PQ-trees and PC-trees are data structures that represent sets of linear and circular orders, respectively, subject to constraints that specific subsets of elements have to be consecutive. While equivalent to each other, PC-trees are conceptually much simpler than PQ-trees; updating a PC-tree so that a set of elements becomes consecutive requires only a single operation, whereas PQ-trees use an update procedure that is described in terms of nine transformation templates that have to be recursively matched and applied. Despite these theoretical advantages, to date no practical PC-tree implementation is available. This might be due to the original description by Hsu and McConnell [14] in some places only sketching the details of the implementation. In this paper, we describe two alternative implementations of PC-trees. For the first one, we follow the approach by Hsu and McConnell, filling in the necessary details and also proposing improvements on the original algorithm. For the second one, we use a different technique for efficiently representing the tree using a Union-Find data structure. In an extensive experimental evaluation we compare our implementations to a variety of other implementations of PQ-trees that are available on the web as part of academic and other software libraries. Our results show that both PC-tree implementations beat their closest fully correct competitor, the PQ-tree implementation from the OGDF library [6, 15], by a factor of 2 to 4, showing that PC-trees are not only conceptually simpler but also fast in practice. Moreover, we find the Union-Find-based implementation, while having a slightly worse asymptotic runtime, to be twice as fast as the one based on the description by Hsu and McConnell.
{"title":"Experimental Comparison of PC-Trees and PQ-Trees","authors":"S. D. Fink, Matthias Pfretzschner, Ignaz Rutter","doi":"10.1145/3611653","DOIUrl":"https://doi.org/10.1145/3611653","url":null,"abstract":"PQ-trees and PC-trees are data structures that represent sets of linear and circular orders, respectively, subject to constraints that specific subsets of elements have to be consecutive. While equivalent to each other, PC-trees are conceptually much simpler than PQ-trees; updating a PC-tree so that a set of elements becomes consecutive requires only a single operation, whereas PQ-trees use an update procedure that is described in terms of nine transformation templates that have to be recursively matched and applied. Despite these theoretical advantages, to date no practical PC-tree implementation is available. This might be due to the original description by Hsu and McConnell [14] in some places only sketching the details of the implementation. In this paper, we describe two alternative implementations of PC-trees. For the first one, we follow the approach by Hsu and McConnell, filling in the necessary details and also proposing improvements on the original algorithm. For the second one, we use a different technique for efficiently representing the tree using a Union-Find data structure. In an extensive experimental evaluation we compare our implementations to a variety of other implementations of PQ-trees that are available on the web as part of academic and other software libraries. Our results show that both PC-tree implementations beat their closest fully correct competitor, the PQ-tree implementation from the OGDF library [6, 15], by a factor of 2 to 4, showing that PC-trees are not only conceptually simpler but also fast in practice. Moreover, we find the Union-Find-based implementation, while having a slightly worse asymptotic runtime, to be twice as fast as the one based on the description by Hsu and McConnell.","PeriodicalId":53707,"journal":{"name":"Journal of Experimental Algorithmics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49045127","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}
Sebastian Schlag, Tobias Heuer, Lars Gottesbüren, Yaroslav Akhremtsev, Christian Schulz, P. Sanders
Hypergraphs are a generalization of graphs where edges (aka nets) are allowed to connect more than two vertices. They have a similarly wide range of applications as graphs. This article considers the fundamental and intensively studied problem of balanced hypergraph partitioning (BHP), which asks for partitioning the vertices into k disjoint blocks of bounded size while minimizing an objective function over the hyperedges. Here, we consider the two most commonly used objectives: the cut-net metric and the connectivity metric. We describe our open-source hypergraph partitioner KaHyPar which is based on the successful multi-level approach—driving it to the extreme of using one level for (almost) every vertex. Using carefully designed data structures and dynamic update techniques, this approach turns out to have a very good time–quality tradeoff. We present two preprocessing techniques—pin sparsification using locality-sensitive hashing (LSH) and community detection based on the Louvain algorithm. The community structure is used to guide the coarsening process that incrementally contracts vertices. Portfolio-based partitioning of the contracted hypergraph then already achieves a good initial solution. While reversing the contraction process, a combination of several refinement techniques achieves a good final partitioning. In particular, we support a highly-localized local search that can directly produce a k-way partitioning and complement this with flow-based techniques that take a more global view. Optionally, a memetic algorithm evolves a pool of solution candidates to an overall good solution. We evaluate KaHyPar for a large set of instances from a wide range of application domains. With respect to quality, KaHyPar outperforms all previously considered systems that can handle large hypergraphs such as hMETIS, PaToH, Mondriaan, or Zoltan. Somewhat surprisingly, to some extend, this even extends to graph partitioners such as KaHIP when considering the special case of graphs. KaHyPar is also faster than most of these systems except for PaToH which represents a different speed–quality tradeoff.
{"title":"High-Quality Hypergraph Partitioning","authors":"Sebastian Schlag, Tobias Heuer, Lars Gottesbüren, Yaroslav Akhremtsev, Christian Schulz, P. Sanders","doi":"10.1145/3529090","DOIUrl":"https://doi.org/10.1145/3529090","url":null,"abstract":"Hypergraphs are a generalization of graphs where edges (aka nets) are allowed to connect more than two vertices. They have a similarly wide range of applications as graphs. This article considers the fundamental and intensively studied problem of balanced hypergraph partitioning (BHP), which asks for partitioning the vertices into k disjoint blocks of bounded size while minimizing an objective function over the hyperedges. Here, we consider the two most commonly used objectives: the cut-net metric and the connectivity metric. We describe our open-source hypergraph partitioner KaHyPar which is based on the successful multi-level approach—driving it to the extreme of using one level for (almost) every vertex. Using carefully designed data structures and dynamic update techniques, this approach turns out to have a very good time–quality tradeoff. We present two preprocessing techniques—pin sparsification using locality-sensitive hashing (LSH) and community detection based on the Louvain algorithm. The community structure is used to guide the coarsening process that incrementally contracts vertices. Portfolio-based partitioning of the contracted hypergraph then already achieves a good initial solution. While reversing the contraction process, a combination of several refinement techniques achieves a good final partitioning. In particular, we support a highly-localized local search that can directly produce a k-way partitioning and complement this with flow-based techniques that take a more global view. Optionally, a memetic algorithm evolves a pool of solution candidates to an overall good solution. We evaluate KaHyPar for a large set of instances from a wide range of application domains. With respect to quality, KaHyPar outperforms all previously considered systems that can handle large hypergraphs such as hMETIS, PaToH, Mondriaan, or Zoltan. Somewhat surprisingly, to some extend, this even extends to graph partitioners such as KaHIP when considering the special case of graphs. KaHyPar is also faster than most of these systems except for PaToH which represents a different speed–quality tradeoff.","PeriodicalId":53707,"journal":{"name":"Journal of Experimental Algorithmics","volume":"27 1","pages":"1 - 39"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46717887","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}
Hyperbolicity is a graph parameter that indicates how much the shortest-path distance metric of a graph deviates from a tree metric. It is used in various fields such as networking, security, and bioinformatics for the classification of complex networks, the design of routing schemes, and the analysis of graph algorithms. Despite recent progress, computing the hyperbolicity of a graph remains challenging. Indeed, the best known algorithm has time complexity O(n3.69), which is prohibitive for large graphs, and the most efficient algorithms in practice have space complexity O(n2). Thus, time as well as space are bottlenecks for computing the hyperbolicity. In this article, we design a tool for enumerating all far-apart pairs of a graph by decreasing distances. A node pair (u, v) of a graph is far-apart if both v is a leaf of all shortest-path trees rooted at u and u is a leaf of all shortest-path trees rooted at v. This notion was previously used to drastically reduce the computation time for hyperbolicity in practice. However, it required the computation of the distance matrix to sort all pairs of nodes by decreasing distance, which requires an infeasible amount of memory already for medium-sized graphs. We present a new data structure that avoids this memory bottleneck in practice and for the first time enables computing the hyperbolicity of several large graphs that were far out of reach using previous algorithms. For some instances, we reduce the memory consumption by at least two orders of magnitude. Furthermore, we show that for many graphs, only a very small fraction of far-apart pairs has to be considered for the hyperbolicity computation, explaining this drastic reduction of memory. As iterating over far-apart pairs in decreasing order without storing them explicitly is a very general tool, we believe that our approach might also be relevant to other problems.
{"title":"Enumeration of Far-apart Pairs by Decreasing Distance for Faster Hyperbolicity Computation","authors":"D. Coudert, A. Nusser, L. Viennot","doi":"10.1145/3569169","DOIUrl":"https://doi.org/10.1145/3569169","url":null,"abstract":"Hyperbolicity is a graph parameter that indicates how much the shortest-path distance metric of a graph deviates from a tree metric. It is used in various fields such as networking, security, and bioinformatics for the classification of complex networks, the design of routing schemes, and the analysis of graph algorithms. Despite recent progress, computing the hyperbolicity of a graph remains challenging. Indeed, the best known algorithm has time complexity O(n3.69), which is prohibitive for large graphs, and the most efficient algorithms in practice have space complexity O(n2). Thus, time as well as space are bottlenecks for computing the hyperbolicity. In this article, we design a tool for enumerating all far-apart pairs of a graph by decreasing distances. A node pair (u, v) of a graph is far-apart if both v is a leaf of all shortest-path trees rooted at u and u is a leaf of all shortest-path trees rooted at v. This notion was previously used to drastically reduce the computation time for hyperbolicity in practice. However, it required the computation of the distance matrix to sort all pairs of nodes by decreasing distance, which requires an infeasible amount of memory already for medium-sized graphs. We present a new data structure that avoids this memory bottleneck in practice and for the first time enables computing the hyperbolicity of several large graphs that were far out of reach using previous algorithms. For some instances, we reduce the memory consumption by at least two orders of magnitude. Furthermore, we show that for many graphs, only a very small fraction of far-apart pairs has to be considered for the hyperbolicity computation, explaining this drastic reduction of memory. As iterating over far-apart pairs in decreasing order without storing them explicitly is a very general tool, we believe that our approach might also be relevant to other problems.","PeriodicalId":53707,"journal":{"name":"Journal of Experimental Algorithmics","volume":"27 1","pages":"1 - 29"},"PeriodicalIF":0.0,"publicationDate":"2021-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46903386","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}
Vertex connectivity is a well-studied concept in graph theory with numerous applications. A graph is k-connected if it remains connected after removing any k −1 vertices. The vertex connectivity of a graph is the maximum k such that the graph is k-connected. There is a long history of algorithmic development for efficiently computing vertex connectivity. Recently, two near linear-time algorithms for small k were introduced by Forster et al. [SODA 2020]. Prior to that, the best-known algorithm was one by Henzinger et al. [FOCS 1996] with quadratic running time when k is small. In this article, we study the practical performance of the algorithms by Forster et al. In addition, we introduce a new heuristic on a key subroutine called local cut detection, which we call degree counting. We prove that the new heuristic improves space-efficiency (which can be good for caching purposes) and allows the subroutine to terminate earlier. According to experimental results on random graphs with planted vertex cuts, random hyperbolic graphs, and real-world graphs with vertex connectivity between 4 and 8, the degree counting heuristic offers a factor of 2–4 speedup over the original non-degree counting version for small graphs and almost 20 times for some graphs with millions of edges. It also outperforms the previous state-of-the-art algorithm by Henzinger et al., even on relatively small graphs.
{"title":"Engineering Nearly Linear-time Algorithms for Small Vertex Connectivity","authors":"Max Franck, Sorrachai Yingchareonthawornchai","doi":"10.1145/3564822","DOIUrl":"https://doi.org/10.1145/3564822","url":null,"abstract":"Vertex connectivity is a well-studied concept in graph theory with numerous applications. A graph is k-connected if it remains connected after removing any k −1 vertices. The vertex connectivity of a graph is the maximum k such that the graph is k-connected. There is a long history of algorithmic development for efficiently computing vertex connectivity. Recently, two near linear-time algorithms for small k were introduced by Forster et al. [SODA 2020]. Prior to that, the best-known algorithm was one by Henzinger et al. [FOCS 1996] with quadratic running time when k is small. In this article, we study the practical performance of the algorithms by Forster et al. In addition, we introduce a new heuristic on a key subroutine called local cut detection, which we call degree counting. We prove that the new heuristic improves space-efficiency (which can be good for caching purposes) and allows the subroutine to terminate earlier. According to experimental results on random graphs with planted vertex cuts, random hyperbolic graphs, and real-world graphs with vertex connectivity between 4 and 8, the degree counting heuristic offers a factor of 2–4 speedup over the original non-degree counting version for small graphs and almost 20 times for some graphs with millions of edges. It also outperforms the previous state-of-the-art algorithm by Henzinger et al., even on relatively small graphs.","PeriodicalId":53707,"journal":{"name":"Journal of Experimental Algorithmics","volume":" ","pages":"1 - 29"},"PeriodicalIF":0.0,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48606251","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}
K. Buchin, Alexander Hill, S. Fekete, Linda Kleist, I. Kostitsyna, Dominik Krupke, R. Lambers, Martijn Struijs
We consider a spectrum of geometric optimization problems motivated by contexts such as satellite communication and astrophysics. In the problem Minimum Scan Cover with Angular Costs, we are given a graph G that is embedded in Euclidean space. The edges of G need to be scanned, i.e., probed from both of their vertices. To scan their edge, two vertices need to face each other; changing the heading of a vertex incurs some cost in terms of energy or rotation time that is proportional to the corresponding rotation angle. Our goal is to compute schedules that minimize the following objective functions: (i) in Minimum Makespan Scan Cover (MSC-MS), this is the time until all edges are scanned; (ii) in Minimum Total Energy Scan Cover (MSC-TE), the sum of all rotation angles; and (iii) in Minimum Bottleneck Energy Scan Cover (MSC-BE), the maximum total rotation angle at one vertex. Previous theoretical work on MSC-MS revealed a close connection to graph coloring and the cut cover problem, leading to hardness and approximability results. In this article, we present polynomial-time algorithms for one-dimensional (1D) instances of MSC-TE and MSC-BE but NP-hardness proofs for bipartite 2D instances. For bipartite graphs in 2D, we also give 2-approximation algorithms for both MSC-TE and MSC-BE. Most importantly, we provide a comprehensive study of practical methods for all three problems. We compare three different mixed-integer programming and two constraint programming approaches and show how to compute provably optimal solutions for geometric instances with up to 300 edges. Additionally, we compare the performance of different meta-heuristics for even larger instances.
{"title":"Minimum Scan Cover and Variants: Theory and Experiments","authors":"K. Buchin, Alexander Hill, S. Fekete, Linda Kleist, I. Kostitsyna, Dominik Krupke, R. Lambers, Martijn Struijs","doi":"10.1145/3567674","DOIUrl":"https://doi.org/10.1145/3567674","url":null,"abstract":"We consider a spectrum of geometric optimization problems motivated by contexts such as satellite communication and astrophysics. In the problem Minimum Scan Cover with Angular Costs, we are given a graph G that is embedded in Euclidean space. The edges of G need to be scanned, i.e., probed from both of their vertices. To scan their edge, two vertices need to face each other; changing the heading of a vertex incurs some cost in terms of energy or rotation time that is proportional to the corresponding rotation angle. Our goal is to compute schedules that minimize the following objective functions: (i) in Minimum Makespan Scan Cover (MSC-MS), this is the time until all edges are scanned; (ii) in Minimum Total Energy Scan Cover (MSC-TE), the sum of all rotation angles; and (iii) in Minimum Bottleneck Energy Scan Cover (MSC-BE), the maximum total rotation angle at one vertex. Previous theoretical work on MSC-MS revealed a close connection to graph coloring and the cut cover problem, leading to hardness and approximability results. In this article, we present polynomial-time algorithms for one-dimensional (1D) instances of MSC-TE and MSC-BE but NP-hardness proofs for bipartite 2D instances. For bipartite graphs in 2D, we also give 2-approximation algorithms for both MSC-TE and MSC-BE. Most importantly, we provide a comprehensive study of practical methods for all three problems. We compare three different mixed-integer programming and two constraint programming approaches and show how to compute provably optimal solutions for geometric instances with up to 300 edges. Additionally, we compare the performance of different meta-heuristics for even larger instances.","PeriodicalId":53707,"journal":{"name":"Journal of Experimental Algorithmics","volume":"27 1","pages":"1 - 28"},"PeriodicalIF":0.0,"publicationDate":"2021-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47944085","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}
In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are implemented and tested on real datasets, and their practical potential is far from understood. Here, we present a quick reference guide to recent engineering and theory results in the area of fully dynamic graph algorithms.
{"title":"Recent Advances in Fully Dynamic Graph Algorithms – A Quick Reference Guide","authors":"Kathrin Hanauer, M. Henzinger, Christian Schulz","doi":"10.1145/3555806","DOIUrl":"https://doi.org/10.1145/3555806","url":null,"abstract":"In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are implemented and tested on real datasets, and their practical potential is far from understood. Here, we present a quick reference guide to recent engineering and theory results in the area of fully dynamic graph algorithms.","PeriodicalId":53707,"journal":{"name":"Journal of Experimental Algorithmics","volume":"27 1","pages":"1 - 45"},"PeriodicalIF":0.0,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46900888","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}
Partitioning graphs into blocks of roughly equal size is a widely used tool when processing large graphs. Currently, there is a gap observed in the space of available partitioning algorithms. On the one hand, there are streaming algorithms that have been adopted to partition massive graph data on small machines. In the streaming model, vertices arrive one at a time including their neighborhood, and then have to be assigned directly to a block. These algorithms can partition huge graphs quickly with little memory, but they produce partitions with low solution quality. On the other hand, there are offline (shared-memory) multilevel algorithms that produce partitions with high-quality but also need a machine with enough memory to partition huge networks. In this work, we make a first step to close this gap by presenting an algorithm that computes significantly improved partitions of huge graphs using a single machine with little memory in a streaming setting. First, we adopt the buffered streaming model which is a more reasonable approach in practice. In this model, a processing element can store a buffer of nodes alongside with their edges before making assignment decisions. When our algorithm receives a batch of nodes, we build a model graph that represents the nodes of the batch and the already present partition structure. This model enables us to apply multilevel algorithms and in turn, on cheap machines, compute much higher quality solutions of huge graphs than previously possible. To partition the model graph, we develop a multilevel algorithm that optimizes an objective function that has previously been shown to be effective for the streaming setting. Surprisingly, this also removes the dependency on the number of blocks k from the running time compared to the previous state-of-the-art. Overall, our algorithm computes, on average, 75.9% better solutions than Fennel [35] using a very small buffer size. In addition, for large values of k our algorithm becomes faster than Fennel.
{"title":"Buffered Streaming Graph Partitioning","authors":"Marcelo Fonseca Faraj, Christian Schulz","doi":"10.1145/3546911","DOIUrl":"https://doi.org/10.1145/3546911","url":null,"abstract":"Partitioning graphs into blocks of roughly equal size is a widely used tool when processing large graphs. Currently, there is a gap observed in the space of available partitioning algorithms. On the one hand, there are streaming algorithms that have been adopted to partition massive graph data on small machines. In the streaming model, vertices arrive one at a time including their neighborhood, and then have to be assigned directly to a block. These algorithms can partition huge graphs quickly with little memory, but they produce partitions with low solution quality. On the other hand, there are offline (shared-memory) multilevel algorithms that produce partitions with high-quality but also need a machine with enough memory to partition huge networks. In this work, we make a first step to close this gap by presenting an algorithm that computes significantly improved partitions of huge graphs using a single machine with little memory in a streaming setting. First, we adopt the buffered streaming model which is a more reasonable approach in practice. In this model, a processing element can store a buffer of nodes alongside with their edges before making assignment decisions. When our algorithm receives a batch of nodes, we build a model graph that represents the nodes of the batch and the already present partition structure. This model enables us to apply multilevel algorithms and in turn, on cheap machines, compute much higher quality solutions of huge graphs than previously possible. To partition the model graph, we develop a multilevel algorithm that optimizes an objective function that has previously been shown to be effective for the streaming setting. Surprisingly, this also removes the dependency on the number of blocks k from the running time compared to the previous state-of-the-art. Overall, our algorithm computes, on average, 75.9% better solutions than Fennel [35] using a very small buffer size. In addition, for large values of k our algorithm becomes faster than Fennel.","PeriodicalId":53707,"journal":{"name":"Journal of Experimental Algorithmics","volume":"27 1","pages":"1 - 26"},"PeriodicalIF":0.0,"publicationDate":"2021-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43243122","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}
{"title":"Parameterized Complexity: The Main Ideas and Connections to Practical Computing","authors":"M. Fellows","doi":"10.1007/3-540-36383-1_3","DOIUrl":"https://doi.org/10.1007/3-540-36383-1_3","url":null,"abstract":"","PeriodicalId":53707,"journal":{"name":"Journal of Experimental Algorithmics","volume":"73 1","pages":"1-19"},"PeriodicalIF":0.0,"publicationDate":"2000-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74185909","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}
{"title":"Algorithm Engineering for Parallel Computation","authors":"David A. Bader, B. Moret, P. Sanders","doi":"10.1007/3-540-36383-1_1","DOIUrl":"https://doi.org/10.1007/3-540-36383-1_1","url":null,"abstract":"","PeriodicalId":53707,"journal":{"name":"Journal of Experimental Algorithmics","volume":"12 1","pages":"1-23"},"PeriodicalIF":0.0,"publicationDate":"2000-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81915535","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}
{"title":"Reconstructing Optimal Phylogenetic Trees: A Challenge in Experimental Algorithmics","authors":"B. Moret, T. Warnow","doi":"10.1007/3-540-36383-1_8","DOIUrl":"https://doi.org/10.1007/3-540-36383-1_8","url":null,"abstract":"","PeriodicalId":53707,"journal":{"name":"Journal of Experimental Algorithmics","volume":"78 1","pages":"163-180"},"PeriodicalIF":0.0,"publicationDate":"2000-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76394356","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}
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