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Heuristic algorithms for the Maximum Colorful Subtree problem [article]

Kai Dührkop, Marie Anne Lataretu, W. Timothy J. White, Sebastian Böcker
2018 arXiv   pre-print
Here, we comprehensively evaluate the performance of several heuristic algorithms for the problem against an exact algorithm.  ...  In metabolomics, small molecules are structurally elucidated using tandem mass spectrometry (MS/MS); this resulted in the computational Maximum Colorful Subtree problem, which is NP-hard.  ...  Source code for all other heuristics will be made available upon request. Instances will be made available from our website.  ... 
arXiv:1801.07456v3 fatcat:itcnqkpesrhtlnzpcle2m7rml4

Heuristic Algorithms for the Maximum Colorful Subtree Problem

Kai Dührkop, Marie A. Lataretu, W. Timothy J. White, Sebastian Böcker, Michael Wagner
2018 Workshop on Algorithms in Bioinformatics  
Here, we comprehensively evaluate the performance of several heuristic algorithms for the problem.  ...  In metabolomics, small molecules are structurally elucidated using tandem mass spectrometry (MS/MS); this computational task can be formulated as the Maximum Colorful Subtree problem, which is NP-hard.  ...  Conclusion We have presented heuristics for the Maximum Colorful Subtree problem.  ... 
doi:10.4230/lipics.wabi.2018.23 dblp:conf/wabi/DuhrkopLWB18 fatcat:mvpcczjxwrhxjj4r7vai3lzylq

Finding Maximum Colorful Subtrees in Practice [chapter]

Imran Rauf, Florian Rasche, François Nicolas, Sebastian Böcker
2012 Lecture Notes in Computer Science  
log likelihood that they are real Maximum colorful subtree problem.  ...  There is no O(|V| 1−ε ) approximation algorithm for the Maximum Subtree problem for any ε > 0, unless P = NP. • every peak is created from only one fragment (no peak double counting) • every fragment originates  ... 
doi:10.1007/978-3-642-29627-7_22 fatcat:kq2ervbd7rhshoozwhqeipbqjm

Finding Maximum Colorful Subtrees in Practice

Imran Rauf, Florian Rasche, François Nicolas, Sebastian Böcker
2013 Journal of Computational Biology  
log likelihood that they are real Maximum colorful subtree problem.  ...  There is no O(|V| 1−ε ) approximation algorithm for the Maximum Subtree problem for any ε > 0, unless P = NP. • every peak is created from only one fragment (no peak double counting) • every fragment originates  ... 
doi:10.1089/cmb.2012.0083 pmid:23509858 fatcat:msyhhzicmvcwdivz5tn6je7vj4

Towards de novo identification of metabolites by analyzing tandem mass spectra

S. Bocker, F. Rasche
2008 Bioinformatics  
Unfortunately, finding this subtree is NP-hard. We suggest three exact algorithms (including one fixedparameter tractable algorithm) as well as two heuristics to solve the problem.  ...  Tests on real mass spectra show that the FPT algorithm and the heuristics solve the problem suitably fast and provide excellent results: for all 32 test compounds the correct solution was among the top  ...  for the manual identification of the fragmentation tree.  ... 
doi:10.1093/bioinformatics/btn270 pmid:18689839 fatcat:tpwxppijevcb3micppvtdo446u

Computing Fragmentation Trees from Metabolite Multiple Mass Spectrometry Data [chapter]

Kerstin Scheubert, Franziska Hufsky, Florian Rasche, Sebastian Böcker
2011 Lecture Notes in Computer Science  
We propose to use MS n data for the computation of fragmentation trees, and present the Colorful Subtree Closure problem to formalize this task: There, we search for a colorful subtree inside a vertex-colored  ...  We then present an exact dynamic programming algorithm, which is parameterized by the number of colors in the graph and is swift in practice.  ...  We thank Aleš Svatoš and Ravi Kumar Maddula from the Max Planck Institute for Chemical Ecology in Jena, Germany for supplying us with the test data. K.  ... 
doi:10.1007/978-3-642-20036-6_36 fatcat:ook5t6tzlba75fds34aqrgk5zm

Computing Fragmentation Trees from Metabolite Multiple Mass Spectrometry Data

Kerstin Scheubert, Franziska Hufsky, Florian Rasche, Sebastian Böcker
2011 Journal of Computational Biology  
We propose to use MS n data for the computation of fragmentation trees, and present the Colorful Subtree Closure problem to formalize this task: There, we search for a colorful subtree inside a vertex-colored  ...  We then present an exact dynamic programming algorithm, which is parameterized by the number of colors in the graph and is swift in practice.  ...  We thank Aleš Svatoš and Ravi Kumar Maddula from the Max Planck Institute for Chemical Ecology in Jena, Germany for supplying us with the test data. K.  ... 
doi:10.1089/cmb.2011.0168 pmid:22035289 fatcat:eswodvv2nrepfmdb4i7unucmhu

Multiple Mass Spectrometry Fragmentation Trees Revisited: Boosting Performance and Quality [chapter]

Kerstin Scheubert, Franziska Hufsky, Sebastian Böcker
2014 Lecture Notes in Computer Science  
We present an Integer Linear Program for solving the Combined Colorful Subtree problem, which is orders of magnitude faster than the currently best algorithm which is based on dynamic programming.  ...  Thus, we show for the first time that using MS n data can improve the quality of fragmentation trees.  ...  Acknowledgements We thank Aleš Svatoš and Ravi Kumar Maddula from the Max Planck Institute for Chemical Ecology in Jena, Germany for supplying us with the test data.  ... 
doi:10.1007/978-3-662-44753-6_17 fatcat:utyghm3sjbaapfmicx42mo3xyq

Automatically Generated Algorithms for the Vertex Coloring Problem

Carlos Contreras Bolton, Gustavo Gatica, Víctor Parada, Aaron Alain-Jon Golden
2013 PLoS ONE  
In this paper, we propose exploring the heuristics space for the vertex coloring problem using evolutionary algorithms.  ...  Some of the best computational results obtained for this problem are consequences of hybridizing the various known heuristics.  ...  The generated algorithms find optimum solutions for some problems, as do existing heuristics.  ... 
doi:10.1371/journal.pone.0058551 pmid:23516506 pmcid:PMC3596313 fatcat:gvwszcgtjzchvpcxozleodawki

Page 6844 of Mathematical Reviews Vol. , Issue 91M [page]

1991 Mathematical Reviews  
It turns out that with this linear order, the well-known greedy heuristic ‘always use the smallest available color’ yields an exact coloring algorithm for interval graphs.  ...  Introduction: “A linear time algorithm for the subtree isomorphism problem for rooted ordered trees has recently been presented by Makinen in the paper cited in the heading.  ... 

Some Modifications of Sugiyama Approach [chapter]

Danil E. Baburin
2002 Lecture Notes in Computer Science  
The main features of the algorithm are that the edges are orthogonal and that each edge has at most two bends.  ...  We present a graph drawing algorithm that was developed as an extension of the hierarchical layout method of Sugiyama [4] .  ...  Now our goal could be formulated in terms of a coloring problem for G'. Vertices of G' need to be colored in a minimum number of colors so that any adjusted vertices would have different colors.  ... 
doi:10.1007/3-540-36151-0_36 fatcat:hpvpnzff5bh45oblgu4qu26nsa

On an edge ranking problem of trees and graphs

Ananth.V. Iyer, H.Donald Ratliff, Gopalakrishnan Vijayan
1991 Discrete Applied Mathematics  
The main result in the paper is an O(n log n) time approximation algorithm for edge ranking of trees, which has a worst case performance ratio of 2.  ...  The edge ranking problem is that of finding the smallest k for which a graph has a k-edge ranking.  ...  We are, however, responsibie for errors, if any, in the manuscript,  ... 
doi:10.1016/0166-218x(91)90012-l fatcat:jszvuvywc5fvfjqkymg3b676yu

TRASA: TRaffic Aware Slot Assignment Algorithm in Wireless Sensor Networks [article]

Ichrak Amdouni, Pascale Minet (INRIA Rocquencourt)
2012 arXiv   pre-print
In this paper, we prove that the time slot assignment problem is NP-complete when p-hop nodes are not assigned the same slot, with 1 <= p <= h for any strictly positive integer h.  ...  We evaluate the performance of TRASA for different heuristics and prove that it provides an optimized spatial reuse and a minimized cycle length.  ...  Figure 4 (d) shows that the maximum size of buffers required by a node in heuristic = 1 is lower than in heuristic = 2.  ... 
arXiv:1209.2806v1 fatcat:q243sa3nsfgpbg2blohv2jerl4

TRASA: Traffic aware slot assignment algorithm in wireless sensor networks

Ichrak Amdouni, Pascale Minet
2012 2012 International Conference on Communications and Information Technology (ICCIT)  
Figure 4 (d) shows that the maximum size of buffers required by a node in heuristic = 1 is lower than in heuristic = 2.  ...  For the smallest color c i not yet considered, we add to the cycle a number of slots equal to the maximum traffic demand of nodes in N i , denoted max di .  ... 
doi:10.1109/iccitechnol.2012.6285816 fatcat:pr3f4nvsdfcahd2wxksyhdn5sa

Engineering an Efficient Canonical Labeling Tool for Large and Sparse Graphs [chapter]

Tommi Junttila, Petteri Kaski
2007 2007 Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments (ALENEX)  
Within the general framework of backtracking algorithms based on individualization and refinement, data structures, subroutines, and pruning heuristics especially for fast handling of large and sparse  ...  The problem of canonically labeling a graph is studied.  ...  The authors thank Jani Jaakkola and Pekka Niklander at the Department of Computer Science of University of Helsinki for providing computing resources for the experiments.  ... 
doi:10.1137/1.9781611972870.13 dblp:conf/alenex/JunttilaK07 fatcat:c5tcgchf5jfjbg5ww5l65k6gvu
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