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A Weakly Robust PTAS for Minimum Clique Partition in Unit Disk Graphs [chapter]

Imran A. Pirwani, Mohammad R. Salavatipour
2010 Lecture Notes in Computer Science  
We consider the problem of partitioning the set of vertices of a given unit disk graph (UDG) into a minimum number of cliques.  ...  Our main result is a weakly robust polynomial time approximation scheme (PTAS) for UDGs expressed with edge-lengths, it either (i) computes a clique partition or (ii) gives a certificate that the graph  ...  Acknowledgments We thank Sriram Pemmaraju, Lorna Stewart, and Zoya Svitkina for helpful discussions. Our thanks to an anonymous source for pointing out the result of Capoyleas et al. [4] .  ... 
doi:10.1007/978-3-642-13731-0_19 fatcat:hsqhdfy6arglhd7gtzdg3ycq6a

A Weakly Robust PTAS for Minimum Clique Partition in Unit Disk Graphs

Imran A. Pirwani, Mohammad R. Salavatipour
2011 Algorithmica  
We consider the problem of partitioning the set of vertices of a given unit disk graph (UDG) into a minimum number of cliques.  ...  Our main result is a weakly robust polynomial time approximation scheme (PTAS) for UDGs expressed with edge-lengths, it either (i) computes a clique partition or (ii) gives a certificate that the graph  ...  Acknowledgments We thank Sriram Pemmaraju, Lorna Stewart, and Zoya Svitkina for helpful discussions. Our thanks to an anonymous source for pointing out the result of Capoyleas et al. [4] .  ... 
doi:10.1007/s00453-011-9503-8 fatcat:atjx2d4nzzbehej7pyxtryz6fe

Treewidth-Pliability and PTAS for Max-CSPs [article]

Miguel Romero, Marcin Wrochna, Stanislav Živný
2020 arXiv   pre-print
We identify a sufficient condition, treewidth-pliability, that gives a polynomial-time approximation scheme (PTAS) for a large class of Max-2-CSPs parametrised by the class of allowed constraint graphs  ...  Treewidth-pliability turns out to be a robust notion that can be defined in several equivalent ways, including characterisations via size, treedepth, or the Hadwiger number.  ...  One example is intersection graphs of unit disks whose centers are at least some constant apart (capturing some applications of the closely related shifting technique of Hochbaum and Maass [HM85] for  ... 
arXiv:1911.03204v3 fatcat:po24s6f6zvh2zaqghlukgra4ie

Sentiment Analysis [chapter]

2017 Encyclopedia of Machine Learning and Data Mining  
A major challenge for the graph-based approaches is to find a balanced partitioning of the graph (e.g., in a degenerate scenario, one can propose an unbalanced, undesirable partition in which, except for  ...  The algorithm starts with the original graph and repeatedly adds random noise to the weights of the edges. Then, for each modified graph, it finds a partitioning by using minimum cuts.  ...  It might then be possible to learn, for example, that taking action action234 in state state42 is worth 6. 2 and leads to state state654321.  ... 
doi:10.1007/978-1-4899-7687-1_100512 fatcat:ce4yyqo2czftzcx2kbauglh3fu

Spike-Timing-Dependent Plasticity [chapter]

2017 Encyclopedia of Machine Learning and Data Mining  
A major challenge for the graph-based approaches is to find a balanced partitioning of the graph (e.g., in a degenerate scenario, one can propose an unbalanced, undesirable partition in which, except for  ...  The algorithm starts with the original graph and repeatedly adds random noise to the weights of the edges. Then, for each modified graph, it finds a partitioning by using minimum cuts.  ...  It might then be possible to learn, for example, that taking action action234 in state state42 is worth 6. 2 and leads to state state654321.  ... 
doi:10.1007/978-1-4899-7687-1_774 fatcat:2jprihjaxfbtpb3ttwuuz3u34y

Algorithm engineering in geometric network planning and data mining [article]

Martin P. Seybold, Universität Stuttgart, Universität Stuttgart
2019
Geometric Network Planning: In the d-dimensional Generalized Minimum Manhattan Network problem (d-GMMN) one is interested in finding a minimum cost rectilinear network N connecting a given set of n pairs  ...  graph [...]  ...  See Algorithm 5 for a search of a minimum bottleneck value path in G r .  ... 
doi:10.18419/opus-10217 fatcat:h7zw3iqvj5bnnmp3evwgampjkm

Dagstuhl Reports, Volume 5, Issue 3, March 2015, Complete Issue [article]

2015
Argument Sharing Exemplars Besides inspecting concrete example annotations in the AMR bank, a more general inventory of phenomena that cause reentrancies in semantic graphs due to argument sharing is of  ...  -Formal Models of Graph Transformation in Natural Language Processing  ...  point set [2] , or the problem of finding cliques of maximum size in the visiblity graph of a simple polygon [3, 4] .  ... 
doi:10.4230/dagrep.5.3 fatcat:frrv4bul5rhfhh3jo4hv5l5uoi

Birand_columbia_0054D_12551.pdf [article]

2017
As a result, the Internet is an extremely heterogeneous network in which a multitude of wireless, electronic, and optical devices coexist.  ...  In this thesis, we study cross-layer and cross-domain op-  ...  Although it is well-known that the unit disk model may not capture realistic connectivity relations [107] , it still provides a reasonable abstraction.  ... 
doi:10.7916/d82v2psm fatcat:blvxrsnpzbf7jekstnqzmxx52q