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Approximation Algorithms for Generalized MST and TSP in Grid Clusters [article]

Binay Bhattacharya, Ante Ćustić, Akbar Rafiey, Arash Rafiey, Vladyslav Sokol
2015 arXiv   pre-print
We give a (1+4√(2)+ϵ) and (1.5+8√(2)+ϵ)-approximation algorithm for these two problems in the described setting, respectively.  ...  Our motivation is based on the problem posed in [7] for a constant approximation algorithm.  ...  Acknowledgment: We would like to thank Geoffrey Exoo for many usefull discussions.  ... 
arXiv:1507.04438v1 fatcat:bu3wz75myfevblogdzy2rs77b4

Approximating the minimum weight spanning tree of a set of points in the Hausdorff metric

Victor Alvarez, Raimund Seidel
2010 Computational geometry  
We show that if the weight of MST(P ) is to be approximated, then in general Q must be large. If the shape of MST(P ) is to be approximated, then this is always possible with a small Q.  ...  We study the problem of approximating MST(P ), the minimum weight spanning tree of a set P of n points in [0, 1] d , by a spanning tree of some subset Q ⊂ P .  ...  Acknowledgements The first author was supported by IMPRS-CS, the International Max-Planck Reseach School for Computer Science, and also by the Research Training Group 623 "Performance Guarantees for Computer  ... 
doi:10.1016/j.comgeo.2009.04.005 fatcat:4r4hfnkgrrhq7k5fabmmoi6yoe

Solving the Large-Scale TSP Problem in 1 h: Santa Claus Challenge 2020

Radu Mariescu-Istodor, Pasi Fränti
2021 Frontiers in Robotics and AI  
The scalability of traveling salesperson problem (TSP) algorithms for handling large-scale problem instances has been an open problem for a long time.  ...  We arranged a so-called Santa Claus challenge and invited people to submit their algorithms to solve a TSP problem instance that is larger than 1 M nodes given only 1 h of computing time.  ...  Solving TSP for one cluster would require O(N) time and O(N 1.5 ) for all √N clusters. With our data (≈1.4 M points), we would have approximately 1,200 clusters.  ... 
doi:10.3389/frobt.2021.689908 pmid:34671647 pmcid:PMC8520904 fatcat:7gsikz4oo5blpb7d76gzlcrxhu

2D and 3D Traveling Salesman Problem

Yll Haxhimusa, Edward Carpenter, Joseph Catrambone, David Foldes, Emil Stefanov, Laura Arns, Zygmunt Pizlo
2011 Journal of Problem Solving  
clustering in a 3D space and coarse-to-fine production of a tour.  ...  The same algorithm can account for the results with 2D and 3D problems, which suggests that deterioration of performance in the 3D space can be attributed to geometrical relations between hierarchical  ...  Y.H. was also partially supported by FWF-P20134-N13 and FWF-S9103-N04.  ... 
doi:10.7771/1932-6246.1096 fatcat:tmyvcd5uorgk5gqzrolpaqhaga

Clustering, Randomness, and Regularity: Spatial Distributions and Human Performance on the Traveling Salesperson Problem and Minimum Spanning Tree Problem

Matthew Dry, Kym Preiss, Johan Wagemans
2012 Journal of Problem Solving  
Following this we report an experiment in which the participants were asked to solve TSP and MST-P test stimuli that had been generated to be either highly clustered, random, or highly regular.  ...  The results indicate that for both the TSP and MST-P the participants tended to produce better quality solutions when the stimuli were highly clustered compared to random, and similarly, better quality  ...  For the regular stimuli we initially generated stimuli in which the nodes were uniformly distributed in a 7x7 grid.  ... 
doi:10.7771/1932-6246.1117 fatcat:u52afxdwzzhyxckvan5w4rfsfm

A Novel Feature-Based Approach to Characterize Algorithm Performance for the Traveling Salesman Problem [article]

Olaf Mersmann, Bernd Bischl, Heike Trautmann, Markus Wagner, Frank Neumann
2012 arXiv   pre-print
With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem (TSP).  ...  We take a statistical approach and examine the features of TSP instances that make the problem either hard or easy to solve.  ...  Acknowledgements This work was partly supported by the Collaborative Research Center SFB 823, the Graduate School of Energy Efficient Production and Logistics and the Research Training Group "Statistical  ... 
arXiv:1208.2318v1 fatcat:mh7xoop2bjedjlbenvgjryupz4

Approximative graph pyramid solution of the E-TSP

Yll Haxhimusa, Walter G. Kropatsch, Zygmunt Pizlo, Adrian Ion
2009 Image and Vision Computing  
Isolating processing used by humans to solve computationally hard problems is of general importance to psychology community and might lead to advances in pattern recognition.  ...  Expanding this tour solution in a top-down manner, to the lower levels of the pyramid, leads to an approximate solution.  ...  We also thank Andreas Lehrbaum and Joe Catrambone for their help in performing the experimental results.  ... 
doi:10.1016/j.imavis.2008.06.016 fatcat:yjxkfkwxejakrdmwcabgpxdg4i

A feature-based comparison of local search and the christofides algorithm for the travelling salesperson problem

Samadhi Nallaperuma, Markus Wagner, Frank Neumann, Bernd Bischl, Olaf Mersmann, Heike Trautmann
2013 Proceedings of the twelfth workshop on Foundations of genetic algorithms XII - FOGA XII '13  
We use an evolutionary algorithm approach to construct easy and hard instances for the Christofides algorithm, where we measure hardness in terms of approximation ratio.  ...  With this paper, we contribute to this research direction and carry out a feature based comparison of local search and the well-known Christofides approximation algorithm for the Traveling Salesperson  ...  Different TSP instance sizes are considered for the analysis. Cities are generated in [0, 1] 2 and placed on a discretised grid enabling cross comparison of features.  ... 
doi:10.1145/2460239.2460253 dblp:conf/foga/Nallaperuma0NBMT13 fatcat:ptivc7zxyjb53doa3jt4lwxhfe

The Traveling Salesman Problem under Squared Euclidean Distances

Fred Van Nijnatten, René Sitters, Gerhard J. Woeginger, Alexander Wolff, Mark De Berg, Marc Herbstritt
2010 Symposium on Theoretical Aspects of Computer Science  
We design a 5-approximation algorithm for Tsp(2,2) and generalize this result to obtain an approximation factor of 3 α−1 + √ 6 α /3 for d = 2 and all α 2.  ...  We present a polynomial-time approximation scheme for Rev-Tsp(2, α) with α 2, and we show that Rev-Tsp(d, α) is apx-hard if d 3 and α > 1.  ...  The algorithm of Bender and Chekuri is a 2 α+1 -approximation for Tsp( · , α).  ... 
doi:10.4230/lipics.stacs.2010.2458 dblp:conf/stacs/NijnattenSWWB10 fatcat:kbwl6mbmtjf2ziqr2xts575mju

The Traveling Salesman Problem Under Squared Euclidean Distances [article]

Mark de Berg and Fred van Nijnatten and René Sitters and Gerhard J. Woeginger and Alexander Wolff
2010 arXiv   pre-print
We design a 5-approximation algorithm for TSP(2,2) and generalize this result to obtain an approximation factor of 3^α-1+√(6)^α/3 for d=2 and all α>2.  ...  We present a polynomial-time approximation scheme for Rev-TSP(2,α) with α>2, and we show that Rev-TSP(d, α) is APX-hard if d>3 and α>1.  ...  The algorithm of Bender and Chekuri is a 2 α+1 -approximation for Tsp( · , α).  ... 
arXiv:1001.0236v3 fatcat:dk2ic7bm2rhalgzsfv5bwfnzwe

A novel feature-based approach to characterize algorithm performance for the traveling salesperson problem

Olaf Mersmann, Bernd Bischl, Heike Trautmann, Markus Wagner, Jakob Bossek, Frank Neumann
2013 Annals of Mathematics and Artificial Intelligence  
With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesperson problem (TSP).  ...  We take a statistical approach and examine the features of TSP instances that make the problem either hard or easy to solve.  ...  Acknowledgements This work was partly supported by the Collaborative Research Center SFB 823, the Graduate School of Energy Efficient Production and Logistics and the Research Training Group "Statistical  ... 
doi:10.1007/s10472-013-9341-2 fatcat:ylefkojfzrfypmkat5oguirs7y

Lossless Geometry Compression for Steady-State and Time-Varying Irregular Grids [article]

Dan Chen, Yi-Jen Chiang, Nasir Memon, Xiaolin Wu
2006 EUROVIS 2005: Eurographics / IEEE VGTC Symposium on Visualization  
In this paper we investigate the problem of lossless geometry compression of irregular-grid volume data represented as a tetrahedral mesh.  ...  We propose a novel lossless compression technique that effectively predicts, models, and encodes geometry data for both steady-state (i.e., with only a single time step) and time-varying datasets.  ...  Minimum Spanning Tree (MST) based approximation algorithm.  ... 
doi:10.2312/vissym/eurovis06/275-282 fatcat:2lconznkefcjfkuzfseuzrfbx4

Parameter Prediction Based on Features of Evolved Instances for Ant Colony Optimization and the Traveling Salesperson Problem [chapter]

Samadhi Nallaperuma, Markus Wagner, Frank Neumann
2014 Lecture Notes in Computer Science  
In this paper, we build a parameter prediction model for the Traveling Salesperson problem based on features of evolved instances.  ...  Understanding the reasons for the performance and the influence of its different parameter settings has become an interesting problem.  ...  We thank Bernd Bischl for early discussions, Heike Trautmann and Olaf Mersmann for the feedback on the preliminary version of this research.  ... 
doi:10.1007/978-3-319-10762-2_10 fatcat:4igqg3tbhnhwvfmsa35x6m5st4

Streaming Algorithms for Geometric Steiner Forest [article]

Artur Czumaj, Shaofeng H.-C. Jiang, Robert Krauthgamer, Pavel Veselý
2021 arXiv   pre-print
We complement our streaming algorithm for the Steiner forest problem with simple arguments showing that any finite approximation requires Ω(k) bits of space.  ...  Each input point x∈ X arrives with its color (x) ∈ [k], and as usual for dynamic geometric streams, the input points are restricted to the discrete grid {0, ..., Δ}^2.  ...  In fact, the currently best streaming algorithms known for TSP and Steiner tree only achieve O(1)-approximation, and follow by a trivial application of the MST streaming algorithm.  ... 
arXiv:2011.04324v3 fatcat:7pq4rn7v7fc5xliauchjsnd2ty

Power Assignment Problems in Wireless Communication [article]

Stefan Funke, Soeren Laue, Zvi Lotker, Rouven Naujoks
2006 arXiv   pre-print
Further results include a constant approximation algorithm for the TSP problem under squared (non-metric!)  ...  We improve the running time for obtaining a (1+ϵ)-approximate solution for this problem from n^((α/ϵ)^O(d)) as reported by Bilo et al.  ...  Why Euclidean TSP does not work A 6-Approximation Algorithm In this section we will describe an algorithm which computes a 6-approximation for the TSP under squared Euclidean distance.  ... 
arXiv:cs/0612121v1 fatcat:cdjjn5mskngflm4ebiilgc65ua
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