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(Sub)linear kernels for edge modification problems towards structured graph classes [article]

Gabriel Bathie
2021 arXiv   pre-print
In a (parameterized) graph edge modification problem, we are given a graph G, an integer k and a (usually well-structured) class of graphs 𝒢, and ask whether it is possible to transform G into a graph  ...  Parameterized graph edge modification problems received considerable attention in the last decades. In this paper, we focus on finding small kernels for edge modification problems.  ...  Is there an O(k 1−ε ) kernel for Clique + IS Deletion for some ε > 0? Moreover, it is plausible that other edge modification problems towards highly structured classes also admit a sublinear kernel.  ... 
arXiv:2105.09566v2 fatcat:udb6bfgylrbebeyz2iohs647v4

(Sub)linear Kernels for Edge Modification Problems Towards Structured Graph Classes

Gabriel Bathie, Nicolas Bousquet, Théo Pierron, Petr A. Golovach, Meirav Zehavi
2021
In a (parameterized) graph edge modification problem, we are given a graph G, an integer k and a (usually well-structured) class of graphs 𝒢, and ask whether it is possible to transform G into a graph  ...  Parameterized graph edge modification problems received considerable attention in the last decades. In this paper, we focus on finding small kernels for edge modification problems.  ...  I P E C 2 0 2 1 8:4 (Sub)linear Kernels for Edge Modification Problems FPT [6] . Ghosh et al.  ... 
doi:10.4230/lipics.ipec.2021.8 fatcat:sj75dcxxh5e7znrqjmpmqbznre

LEO: Line End Optimizer for Sub-7nm Technology Nodes

Diwesh Pandey, Gustavo E. Tellez, James Leland
2022 Proceedings of the 2022 International Symposium on Physical Design  
Our plugin consists of a practical line-end optimization (LEO) algorithm, which solves most line-end problems in a few minutes, even for very large designs.  ...  Sub-7nm technology nodes have introduced new challenges, specifically in the lower metal layers.  ...  . • A partitioning of the problem into sub-problems. • A solution to the LEO problem, which also returns unsolved sub-problems. • Rip-up and reroute of the wires and vias involved in the unsolved sub-problem  ... 
doi:10.1145/3505170.3506726 fatcat:fjts76wcdzgzzpa5olc666dzsm

Learning directed acyclic graph SPNs in sub-quadratic time

Amur Ghose, Priyank Jaini, Pascal Poupart
2020 International Journal of Approximate Reasoning  
Therefore, the problem we wish to solve is a k-way min cut problem for cutting edges so that the graph splits into k components and the edges that are cut have the smallest sum (or smallest maximum in  ...  Graph partitioning & maximum spanning tree Given a graph G = (V , E) with vertex set V and edge set E, the graph partitioning problem is to partition the graph G in to different components having certain  ... 
doi:10.1016/j.ijar.2020.01.005 fatcat:xnbnxmevxzc7vmr4cdo7dahfje

GADGET SVM: A Gossip-bAseD sub-GradiEnT Solver for Linear SVMs [article]

Haimonti Dutta, Nitin Nataraj
2018 arXiv   pre-print
In this paper, we present a distributed algorithm for learning linear Support Vector Machines in the primal form for binary classification called Gossip-bAseD sub-GradiEnT (GADGET) SVM.  ...  SVMs are extensively used for solving classification problems.  ...  Furthermore, DSVM always works towards optimality and can produce an -accurate solution for any > 0.  ... 
arXiv:1812.02261v1 fatcat:blv5j53wsvdavfkhaoyijpdpy4

RisGraph: A Real-Time Streaming System for Evolving Graphs [article]

Guanyu Feng, Zixuan Ma, Daixuan Li, Xiaowei Zhu, Yanzheng Cai, Wentao Han, Wenguang Chen
2020 arXiv   pre-print
The evaluation shows RisGraph can ingest millions of updates per second and its 99.9%ile latency is within 20 milliseconds for graphs with hundreds of millions of vertices and billions of edges on a single  ...  In processing these evolving graphs, the combination of update workloads (updating vertices and edges in a streaming manner) and analytical (performing graph algorithms incrementally) workloads is ubiquitous  ...  Meanwhile, the conclusions in Section 3 show that AFF is frequently small, therefore our data structure should be optimized towards faster modifications first.  ... 
arXiv:2004.00803v1 fatcat:fgrs6xtuwbagxdu2hy6o32bdka

An overview of kernelization algorithms for graph modification problems

Yunlong Liu, Jianxin Wang, Jiong Guo
2014 Tsinghua Science and Technology  
In this paper, we survey the kernelization algorithms for four types of graph modification problems, which include vertex deletion problems, edge editing problems, edge deletion problems, and edge completion  ...  Kernelization algorithms for graph modification problems are important ingredients in parameterized computation theory.  ...  Hence, in the reduced graph G 0 , jY .G 0 /j 2jX.G 0 /j results in a linear kernel for this problem.  ... 
doi:10.1109/tst.2014.6867517 fatcat:qp5ba7mwdfd3fjvei2n7of4khi

On the Complexity of Sequence to Graph Alignment [article]

Chirag Jain, Haowen Zhang, Yu Gao, Srinivas Aluru
2019 bioRxiv   pre-print
In this paper, we study sequence to graph alignment problems under Hamming and edit distance models, and linear and affine gap penalty functions, for multiple variants of the problem that allow changes  ...  For the case where only changes to the sequence are permitted, we present an O(|V|+m|E|) time algorithm, where m denotes the query size, and V and E denote the vertex and edge sets of the graph, respectively  ...  The deletion and insertion weighted edges in the alignment graph for linear gap penalty are shifted to deletion sub-graph and insertion sub-graph, respectively.  ... 
doi:10.1101/522912 fatcat:2avas7kkonbibmgjmjysko6aiq

An FPT Algorithm and a Polynomial Kernel for Linear Rankwidth-1 Vertex Deletion

Mamadou Moustapha Kanté, Eun Jung Kim, O-joung Kwon, Christophe Paul
2016 Algorithmica  
Motivated from the results on graph modification problems into graphs of bounded treewidth or pathwidth, we investigate a graph modification problem into the class of graphs having linear rankwidth at  ...  To fix this issue, we define the necklace graphs and investigate their structural properties. We also show that the LRW1-Vertex Deletion has a polynomial kernel.  ...  We consider the problem Linear rankwidth-w Vertex Deletion when w = 1. A next step is to investigate the problem for bigger w, or for any fixed w.  ... 
doi:10.1007/s00453-016-0230-z fatcat:awtnklgmqfg7ddt5uriqqodnx4

Extracting Biomolecular Interactions Using Semantic Parsing of Biomedical Text [article]

Sahil Garg, Aram Galstyan, Ulf Hermjakob, Daniel Marcu
2015 arXiv   pre-print
kernel learning framework to enable concurrent exploitation of automatically induced AMR (semantic) and dependency structure (syntactic) representations.  ...  previous approaches that infer relations on a sentence-by-sentence basis, we expand our framework to enable consistent predictions over sets of sentences (documents); (iii) We further modify and expand a graph  ...  We believe this notion of edge-similarly is quite general and will have applicability for a wider class of problems involving graph kernels.  ... 
arXiv:1512.01587v1 fatcat:ad6n6sx67ra5phu6n2xmkcw34m

A survey of kernels for structured data

Thomas Gärtner
2003 SIGKDD Explorations  
Development of kernels for structured data has mostly been motivated and guided by , real-world' problems .  ...  Instead, this paper intends to give an introduction to kernel functions defined on structured data. For that, we assume some basic familiarity with linear algebra.  ... 
doi:10.1145/959242.959248 fatcat:tw6wrmjndvbkbjw4g4jsycurhi

Graph Kernel Neural Networks [article]

Luca Cosmo, Giorgia Minello, Michael Bronstein, Emanuele Rodolà, Luca Rossi, Andrea Torsello
2021 arXiv   pre-print
In this paper, we propose to use graph kernels, i.e., kernel functions that compute an inner product on graphs, to extend the standard convolution operator to the graph domain.  ...  Our architecture allows to plug-in any type and number of graph kernels and has the added benefit of providing some interpretability in terms of the structural masks that are learned during the training  ...  These are often graph classification problems, where structure provides the most relevant information for classification, while node/edge features take a secondary role.  ... 
arXiv:2112.07436v1 fatcat:gdfwqmmtlvbhvnk7oiums7vhdi

Comparison of Descriptor Spaces for Chemical Compound Retrieval and Classification

Nikil Wale, George Karypis
2006 IEEE International Conference on Data Mining. Proceedings  
of the molecular graphs.  ...  statistically outperform previously developed schemes based on the widely used fingerprint-and Maccs keys-based descriptors, as well as recently introduced descriptors obtained by mining and analyzing the structure  ...  Frequent Sub-structures (FS) A number of methods have been proposed in recent years to find frequently occurring sub-structures in a chemical graph database [26, 32, 36, 51] .  ... 
doi:10.1109/icdm.2006.39 dblp:conf/icdm/WaleK06 fatcat:7xhqmjytn5gxjhorz3vdzquctu

Exact and Inexact Graph Matching: Methodology and Applications [chapter]

Kaspar Riesen, Xiaoyi Jiang, Horst Bunke
2010 Managing and Mining Graph Data  
The process of evaluating the similarity of graphs is referred to as graph matching. Two approaches to this task exist, viz. exact and inexact graph matching.  ...  The former approach aims at finding a strict correspondence between two graphs to be matched, while the latter is able to cope with errors and measures the difference of two graphs in a broader sense.  ...  The main problem of spectral methods is that they are rather sensitive towards structural errors, such as missing or spurious nodes.  ... 
doi:10.1007/978-1-4419-6045-0_7 dblp:series/ads/RiesenJB10 fatcat:mr2bpz5xwnbiva5x3mxbzqrnhm

Multi-scale Hierarchical Segmentation

L. D. Griffin, G. P. Robinson, A. C. F. Colchester
1993 Procedings of the British Machine Vision Conference 1993  
The problem occurs in those equivalence classes that have an internal edge stronger than some external edge. The remedy is simple. The weakest external edge of each equivalence class is determined.  ...  A pointer is set across the weakest edge of each object (i.e. towards the object with which it wants to merge first). This set of pointers groups the nodes into equivalence classes.  ... 
doi:10.5244/c.7.29 dblp:conf/bmvc/GriffinRC93 fatcat:fqjxxesnpbaczm2ra2mcq3766i
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