arXiv - CS - Data Structures and Algorithms最新文献_第5页

V-Words, Lyndon Words and Galois Words V字词、林登字词和伽罗瓦字词

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-04 DOI: arxiv-2409.02757

Jacqueline W. Daykin, Neerja Mhaskar, W. F. Smyth

引用次数: 0

Revisiting ILP Models for Exact Crossing Minimization in Storyline Drawings 重新审视故事情节图中精确交叉最小化的 ILP 模型

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-04 DOI: arxiv-2409.02858

Alexander Dobler, Michael Jünger, Paul J. Jünger, Julian Meffert, Petra Mutzel, Martin Nöllenburg

{"title":"Revisiting ILP Models for Exact Crossing Minimization in Storyline Drawings","authors":"Alexander Dobler, Michael Jünger, Paul J. Jünger, Julian Meffert, Petra Mutzel, Martin Nöllenburg","doi":"arxiv-2409.02858","DOIUrl":"https://doi.org/arxiv-2409.02858","url":null,"abstract":"Storyline drawings are a popular visualization of interactions of a set of\u0000characters over time, e.g., to show participants of scenes in a book or movie.\u0000Characters are represented as $x$-monotone curves that converge vertically for\u0000interactions and diverge otherwise. Combinatorially, the task of computing\u0000storyline drawings reduces to finding a sequence of permutations of the\u0000character curves for the different time points, with the primary objective\u0000being crossing minimization of the induced character trajectories. In this\u0000paper, we revisit exact integer linear programming (ILP) approaches for this\u0000NP-hard problem. By enriching previous formulations with additional\u0000problem-specific insights and new heuristics, we obtain exact solutions for an\u0000extended new benchmark set of larger and more complex instances than had been\u0000used before. Our experiments show that our enriched formulations lead to better\u0000performing algorithms when compared to state-of-the-art modelling techniques.\u0000In particular, our best algorithms are on average 2.6-3.2 times faster than the\u0000state-of-the-art and succeed in solving complex instances that could not be\u0000solved before within the given time limit. Further, we show in an ablation\u0000study that our enrichment components contribute considerably to the performance\u0000of the new ILP formulation.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226007","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}

引用次数: 0

Minimizing Cost Rather Than Maximizing Reward in Restless Multi-Armed Bandits 在不安分的多臂强盗中尽量降低成本，而不是尽量增加回报

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-04 DOI: arxiv-2409.03071

R. Teal Witter, Lisa Hellerstein

{"title":"Minimizing Cost Rather Than Maximizing Reward in Restless Multi-Armed Bandits","authors":"R. Teal Witter, Lisa Hellerstein","doi":"arxiv-2409.03071","DOIUrl":"https://doi.org/arxiv-2409.03071","url":null,"abstract":"Restless Multi-Armed Bandits (RMABs) offer a powerful framework for solving\u0000resource constrained maximization problems. However, the formulation can be\u0000inappropriate for settings where the limiting constraint is a reward threshold\u0000rather than a budget. We introduce a constrained minimization problem for RMABs\u0000that balances the goal of achieving a reward threshold while minimizing total\u0000cost. We show that even a bi-criteria approximate version of the problem is\u0000PSPACE-hard. Motivated by the hardness result, we define a decoupled problem,\u0000indexability and a Whittle index for the minimization problem, mirroring the\u0000corresponding concepts for the maximization problem. Further, we show that the\u0000Whittle index for the minimization problem can easily be computed from the\u0000Whittle index for the maximization problem. Consequently, Whittle index results\u0000on RMAB instances for the maximization problem give Whittle index results for\u0000the minimization problem. Despite the similarities between the minimization and\u0000maximization problems, solving the minimization problem is not as simple as\u0000taking direct analogs of the heuristics for the maximization problem. We give\u0000an example of an RMAB for which the greedy Whittle index heuristic achieves the\u0000optimal solution for the maximization problem, while the analogous heuristic\u0000yields the worst possible solution for the minimization problem. In light of\u0000this, we present and compare several heuristics for solving the minimization\u0000problem on real and synthetic data. Our work suggests the importance of\u0000continued investigation into the minimization problem.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"95 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225981","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}

引用次数: 0

Hadamard Row-Wise Generation Algorithm Hadamard 行向生成算法

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-04 DOI: arxiv-2409.02406

Brayan Monroy, Jorge Bacca

引用次数: 0

The Parameterized Complexity of Extending Stack Layouts 扩展堆栈布局的参数化复杂性

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-04 DOI: arxiv-2409.02833

Thomas Depian, Simon D. Fink, Robert Ganian, Martin Nöllenburg

引用次数: 0

Accelerating Graph Neural Networks with a Novel Matrix Compression Format 用新颖的矩阵压缩格式加速图神经网络

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-03 DOI: arxiv-2409.02208

João N. F. Alves, Samir Moustafa, Siegfried Benkner, Alexandre P. Francisco, Wilfried N. Gansterer, Luís M. S. Russo

{"title":"Accelerating Graph Neural Networks with a Novel Matrix Compression Format","authors":"João N. F. Alves, Samir Moustafa, Siegfried Benkner, Alexandre P. Francisco, Wilfried N. Gansterer, Luís M. S. Russo","doi":"arxiv-2409.02208","DOIUrl":"https://doi.org/arxiv-2409.02208","url":null,"abstract":"The inference and training stages of Graph Neural Networks (GNNs) are often\u0000dominated by the time required to compute a long sequence of matrix\u0000multiplications between the sparse graph adjacency matrix and its embedding. To\u0000accelerate these stages, we first propose the Compressed Binary Matrix (CBM)\u0000storage format to succinctly represent the binary adjacency matrix of an\u0000unweighted graph. Then, we show how to generalize this representation to\u0000normalized adjacency matrices of unweighted graphs which arise in the context\u0000of GNNs. Finally, we develop efficient matrix multiplication kernels based on\u0000this compressed representation. The matrix multiplication kernels proposed in\u0000this work never require more scalar operations than classic sparse matrix\u0000multiplication algorithms. Experimental evaluation shows that the matrix\u0000multiplication strategies proposed outperform the current state-of-the-art\u0000implementations provided by Intel MKL, achieving speedups close to 5$times$.\u0000Furthermore, our optimized matrix-multiplication strategies accelerated the\u0000inference time of a GNN by up to $3times$.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202661","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}

引用次数: 0

Weakly Leveled Planarity with Bounded Span 有界跨度的弱水平平面性

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-03 DOI: arxiv-2409.01889

Michael Bekos, Giordano Da Lozzo, Fabrizio Frati, Siddharth Gupta, Philipp Kindermann, Giuseppe Liotta, Ignaz Rutter, Ioannis G. Tollis

{"title":"Weakly Leveled Planarity with Bounded Span","authors":"Michael Bekos, Giordano Da Lozzo, Fabrizio Frati, Siddharth Gupta, Philipp Kindermann, Giuseppe Liotta, Ignaz Rutter, Ioannis G. Tollis","doi":"arxiv-2409.01889","DOIUrl":"https://doi.org/arxiv-2409.01889","url":null,"abstract":"This paper studies planar drawings of graphs in which each vertex is\u0000represented as a point along a sequence of horizontal lines, called levels, and\u0000each edge is either a horizontal segment or a strictly $y$-monotone curve. A\u0000graph is $s$-span weakly leveled planar if it admits such a drawing where the\u0000edges have span at most $s$; the span of an edge is the number of levels it\u0000touches minus one. We investigate the problem of computing $s$-span weakly\u0000leveled planar drawings from both the computational and the combinatorial\u0000perspectives. We prove the problem to be para-NP-hard with respect to its\u0000natural parameter $s$ and investigate its complexity with respect to widely\u0000used structural parameters. We show the existence of a polynomial-size kernel\u0000with respect to vertex cover number and prove that the problem is FPT when\u0000parameterized by treedepth. We also present upper and lower bounds on the span\u0000for various graph classes. Notably, we show that cycle trees, a family of $2$-outerplanar graphs\u0000generalizing Halin graphs, are $Theta(log n)$-span weakly leveled planar and\u0000$4$-span weakly leveled planar when $3$-connected. As a byproduct of these\u0000combinatorial results, we obtain improved bounds on the edge-length ratio of\u0000the graph families under consideration.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"93 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202667","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}

引用次数: 0

The NTU Partitioned Matching Game for International Kidney Exchange Programs 北大国际肾脏交流项目的分区匹配游戏

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-02 DOI: arxiv-2409.01452

Gergely Csáji, Tamás Király, Zsuzsa Mészáros-Karkus

{"title":"The NTU Partitioned Matching Game for International Kidney Exchange Programs","authors":"Gergely Csáji, Tamás Király, Zsuzsa Mészáros-Karkus","doi":"arxiv-2409.01452","DOIUrl":"https://doi.org/arxiv-2409.01452","url":null,"abstract":"Motivated by the real-world problem of international kidney exchange (IKEP),\u0000[Bir'o et al., Generalized Matching Games for International Kidney Exchange,\u00002019] introduced a generalized transferable utility matching game featuring a\u0000partition of the vertex set of a graph into players, and analyzed its\u0000complexity. We explore the non-transferable utility (NTU) variant of the game,\u0000where the utility of players is given by the number of their matched vertices.\u0000The NTU version is arguably a more natural model of the international kidney\u0000exchange program, as the utility of a participating country mostly depends on\u0000how many of its patients receive a kidney, which is non-transferable by nature.\u0000We study the core of this game, which suitably captures the notion of stability\u0000of an IKEP, as it precludes incentives to deviate from the proposed solution\u0000for any possible coalition of the players. We prove computational complexity results about the weak and strong cores\u0000under various assumptions on the players. In particular, we show that if every\u0000player has two vertices, which can be considered as an NTU matching game with\u0000couples, then the weak core is always non-empty, and the existence of a strong\u0000core solution can be decided in polynomial time. In contrast, it is NP-hard to\u0000decide whether the strong core is empty when each player has three vertices. We\u0000also show that if the number of players is constant, then the non-emptiness of\u0000the weak and strong cores is polynomial-time decidable.","PeriodicalId":501525,"journal":{"name":"arXiv - CS - Data Structures and Algorithms","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227802","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}

引用次数: 0

Survey of Results on the ModPath and ModCycle Problems 关于 ModPath 和 ModCycle 问题的成果概览

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-01 DOI: arxiv-2409.00770

Antoine Amarilli

引用次数: 0

ExpoSort: Beating the quasi-polynomial-time barrier for reluctant sorting ExpoSort：打破勉强排序的准多项式时间障碍

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-09-01 DOI: arxiv-2409.00794

Mikkel Abrahamsen

引用次数: 0