of experimental and theoretical work have produced precise thermodynamic parameters and efficient algorithms to predict, from sequence, the secondary structure of RNA molecules. On top of the skeleton, the nucleotides form an intricate network of interactions that are not captured by present thermodynamic models. This network has been shown to be composed of modular motifs, that are linked to function, and have been leveraged for better prediction and design. A peculiar subclass of complex structural motifs are those connecting RNA regions far away in the secondary structure. They are crucial to predict since they determine the global shape of the molecule, therefore important for the function. In this paper, we show by using our graph approach that the context is important for the formation of conserved complex structural motifs. We furthermore show that a natural classification of structural variants of the motifs emerges from their context. We explore the cases of three known motif families and we exhibit their experimentally emerging classification. 2012 ACM Subject Classification Applied computing → Molecular structural biology","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"86 1","pages":"19:1-19:18"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83387275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4230/LIPIcs.SEA.2021.15
F. Cazals, Bernard Delmas, Timothée O'Donnell
The center of mass of a point set lying on a manifold generalizes the celebrated Euclidean centroid, and is ubiquitous in statistical analysis in non Euclidean spaces. In this work, we give a complete characterization of the weighted p-mean of a finite set of angular values on S1, based on a decomposition of S1 such that the functional of interest has at most one local minimum per cell. This characterization is used to show that the problem is decidable for rational angular values –a consequence of Lindemann’s theorem on the transcendence of π, and to develop an effective algorithm parameterized by exact predicates. A robust implementation of this algorithm based on multi-precision interval arithmetic is also presented, and is shown to be effective for large values of n and p. We use it as building block to implement the k-means and k-means++ clustering algorithms on the flat torus, with applications to clustering protein molecular conformations. These algorithms are available in the Structural Bioinformatics Library (http://sbl.inria.fr). Our derivations are of interest in two respects. First, efficient p-mean calculations are relevant to develop principal components analysis on the flat torus encoding angular spaces–a particularly important case to describe molecular conformations. Second, our two-stage strategy stresses the interest of combinatorial methods for p-means, also emphasizing the role of numerical issues. 2012 ACM Subject Classification Theory of computation → Computational geometry
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