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Fixed-parameter algorithms for DAG Partitioning

René van Bevern, Robert Bredereck, Morgan Chopin, Sepp Hartung, Falk Hüffner, André Nichterlein, Ondřej Suchý
2017 Discrete Applied Mathematics  
DAG Partitioning is NP-hard. We show an algorithm to solve DAG Partitioning in O(2^k · (n+m)) time, that is, in linear time for fixed k.  ...  Our experiments show that, in combination, they can optimally solve DAG Partitioning on simulated citation networks within five minutes for k≤190 and m being 10^7 and larger.  ...  Acknowledgments We are thankful to Rolf Niedermeier and to the anonymous referees of CIAC'13 and Discrete Applied Mathematics for helpful comments.  ... 
doi:10.1016/j.dam.2016.12.002 fatcat:jxaymsutbzgybhzlp3cn23xh5a

Parameterized Complexity of DAG Partitioning [chapter]

René van Bevern, Robert Bredereck, Morgan Chopin, Sepp Hartung, Falk Hüffner, André Nichterlein, Ondřej Suchý
2013 Lecture Notes in Computer Science  
Finally, given a tree decomposition of width w, we show how to solve DAG Partitioning in 2 O(w 2 ) · n time, improving a known algorithm for the parameter pathwidth.  ...  We show that it can be solved in O(2 k ·n 2 ) time, where k is the number of edge deletions, proving fixed-parameter tractability for parameter k.  ...  Outlook We have presented two parameterized algorithms for DAG Partitioning, one with parameter solution size k and one with parameter treewidth w.  ... 
doi:10.1007/978-3-642-38233-8_5 fatcat:synxwc53xrhxhclewowtegeesa

The Burning Number of Directed Graphs: Bounds and Computational Complexity [article]

Remie Janssen
2020 arXiv   pre-print
Finally, we give a fixed-parameter algorithm to find the burning number of a digraph, with a parameter inspired by research in phylogenetic networks.  ...  The hardness question yields more surprising results: finding the burning number of a directed tree is NP-hard, but FPT; however, it is W[2]-complete for DAGs.  ...  The author would like to thank Josse van Dobben de Bruyn for bringing graph burning to his attention, and Mark Jones for lending his expertise in parametrized complexity.  ... 
arXiv:2001.03381v1 fatcat:d7jq2mojcjcatdbwd6ypmmafzq

Estimation of Gaussian directed acyclic graphs using partial ordering information with an application to dairy cattle data [article]

Syed Rahman, Kshitij Khare, George Michailidis, Carlos Martinez and Juan Carulla
2019 arXiv   pre-print
domain specific knowledge.We develop an efficient algorithm that solves the posited problem, coined Partition-DAG.  ...  In this paper, motivated by a recent application in dairy science, we develop a method for DAG estimation for the middle scenario, where partition based partial ordering of the nodes is known based on  ...  For each sample size, each of the three algorithms (PC, CCDr, Partition-DAG) was run for each dataset described above for a range of penalty parameter values (for the PC algorithm, the significance level  ... 
arXiv:1902.05173v1 fatcat:y2od7szjpfb5fnxctiqem6w4um

Collaborative hardware/software partition of coarse-grained reconfigurable system using evolutionary ant colony optimization

Dawei Wang, Sikun Li, Yong Dou
2008 2008 Asia and South Pacific Design Automation Conference  
Experimental results show that the method improves the quality and speed of hardware/software partition for coarse-grained reconfigurable system design.  ...  We create a distributed collaborative design environment for system decision engineers, software designers, hardware designers and application algorithm developers.  ...  Pseudo-code for eACOGA algorithm //Input: the configuration of RAAM and DAGs //Outputs: the optimal solutions for partition //Q, , , is the main parameters of ACO 1 Main(){ 2 Generation = 0; 3  ... 
doi:10.1109/aspdac.2008.4484037 dblp:conf/aspdac/WangLD08 fatcat:z4p3hrejxjaudmczu6gydpnhca

Partition MCMC for Inference on Acyclic Digraphs

Jack Kuipers, Giusi Moffa
2017 Journal of the American Statistical Association  
Here we propose a novel algorithm, which employs the underlying combinatorial structure of DAGs to define a new grouping.  ...  MCMC methods, notably structure MCMC, to sample graphs from the posterior distribution given the data are probably the only viable option for Bayesian model averaging.  ...  For simplicity though we sample each move type with a fixed probability.  ... 
doi:10.1080/01621459.2015.1133426 fatcat:cnnoztgakjbbfnerecnrxfghdq

Data-Intensive Workflow Optimization Based on Application Task Graph Partitioning in Heterogeneous Computing Systems

Saima Gulzar Ahmad, Chee Sun Liew, M. Mustafa Rafique, Ehsan Ullah Munir, Samee U. Khan
2014 2014 IEEE Fourth International Conference on Big Data and Cloud Computing  
This paper presents a dual objective Partitioning based Data-intensive Workflow optimization Algorithm (PDWA) for heterogeneous computing systems.  ...  Each partition is mapped to the execution node that gives minimum execution time for that particular partition. PDWA also exploits partial task duplication to reduce the latency.  ...  The DAG is partitioned using the Partition algorithm, shown in Algorithm 2. The DAG is split into suitable number of partitions such that the inter-partition data movement is minimum.  ... 
doi:10.1109/bdcloud.2014.63 dblp:conf/bdcloud/AhmadLRMK14 fatcat:q4vegly4tbg5joh6po3miz3j2e

A large-scale task scheduling algorithm based on clustering and duplication

Wengang Huang, Zhichen Shi, Zheng Xiao, Cen Chen, Kenli Li
2022 Journal of Smart Environments and Green Computing  
Methods: This paper proposes a clustering and duplication-based method for large-scale task scheduling on a limited amount of processors.  ...  Results: We compare our algorithm with the state-of-the-art algorithms in the article.  ...  since DAG partition and task duplication may generate duplicate execution of tasks when the scheduling of tasks is completed. • New parameters for algorithm: We define several parameters used in TDPATD  ... 
doi:10.20517/jsegc.2021.13 fatcat:26kl54rrxjbyvhpsze6dpvfjre

Knowledge Representation Using Decision Trees Constructed Based on Binary Splits

2020 KSII Transactions on Internet and Information Systems  
However, the usual algorithms may split the decision table based on each value, which is not efficient for numerical attributes.  ...  The methodology of this paper is to split the given decision table into binary groups as like the CART algorithm, that uses binary split to work for both categorical and numerical attributes.  ...  Construct DAG for TB and Initialize, S, the set of POPs by using the Algorithm APOPs for BOO of CL-trees proportionate to the parameter NN and GM 3. Normalize the coordinates of S 4.  ... 
doi:10.3837/tiis.2020.10.005 fatcat:ijkh6gwerfgcfgdxw6427tlfaq

Brief Announcement: Treewidth Modulator: Emergency Exit for DFVS

Daniel Lokshtanov, M. S. Ramanujan, Saket Saurabh, Roohani Sharma, Meirav Zehavi, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
In this article, we give a polynomial kernel for DFVS parameterized by the solution size plus the size of any treewidth-η modulator, for any positive integer η.  ...  We also give a polynomial kernel for the problem, which we call Vertex Deletion to treewidth-η DAG, where given as input a directed graph D and a positive integer k, the objective is to decide whether  ...  The question whether DFVS is fixed-parameter tractable was posed as an open problem in the first few papers on fixed-parameter tractability (FPT) [8, 9] .  ... 
doi:10.4230/lipics.icalp.2018.110 dblp:conf/icalp/LokshtanovR0SZ18 fatcat:htkjniifpzb3lgqxsrsqvh22fa

System Level Distributed Cooperative Design of Media SoC Using Application Profiling

Dawei Wang, Peng Zhao, Sikun Li
2009 Journal of Computers  
The method not only utilizes the advantages of application profiling for SoC design, but also pro-vides a framework for multi-field experts to work collaboratively.  ...  SoC design is very complex for multi-fields experts to collaborate on application analysis, system decision and hw/sw co-design.  ...  First, the configurations of DAGs are input, and after the execution of eACOGA algorithm the optimal solutions for partition are output.  ... 
doi:10.4304/jcp.4.1.77-85 fatcat:o3q6zai6ujg65ljj7kcjtghm3a

Some models for scheduling parallel programs with communication delays

Evripidis Bampis, Frédéric Guinand, Denis Trystram
1997 Discrete Applied Mathematics  
The aim of this paper is to present and analyze models for designing parallel programs.  ...  An algorithm that provides an optimal schedule for complete k-at-y trees on a fixed number of processors was presented in [16] .  ...  For instance, let us consider the partition that minimizes the communication cost: the whole DAG is considered as a single job.  ... 
doi:10.1016/s0166-218x(96)00034-0 fatcat:qe3gwnefl5gx7gi6ajivjtvrc4

An Efficient Technique for Hardware/Software Partitioning Process in Codesign

Imene Mhadhbi, Slim Ben Othman, Slim Ben Saoud
2016 Scientific Programming  
The main contribution of this paper is to propose a hybrid FCMPSO partitioning technique, based on Fuzzy C-Means (FCM) and Particle Swarm Optimization (PSO) algorithms suitable for mapping embedded applications  ...  for both binary and multicores target architecture.  ...  The parameters generated from the TGFF input files for our three DAGs graphs are presented in Table 1 .  ... 
doi:10.1155/2016/6382765 fatcat:qmvv5vdbkjdhnlbbpikvxoqgxq

Bayesian structure learning and sampling of Bayesian networks with the R package BiDAG [article]

Polina Suter and Jack Kuipers and Giusi Moffa and Niko Beerenwinkel
2021 arXiv   pre-print
Sampling from the posterior distribution is implemented using either order or partition MCMC. The models and algorithms can handle both discrete and continuous data.  ...  In the first step, we define a reduced search space by means of the PC algorithm or based on prior knowledge.  ...  For each subfigure two pairs of samples of DAGs were obtained by order/partition MCMC schemes.  ... 
arXiv:2105.00488v1 fatcat:ilrskhcojndfro23vsg4en74my

NP-Hardness and Fixed-Parameter Tractability of Realizing Degree Sequences with Directed Acyclic Graphs [chapter]

Sepp Hartung, André Nichterlein
2012 Lecture Notes in Computer Science  
Besides providing several omitted proof details, an important difference compared to the conference version is the proof of fixed-parameter tractability for the parameter "number of arcs minus number of  ...  Furthermore, we classify the problem as fixed-parameter tractable with respect to the parameter "maximum degree".  ...  Acknowledgements We thank Annabell Berger and Matthias Müller-Hannemann for fruitful discussions about DAG Realization.  ... 
doi:10.1007/978-3-642-30870-3_29 fatcat:lewgtyy7gnadzee3pknk5jg6ma
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