Pub Date : 2022-05-03DOI: 10.48550/arXiv.2205.01576
Sara Giuliani, Giuseppe Romana, Massimiliano Rossi
In recent years, pangenomes received increasing attention from the scientific community for their ability to incorporate population variation information and alleviate reference genome bias. Maximal Exact Matches ( MEMs ) and Maximal Unique Matches ( MUMs ) have proven themselves to be useful in multiple bioinformatic contexts, for example short-read alignment and multiple-genome alignment. However, standard techniques using suffix trees and FM-indexes do not scale to a pangenomic level. Recently, Gagie et al. [JACM 20] introduced the r -index that is a Burrows-Wheeler Transform ( BWT )-based index able to handle hundreds of human genomes. Later, Rossi et al. [JCB 22] enabled the computation of MEMs using the r -index, and Boucher et al. [DCC 21] showed how to compute them in a streaming fashion. In this paper, we show how to augment Boucher et al.’s approach to enable the computation of MUMs on the r -index, while preserving the space and time bounds. We add additional O ( r ) samples of the longest common prefix ( LCP ) array, where r is the number of equal-letter runs of the BWT , that permits the computation of the second longest match of the pattern suffix with respect to the input text, which in turn allows the computation of candidate MUMs . We implemented a proof-of-concept of our approach, that we call mum-phinder , and tested on real-world datasets. We compared our approach with competing methods that are able to compute MUMs . We observe that our method is up to 8 times smaller, while up to 19 times slower when the dataset is not highly repetitive, while on highly repetitive data, our method is up to 6.5 times slower and uses up to 25 times less memory.
{"title":"Computing Maximal Unique Matches with the r-index","authors":"Sara Giuliani, Giuseppe Romana, Massimiliano Rossi","doi":"10.48550/arXiv.2205.01576","DOIUrl":"https://doi.org/10.48550/arXiv.2205.01576","url":null,"abstract":"In recent years, pangenomes received increasing attention from the scientific community for their ability to incorporate population variation information and alleviate reference genome bias. Maximal Exact Matches ( MEMs ) and Maximal Unique Matches ( MUMs ) have proven themselves to be useful in multiple bioinformatic contexts, for example short-read alignment and multiple-genome alignment. However, standard techniques using suffix trees and FM-indexes do not scale to a pangenomic level. Recently, Gagie et al. [JACM 20] introduced the r -index that is a Burrows-Wheeler Transform ( BWT )-based index able to handle hundreds of human genomes. Later, Rossi et al. [JCB 22] enabled the computation of MEMs using the r -index, and Boucher et al. [DCC 21] showed how to compute them in a streaming fashion. In this paper, we show how to augment Boucher et al.’s approach to enable the computation of MUMs on the r -index, while preserving the space and time bounds. We add additional O ( r ) samples of the longest common prefix ( LCP ) array, where r is the number of equal-letter runs of the BWT , that permits the computation of the second longest match of the pattern suffix with respect to the input text, which in turn allows the computation of candidate MUMs . We implemented a proof-of-concept of our approach, that we call mum-phinder , and tested on real-world datasets. We compared our approach with competing methods that are able to compute MUMs . We observe that our method is up to 8 times smaller, while up to 19 times slower when the dataset is not highly repetitive, while on highly repetitive data, our method is up to 6.5 times slower and uses up to 25 times less memory.","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"35 1","pages":"22:1-22:16"},"PeriodicalIF":0.0,"publicationDate":"2022-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73530300","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 : 2022-01-05DOI: 10.4230/LIPIcs.SEA.2022.5
Lars Gottesbüren, Tobias Heuer, P. Sanders
We present a shared-memory parallelization of flow-based refinement , which is considered the most powerful iterative improvement technique for hypergraph partitioning at the moment. Flow-based refinement works on bipartitions, so current sequential partitioners schedule it on different block pairs to improve k -way partitions. We investigate two different sources of parallelism: a parallel scheduling scheme and a parallel maximum flow algorithm based on the well-known push-relabel algorithm. In addition to thoroughly engineered implementations, we propose several optimizations that substantially accelerate the algorithm in practice, enabling the use on extremely large hypergraphs (up to 1 billion pins). We integrate our approach in the state-of-the-art parallel multilevel framework Mt-KaHyPar and conduct extensive experiments on a benchmark set of more than 500 real-world hypergraphs, to show that the partition quality of our code is on par with the highest quality sequential code ( KaHyPar ), while being an order of magnitude faster with 10 threads. .
{"title":"Parallel Flow-Based Hypergraph Partitioning","authors":"Lars Gottesbüren, Tobias Heuer, P. Sanders","doi":"10.4230/LIPIcs.SEA.2022.5","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2022.5","url":null,"abstract":"We present a shared-memory parallelization of flow-based refinement , which is considered the most powerful iterative improvement technique for hypergraph partitioning at the moment. Flow-based refinement works on bipartitions, so current sequential partitioners schedule it on different block pairs to improve k -way partitions. We investigate two different sources of parallelism: a parallel scheduling scheme and a parallel maximum flow algorithm based on the well-known push-relabel algorithm. In addition to thoroughly engineered implementations, we propose several optimizations that substantially accelerate the algorithm in practice, enabling the use on extremely large hypergraphs (up to 1 billion pins). We integrate our approach in the state-of-the-art parallel multilevel framework Mt-KaHyPar and conduct extensive experiments on a benchmark set of more than 500 real-world hypergraphs, to show that the partition quality of our code is on par with the highest quality sequential code ( KaHyPar ), while being an order of magnitude faster with 10 threads. .","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"48 1","pages":"5:1-5:21"},"PeriodicalIF":0.0,"publicationDate":"2022-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85796554","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 : 2022-01-01DOI: 10.4230/LIPIcs.SEA.2022.24
A. Gupte, A. Koster, Sascha Kuhnke
We present an iterative algorithm to compute feasible solutions in reasonable running time to quadratically constrained quadratic programs (QCQPs), which form a challenging class of nonconvex continuous optimization. This algorithm is based on a mixed-integer linear program (MILP) which is a restriction of the original QCQP obtained by discretizing all quadratic terms. In each iteration, this MILP restriction is solved to get a feasible QCQP solution. Since the quality of this solution heavily depends on the chosen discretization of the MILP, we iteratively adapt the discretization values based on the MILP solution of the previous iteration. To maintain a reasonable problem size in each iteration of the algorithm, the discretization sizes are fixed at predefined values. Although our algorithm did not always yield good feasible solutions on arbitrary QCQP instances, an extensive computational study on almost 1300 test instances of two different problem classes – box-constrained quadratic programs with complementarity constraints and disjoint bilinear programs, demonstrates the effectiveness of our approach. We compare the quality of our solutions against those from heuristics and local optimization algorithms in two state-of-the-art commercial solvers and observe that on one instance class we clearly outperform the other methods whereas on the other class we obtain competitive results.
{"title":"An Adaptive Refinement Algorithm for Discretizations of Nonconvex QCQP","authors":"A. Gupte, A. Koster, Sascha Kuhnke","doi":"10.4230/LIPIcs.SEA.2022.24","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2022.24","url":null,"abstract":"We present an iterative algorithm to compute feasible solutions in reasonable running time to quadratically constrained quadratic programs (QCQPs), which form a challenging class of nonconvex continuous optimization. This algorithm is based on a mixed-integer linear program (MILP) which is a restriction of the original QCQP obtained by discretizing all quadratic terms. In each iteration, this MILP restriction is solved to get a feasible QCQP solution. Since the quality of this solution heavily depends on the chosen discretization of the MILP, we iteratively adapt the discretization values based on the MILP solution of the previous iteration. To maintain a reasonable problem size in each iteration of the algorithm, the discretization sizes are fixed at predefined values. Although our algorithm did not always yield good feasible solutions on arbitrary QCQP instances, an extensive computational study on almost 1300 test instances of two different problem classes – box-constrained quadratic programs with complementarity constraints and disjoint bilinear programs, demonstrates the effectiveness of our approach. We compare the quality of our solutions against those from heuristics and local optimization algorithms in two state-of-the-art commercial solvers and observe that on one instance class we clearly outperform the other methods whereas on the other class we obtain competitive results.","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"30 1","pages":"24:1-24:14"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74991349","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 : 2022-01-01DOI: 10.4230/LIPIcs.SEA.2022.21
Leo Liberti, Benedetto Manca, Pierre-Louis Poirion
The use of random projections in mathematical programming allows standard solution algorithms to solve instances of much larger sizes, at least approximately. Approximation results have been derived in the relevant literature for many specific problems, as well as for several mathematical programming subclasses. Despite the theoretical developments, it is not always clear that random projections are actually useful in solving mathematical programs in practice. In this paper we provide a computational assessment of the application of random projections to linear programming.
{"title":"Practical Performance of Random Projections in Linear Programming","authors":"Leo Liberti, Benedetto Manca, Pierre-Louis Poirion","doi":"10.4230/LIPIcs.SEA.2022.21","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2022.21","url":null,"abstract":"The use of random projections in mathematical programming allows standard solution algorithms to solve instances of much larger sizes, at least approximately. Approximation results have been derived in the relevant literature for many specific problems, as well as for several mathematical programming subclasses. Despite the theoretical developments, it is not always clear that random projections are actually useful in solving mathematical programs in practice. In this paper we provide a computational assessment of the application of random projections to linear programming.","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"4 9","pages":"21:1-21:15"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91442412","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 : 2022-01-01DOI: 10.4230/LIPIcs.SEA.2022.20
Andrea D’ascenzo, Mattia D’emidio, M. Flammini, G. Monaco
We study digraph k -coloring games where agents are vertices of a directed unweighted graph and arcs represent agents’ mutual unidirectional idiosyncrasies or conflicts. Each agent can select one of k different colors, and her payoff in a given state is given by the number of outgoing neighbors with a different color. Such games model lots of strategic real-world scenarios and are related to several fundamental classes of anti-coordination games. Unfortunately, the problem of understanding whether an instance of the game admits a pure Nash equilibrium is NP-complete [33]. Therefore, in the last few years a relevant research focus has been that of designing polynomial time algorithms able to compute approximate Nash equilibria, i.e., states in which no agent, changing her strategy, can improve her payoff by some bounded multiplicative factor. The only two known algorithms in this respect are those in [14]. While they provide theoretical guarantees, their practical performance over real-world instances so far has not been investigated. In this paper, under the further motivation of the lack of practical approximation algorithms for the problem, we experimentally evaluate the above algorithms with the conclusion that, while they were suitably designed for achieving a bounded worst case behavior, they generally have a poor performance. Therefore, we next focus on classical best-response dynamics, and show that, despite of the fact that they might not always converge, they are very effective in practice. In particular, we provide a strong empirical evidence that they outperform existing methods, since surprisingly they quickly converge to exact Nash equilibria in almost all instances arising in practice. This also shows that, while this class of games is known to not always possess pure Nash equilibria, in almost all cases such equilibria exist and can be efficiently computed, even in a distributed uncoordinated way by a decentralized interaction of the agents. 2012 ACM Subject Classification Theory of computation → Algorithmic game theory and mechanism design; Theory of computation → Quality of equilibria; and analysis of algorithms;
{"title":"Digraph k-Coloring Games: From Theory to Practice","authors":"Andrea D’ascenzo, Mattia D’emidio, M. Flammini, G. Monaco","doi":"10.4230/LIPIcs.SEA.2022.20","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2022.20","url":null,"abstract":"We study digraph k -coloring games where agents are vertices of a directed unweighted graph and arcs represent agents’ mutual unidirectional idiosyncrasies or conflicts. Each agent can select one of k different colors, and her payoff in a given state is given by the number of outgoing neighbors with a different color. Such games model lots of strategic real-world scenarios and are related to several fundamental classes of anti-coordination games. Unfortunately, the problem of understanding whether an instance of the game admits a pure Nash equilibrium is NP-complete [33]. Therefore, in the last few years a relevant research focus has been that of designing polynomial time algorithms able to compute approximate Nash equilibria, i.e., states in which no agent, changing her strategy, can improve her payoff by some bounded multiplicative factor. The only two known algorithms in this respect are those in [14]. While they provide theoretical guarantees, their practical performance over real-world instances so far has not been investigated. In this paper, under the further motivation of the lack of practical approximation algorithms for the problem, we experimentally evaluate the above algorithms with the conclusion that, while they were suitably designed for achieving a bounded worst case behavior, they generally have a poor performance. Therefore, we next focus on classical best-response dynamics, and show that, despite of the fact that they might not always converge, they are very effective in practice. In particular, we provide a strong empirical evidence that they outperform existing methods, since surprisingly they quickly converge to exact Nash equilibria in almost all instances arising in practice. This also shows that, while this class of games is known to not always possess pure Nash equilibria, in almost all cases such equilibria exist and can be efficiently computed, even in a distributed uncoordinated way by a decentralized interaction of the agents. 2012 ACM Subject Classification Theory of computation → Algorithmic game theory and mechanism design; Theory of computation → Quality of equilibria; and analysis of algorithms;","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"39 1","pages":"20:1-20:18"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84827653","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 : 2022-01-01DOI: 10.4230/LIPIcs.SEA.2022.10
Nico Bertram, J. Ellert, J. Fischer
Computing a maximum cut in undirected and weighted graphs is a well studied problem and has many practical solutions that also scale well in shared memory (despite its NP-completeness). For its counterpart in directed graphs, however, we are not aware of practical solutions that also utilize parallelism. We engineer a framework that computes a high quality approximate cut in directed and weighted graphs by using a graph partitioning approach. The general idea is to partition a graph into k subgraphs using a parallel partitioning algorithm of our choice (the first ingredient of our framework). Then, for each subgraph in parallel, we compute a cut using any polynomial time approximation algorithm (the second ingredient). In a final step, we merge the locally computed solutions using a high-quality or exact parallel Max-Dicut algorithm (the third ingredient). On graphs that can be partitioned well, the quality of the computed cut is significantly better than the best cut achieved by any linear time algorithm. This is particularly relevant for large graphs, where linear time algorithms used to be the only feasible option.
{"title":"A Parallel Framework for Approximate Max-Dicut in Partitionable Graphs","authors":"Nico Bertram, J. Ellert, J. Fischer","doi":"10.4230/LIPIcs.SEA.2022.10","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2022.10","url":null,"abstract":"Computing a maximum cut in undirected and weighted graphs is a well studied problem and has many practical solutions that also scale well in shared memory (despite its NP-completeness). For its counterpart in directed graphs, however, we are not aware of practical solutions that also utilize parallelism. We engineer a framework that computes a high quality approximate cut in directed and weighted graphs by using a graph partitioning approach. The general idea is to partition a graph into k subgraphs using a parallel partitioning algorithm of our choice (the first ingredient of our framework). Then, for each subgraph in parallel, we compute a cut using any polynomial time approximation algorithm (the second ingredient). In a final step, we merge the locally computed solutions using a high-quality or exact parallel Max-Dicut algorithm (the third ingredient). On graphs that can be partitioned well, the quality of the computed cut is significantly better than the best cut achieved by any linear time algorithm. This is particularly relevant for large graphs, where linear time algorithms used to be the only feasible option.","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"12 1","pages":"10:1-10:15"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86540919","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 : 2022-01-01DOI: 10.4230/LIPIcs.SEA.2022.7
M. Blesa, Mihail Eduard Popa, M. Serna
We perform here a comparative study on the behaviour of real and synthetic social networks with respect to a selection of nine centrality measures. Some of them are topology based (degree, closeness, betweenness), while others consider the relevance of the actors within the network (Katz, PageRank) or their ability to spread influence through it (Independent Cascade rank, Linear Threshold Rank). We run different experiments on synthetic social networks, with 1K, 10K, and 100K nodes, generated according to the Gaussian Random partition model, the stochastic block model, the LFR benchmark graph model and hyperbolic geometric graphs model. Some real social networks are also considered, with the aim of discovering how do they relate to the synthetic models in terms of centrality. Apart from usual statistical measures, we perform a correlation analysis between all the nine measures. Our results indicate that, in general, the correlation matrices of the different models scale nicely with size. Moreover, the correlation plots distinguish four categories that classify most of the real networks studied here. Those categories have a clear correspondence with particular configurations of the models for synthetic networks.
{"title":"Relating Real and Synthetic Social Networks Through Centrality Measures","authors":"M. Blesa, Mihail Eduard Popa, M. Serna","doi":"10.4230/LIPIcs.SEA.2022.7","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2022.7","url":null,"abstract":"We perform here a comparative study on the behaviour of real and synthetic social networks with respect to a selection of nine centrality measures. Some of them are topology based (degree, closeness, betweenness), while others consider the relevance of the actors within the network (Katz, PageRank) or their ability to spread influence through it (Independent Cascade rank, Linear Threshold Rank). We run different experiments on synthetic social networks, with 1K, 10K, and 100K nodes, generated according to the Gaussian Random partition model, the stochastic block model, the LFR benchmark graph model and hyperbolic geometric graphs model. Some real social networks are also considered, with the aim of discovering how do they relate to the synthetic models in terms of centrality. Apart from usual statistical measures, we perform a correlation analysis between all the nine measures. Our results indicate that, in general, the correlation matrices of the different models scale nicely with size. Moreover, the correlation plots distinguish four categories that classify most of the real networks studied here. Those categories have a clear correspondence with particular configurations of the models for synthetic networks.","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"39 1","pages":"7:1-7:21"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81110596","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 : 2022-01-01DOI: 10.4230/LIPIcs.SEA.2022.14
L. Georgiadis, Dionysios Kefallinos, Anna Mpanti, Stavros D. Nikolopoulos
A classic result of Edmonds states that the maximum number of edge-disjoint arborescences of a directed graph G , rooted at a designated vertex s , equals the minimum cardinality c G ( s ) of an s -cut of G . This concept is related to the edge connectivity λ ( G ) of a strongly connected directed graph G , defined as the minimum number of edges whose deletion leaves a graph that is not strongly connected. In this paper, we address the question of how efficiently we can compute a maximum packing of edge-disjoint arborescences in practice, compared to the time required to determine the edge connectivity of a graph. To that end, we explore the design space of efficient algorithms for packing arborescences of a directed graph in practice and conduct a thorough empirical study to highlight the merits and weaknesses of each technique. In particular, we present an efficient implementation of Gabow’s arborescence packing algorithm and provide a simple but efficient heuristic that significantly improves its running time in practice. Project FANTA (eFficient Algorithms for NeTwork Analysis), number HFRI-FM17-431. H = G − A , and a complete ( k − 1)-intersection T for s on G . It uses the following key concept. An enlarging path consists of an edge e ∈ E + ( A ), and if e ∈ T , an augmenting path P for the ( k − 1)-intersection T − e on H − e . Gabow shows that if V ( A ) ̸ = V ( G ), then there is always an enlarging path.
Edmonds的一个经典结果表明，根于指定顶点s的有向图G的最大边不相交树形数等于G的s -cut的最小基数c G (s)。这个概念与强连接有向图G的边连通性λ (G)有关，定义为其删除后留下非强连接图的最小边数。在本文中，我们解决的问题是，与确定图的边缘连通性所需的时间相比，我们在实践中如何有效地计算边缘不相交树的最大包装。为此，我们在实践中探索了有向图树杈填充的有效算法的设计空间，并进行了彻底的实证研究，以突出每种技术的优点和缺点。特别地，我们提出了Gabow树形打包算法的有效实现，并提供了一个简单而有效的启发式算法，在实践中显著提高了其运行时间。网络分析的高效算法(FANTA)项目，编号hri - fm17 -431。H = G−A，以及s在G上的完全(k−1)交T。它使用以下关键概念。扩展路径由一条边e∈e + (A)组成，如果e∈T，则在H−e上的(k−1)交T−e的扩展路径P。Gabow表明，如果V (A) h = V (G)，则总存在一条扩大路径。
{"title":"An Experimental Study of Algorithms for Packing Arborescences","authors":"L. Georgiadis, Dionysios Kefallinos, Anna Mpanti, Stavros D. Nikolopoulos","doi":"10.4230/LIPIcs.SEA.2022.14","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2022.14","url":null,"abstract":"A classic result of Edmonds states that the maximum number of edge-disjoint arborescences of a directed graph G , rooted at a designated vertex s , equals the minimum cardinality c G ( s ) of an s -cut of G . This concept is related to the edge connectivity λ ( G ) of a strongly connected directed graph G , defined as the minimum number of edges whose deletion leaves a graph that is not strongly connected. In this paper, we address the question of how efficiently we can compute a maximum packing of edge-disjoint arborescences in practice, compared to the time required to determine the edge connectivity of a graph. To that end, we explore the design space of efficient algorithms for packing arborescences of a directed graph in practice and conduct a thorough empirical study to highlight the merits and weaknesses of each technique. In particular, we present an efficient implementation of Gabow’s arborescence packing algorithm and provide a simple but efficient heuristic that significantly improves its running time in practice. Project FANTA (eFficient Algorithms for NeTwork Analysis), number HFRI-FM17-431. H = G − A , and a complete ( k − 1)-intersection T for s on G . It uses the following key concept. An enlarging path consists of an edge e ∈ E + ( A ), and if e ∈ T , an augmenting path P for the ( k − 1)-intersection T − e on H − e . Gabow shows that if V ( A ) ̸ = V ( G ), then there is always an enlarging path.","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"1 1","pages":"14:1-14:16"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75918320","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 : 2022-01-01DOI: 10.4230/LIPIcs.SEA.2022.2
Masakazu Ishihata, Fumiya Tokumasu
Solving paper-and-pencil puzzles is fun for people, and their analysis is also an essential issue in computational complexity theory. There are some practically efficient solvers for some NP-complete puzzles; however, the automatic generation of interesting puzzle instances still stands out as a complex problem because it requires checking whether the generated instance has a unique solution. In this paper, we focus on a puzzle called Nagareru and propose two methods: one is for implicitly enumerating all the solutions of its instance, and the other is for efficiently generating an instance with a unique solution. The former constructs a ZDD that implicitly represents all the solutions. The latter employs the ZDD-based solver as a building block to check the uniqueness of the solution of generated instances. We experimentally showed that the ZDD-based solver was drastically faster than a CSP-based solver, and our generation method created an interesting instance in a reasonable time.
{"title":"Solving and Generating Nagareru Puzzles","authors":"Masakazu Ishihata, Fumiya Tokumasu","doi":"10.4230/LIPIcs.SEA.2022.2","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2022.2","url":null,"abstract":"Solving paper-and-pencil puzzles is fun for people, and their analysis is also an essential issue in computational complexity theory. There are some practically efficient solvers for some NP-complete puzzles; however, the automatic generation of interesting puzzle instances still stands out as a complex problem because it requires checking whether the generated instance has a unique solution. In this paper, we focus on a puzzle called Nagareru and propose two methods: one is for implicitly enumerating all the solutions of its instance, and the other is for efficiently generating an instance with a unique solution. The former constructs a ZDD that implicitly represents all the solutions. The latter employs the ZDD-based solver as a building block to check the uniqueness of the solution of generated instances. We experimentally showed that the ZDD-based solver was drastically faster than a CSP-based solver, and our generation method created an interesting instance in a reasonable time.","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"60 1","pages":"2:1-2:17"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80510423","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 : 2022-01-01DOI: 10.4230/LIPIcs.SEA.2022.9
Ramtin Afshar, M. Goodrich, Evrim Ozel
The completeness of road network data is significant in the quality of various routing services and applications. We introduce an efficient randomized algorithm for exact learning of road networks using simple distance queries, which can find missing roads and improve the quality of routing services. The efficiency of our algorithm depends on a cluster degree parameter, d max , which is an upper bound on the degrees of vertex clusters defined during our algorithm. Unfortunately, we leave open the problem of theoretically bounding d max , although we conjecture that d max is small for road networks and other similar types of graphs. We support this conjecture by experimentally evaluating our algorithm on road network data for the U.S. and 5 European countries of various sizes. This analysis provides experimental evidence that our algorithm issues a quasilinear number of queries in expectation for road networks and similar graphs. of → Graph analysis; Theory of → Random network models;
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