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A Naive Algorithm for Feedback Vertex Set [article]

Yixin Cao
2017 arXiv   pre-print
Given a graph on n vertices and an integer k, the feedback vertex set problem asks for the deletion of at most k vertices to make the graph acyclic.  ...  We show that a greedy branching algorithm, which always branches on an undecided vertex with the largest degree, runs in single-exponential time, i.e., O(c^k· n^2) for some constant c.  ...  Indeed, the research on parameterized algorithms and that on approximation algorithms for the feedback vertex set problem have undergone a similar process.  ... 
arXiv:1707.08684v2 fatcat:37dhpn2xingbpmihsytodby2hy

A Naive Algorithm for Feedback Vertex Set *

Yixin Cao
2018 licensed under Creative Commons License CC-BY 1st Symposium on Simplicity in Algorithms   unpublished
This motivates the study of parameterized algorithms for the feedback vertex set problem, i.e., algorithms that find a feedback vertex set of size at most k in time f (k) · n O(1).  ...  Given a graph G and an integer k, the feedback vertex set problem asks whether G has a feedback vertex set of at most k vertices.  ...  The author would like to thank O-joung Kwon and Saket Saurabh for pointing out a mistake in the introduction of a previous version.  ... 
fatcat:u3mpsstshbenleiqlnfvzlwani

Latent Space Model for Road Networks to Predict Time-Varying Traffic

Dingxiong Deng, Cyrus Shahabi, Ugur Demiryurek, Linhong Zhu, Rose Yu, Yan Liu
2016 Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD '16  
In this paper, we propose a Latent Space Model for Road Networks (LSM-RN) to address these challenges holistically.  ...  By conducting extensive experiments with a large volume of real-world traffic sensor data, we demonstrate the superiority of our framework for real-time traffic prediction on large road networks over competitors  ...  Each time when we make a prediction, we receive the true observations as the feedback. We compare our Incremental algorithm (Inc), with three baseline algorithms: Old, LSM-RN-Naive and LSM-RN-All.  ... 
doi:10.1145/2939672.2939860 dblp:conf/kdd/DengSDZYL16 fatcat:xywooi5wnbhavkrfj4csz7uyda

QSEAfor fuzzy subgraph querying of KEGG pathways

Thair Judeh, Tin Chi Nguyen, Dongxiao Zhu
2012 Proceedings of the ACM Conference on Bioinformatics, Computational Biology and Biomedicine - BCB '12  
Since hierarchies are only inherent in directed acyclic graphs, we have also developed a robust heuristic to heuristically solve the minimum feedback arc set problem.  ...  A plethora of existing techniques already allow for exact or approximate query matching.  ...  S Algorithm 2: Minimum feedback arc set removal 1: Input: An unweighted, directed graph G(V, E) with vertex set V and edge set E 2: using Tarjan's algorithm [24] 5: for i = 1,...  ... 
doi:10.1145/2382936.2382997 dblp:conf/bcb/JudehNZ12 fatcat:djj4fuv7krepvek2poxxo2k2dq

Latent Space Model for Road Networks to Predict Time-Varying Traffic [article]

Dingxiong Deng, Cyrus Shahabi, Ugur Demiryurek, Linhong Zhu, Rose Yu, Yan Liu
2016 arXiv   pre-print
In this paper, we propose a Latent Space Model for Road Networks (LSM-RN) to address these challenges.  ...  By conducting extensive experiments with a large volume of real-world traffic sensor data, we demonstrate the utility superiority of our framework for real-time traffic prediction on large road networks  ...  Each time when we make a prediction, we receive the true observations as the feedback. We compare our Incremental algorithm (Inc), with three baseline algorithms: Old, LSM-RN-Naive and LSM-RN-ALL.  ... 
arXiv:1602.04301v3 fatcat:wxkgr7llenaylj65orwcrjdyju

Parameterized Complexity of 1-Planarity [chapter]

Michael J. Bannister, Sergio Cabello, David Eppstein
2013 Lecture Notes in Computer Science  
A graph is 1-planar if it can be drawn in the plane (vertices as points, edges as curves disjoint from non-incident vertices) so that each edge is crossed at most once (in one point, by one edge) E.g.  ...  For future research: Make usable by reducing dependence on parameter Parameterize by feedback vertex set number?  ...  et al. 2005] Tree-depth: min depth of a tree such that every edge connects ancestor-descendant Kernelization for vertex cover For vertex cover and tree-depth, existence of a finite set of forbidden  ... 
doi:10.1007/978-3-642-40104-6_9 fatcat:ywrfrwdoc5dvlecebsfyrvhacm

Optimization of Pearl's method of conditioning and greedy-like approximation algorithms for the vertex feedback set problem

Ann Becker, Dan Geiger
1996 Artificial Intelligence  
A greedy algorithm, called GA, for the weighted vertex feedback set problem is ialso analyzed and bounds on its performance are given.  ...  The algorithm is based on a reduction to the weighted vertex feedback set problem and a 2-approximation of the latter problem.  ...  A minimum vertex feedback set of a weighted graph G with a weight function w is a vertex feedback set F* of G for which w(F*) is minimum over all vertex feedback sets of G.  ... 
doi:10.1016/0004-3702(95)00004-6 fatcat:3yh2jmjs7jdpxgxeoctmv3upkm

Editorial

David Fernández-Baca
2014 Algorithmica  
In A Generalization of the convex Kakeya problem, Ahn, Bae, Cheong, Gudmundsson,Tokuyama, and Vigneron answer an intriguing geometrical question: given a set of line segments in the plane, what is a convex  ...  They show that there is always an optimal region that is a triangle, and give an optimal algorithm to compute such a triangle.  ...  In The feedback arc set problem with triangle inequality is a vertex cover problem, Mastrolilli shows a surprising connection between feedback arc sets and minimum vertex covers in hypergraphs.  ... 
doi:10.1007/s00453-014-9900-x fatcat:q4pscfbejzcvxaxpze3ufrkiau

A Fully Polynomial Parameterized Algorithm for Counting the Number of Reachable Vertices in a Digraph [article]

Naoto Ohsaka
2021 arXiv   pre-print
Algorithms, 14(3):34:1–34:45, 2018]. We also show that the same result holds for vertex-weighted digraphs, where the task is to compute the total weights of vertices reachable from each vertex.  ...  In this paper, we present an 𝒪(f^3n)-time exact algorithm, where n is the number of vertices in G and f is the feedback edge number of G.  ...  It should be noted that we can omit the reachability set computation for some vertices, because MARK[u] = MARK[v] may hold for u Even when G is a polytree, i.e., m = n − 1, the naive algorithms show  ... 
arXiv:2103.04595v1 fatcat:iaaihfzse5gyrl7gsejoneg7ni

Enumerating Minimal Subset Feedback Vertex Sets

Fedor V. Fomin, Pinar Heggernes, Dieter Kratsch, Charis Papadopoulos, Yngve Villanger
2012 Algorithmica  
The Subset Feedback Vertex Set problem takes as input a pair (G, S), where G = (V, E) is a graph with weights on its vertices, and S ⊆ V .  ...  This is a consequence of the main result of this paper, namely that all minimal subset feedback vertex sets of a graph can be enumerated in time O(1.8638 n ).  ...  So far, this is the best known algorithm for Feedback Vertex Set.  ... 
doi:10.1007/s00453-012-9731-6 fatcat:36irkwu2ofdjjauootvjs3dsme

Enumerating Minimal Subset Feedback Vertex Sets [chapter]

Fedor V. Fomin, Pinar Heggernes, Dieter Kratsch, Charis Papadopoulos, Yngve Villanger
2011 Lecture Notes in Computer Science  
The Subset Feedback Vertex Set problem takes as input a pair (G, S), where G = (V, E) is a graph with weights on its vertices, and S ⊆ V .  ...  This is a consequence of the main result of this paper, namely that all minimal subset feedback vertex sets of a graph can be enumerated in time O(1.8638 n ).  ...  So far, this is the best known algorithm for Feedback Vertex Set.  ... 
doi:10.1007/978-3-642-22300-6_34 fatcat:tpmug2stpbdytdvajd5ewgwenm

Faster fixed parameter tractable algorithms for finding feedback vertex sets

Venkatesh Raman, Saket Saurabh, C. R. Subramanian
2006 ACM Transactions on Algorithms  
A feedback vertex set (fvs) of a graph is a set of vertices whose removal results in an acyclic graph.  ...  We also investigate the fixed parameter complexity of weighted feedback vertex set problem in weighted undirected graphs.  ...  Paulraja for fruitful discussions and comments on earlier drafts of the article, and Santosh Vempala for suggesting the direction for generalization in Theorem 3.  ... 
doi:10.1145/1159892.1159898 fatcat:yr2r4tetjffbbcxh5ug5lmmvwq

Efficient Partial Credit Grading of Proof Blocks Problems [article]

Seth Poulsen, Shubhang Kulkarni, Geoffrey Herman, Matthew West
2022 arXiv   pre-print
We propose a novel algorithm for finding the edit distance from an arbitrary student submission to some correct solution of a Proof Blocks problem.  ...  We benchmark our algorithm on thousands of student submissions from Fall 2020, showing that our novel algorithm can perform over 100 times better than the naive algorithm on real data.  ...  Our empirical analysis shows that this naïve approach will not scale to many students needing feedback at the same time (as in an active learning setting in a large classroom), or to problems of longer  ... 
arXiv:2204.04196v1 fatcat:d3sgzy5direxfpxtxqymxmhvda

Faster Fixed Parameter Tractable Algorithms for Undirected Feedback Vertex Set [chapter]

Venkatesh Raman, Saket Saurabh, C. R. Subramanian
2002 Lecture Notes in Computer Science  
A feedback vertex set (fvs) of a graph is a set of vertices whose removal results in an acyclic graph.  ...  We also investigate the fixed parameter complexity of weighted feedback vertex set problem in weighted undirected graphs.  ...  Paulraja for fruitful discussions and comments on earlier drafts of the article, and Santosh Vempala for suggesting the direction for generalization in Theorem 3.  ... 
doi:10.1007/3-540-36136-7_22 fatcat:x3msdxladjfl7npwsi5zzxzn5y

Identifying and Eliminating Inconsistencies in Mappings across Hierarchical Ontologies [chapter]

Bhavesh Sanghvi, Neeraj Koul, Vasant Honavar
2010 Lecture Notes in Computer Science  
We then explore several polynomial time algorithms for finding suboptimal solutions including a heuristic algorithm for (weighted) minimum feedback arc set problem in DAGs.  ...  Minimal weight feedback arc set. Compute the minimal weight feedback arc set FAS ⊆ E W for G W using Algorithm 3.8 as discussed in Section 3.6.5.  ...  The remaining subset is correct and does not cause any inconsistency in the combined ontology as the set that has been removed is corresponding to a feedback arc set that has been computed using a already  ... 
doi:10.1007/978-3-642-16949-6_24 fatcat:i7ntqmo7f5hdhpgc3qiggmwf7q
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