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Interactive Planarization and Optimization of 3D Meshes

Roi Poranne, Elena Ovreiu, Craig Gotsman
2013 Computer graphics forum (Print)  
Specifically, polyhedral meshes -those having planar faces -are very important, but also notoriously difficult to generate and manipulate efficiently.  ...  We describe an interactive method for computing, optimizing and editing polyhedral meshes.  ...  We would also like to thank Philippe Block and Lorenz Lachauer for introducing us to the optimal lifting problem and the meshes in Fig. 4. C. Gotsman's work was partially supported by the B. and G.  ... 
doi:10.1111/cgf.12005 fatcat:32sugisk5zbuxehkouho4hhgjq

Strip Planarity Testing [chapter]

Patrizio Angelini, Giordano Da Lozzo, Giuseppe Di Battista, Fabrizio Frati
2013 Lecture Notes in Computer Science  
We show that the problem is polynomial-time solvable if G has a fixed planar embedding.  ...  In this paper we introduce and study the strip planarity testing problem, which takes as an input a planar graph G(V, E) and a function γ : V → {1, 2, . . . , k} and asks whether a planar drawing of G  ...  A celebrated result of Hopcroft and Tarjan [20] states that the planarity testing problem is solvable in linear time.  ... 
doi:10.1007/978-3-319-03841-4_4 fatcat:tcn2wccmvfefblzuevhebnqnp4

The complexity of the locally connected spanning tree problem

Leizhen Cai
2003 Discrete Applied Mathematics  
On the other hand, we obtain a linear-time algorithm for ÿnding a locally connected spanning tree in a directed path graph, and a linear-time algorithm for adding fewest edges to a graph to make a given  ...  We prove that the problem of determining whether a graph contains a locally connected spanning tree is NP-complete, even when input graphs are restricted to planar graphs or split graphs.  ...  On the other hand, we will give a linear-time algorithm for ÿnding a locally connected spanning tree in a directed path graph, and a linear-time algorithm for adding fewest edges to a graph to make a given  ... 
doi:10.1016/s0166-218x(02)00417-1 fatcat:sfncnok4ozdc5pkddvkrt5omsm

A Decoupled and Linear Framework for Global Outlier Rejection over Planar Pose Graph [article]

Tianyue Wu, Fei Gao
2022 arXiv   pre-print
It turns out that it runs significantly (sometimes up to over 30 times) faster than the standard and general-purpose GNC while resulting in high-quality estimates.  ...  Thanks to the linearity properties of both the subproblems, our framework requires only linear solvers to optimally solve the optimization problems encountered in GNC.  ...  Decoupling the TLS-based robust PGO problem and introducing a linear representation for planar rotation are the keys to the proposed framework.  ... 
arXiv:2209.08543v1 fatcat:6haz6dogl5gbdniza6jnfkm6ni

Predecessor existence problems for finite discrete dynamical systems

Chris Barrett, Harry B. Hunt, Madhav V. Marathe, S.S. Ravi, Daniel J. Rosenkrantz, Richard E. Stearns, Mayur Thakur
2007 Theoretical Computer Science  
problem -deciding whether there is a unique predecessor and the AMBIGUOUS-PREDECESSOR EXISTENCE (or APRE) problem -given a configuration C and a predecessor C of C, deciding whether there is a different  ...  Our results extend the earlier results of Green, Sutner and Orponen on the complexity of the predecessor existence problem and its variants.  ...  UPRE is D P -complete for (BOOL, S, PLANAR)-SDSs (SyDSs).  ... 
doi:10.1016/j.tcs.2007.04.026 fatcat:gv7e6yrrq5cstp5amuxgfsrqhy

Designing Practical PTASes for Minimum Feedback Vertex Set in Planar Graphs [article]

Glencora Borradaile, Hung Le, Baigong Zheng
2018 arXiv   pre-print
We present two algorithms for the minimum feedback vertex set problem in planar graphs: an O(n n) PTAS using a linear kernel and balanced separator, and a heuristic algorithm using kernelization and local  ...  And our heuristic algorithm can outperform the 2-approximation algorithm on most large planar graphs and provide a trade-off between running time and solution quality, i.e. a "PTAS behavior".  ...  If the function h(k) is linear in k, then we say the problem admits a linear kernel. Bonamy and Kowalik's linear kernel for planar FVS [9] consists of a sequence of 17 reduction rules.  ... 
arXiv:1804.07869v1 fatcat:nrvw3s55f5emxmtgkfywlwwp7e

Analysis situs and image processing [chapter]

Fridrich Sloboda, Bedrich Zat'ko
1997 Lecture Notes in Computer Science  
Furthermore, a new linear time algorithm for the shortest path problem solution is described, and the approximation of the most important characteristic set in image processing is shown.  ...  In the paper a topological approach to approximation of planar Jordan curves and arcs is described.  ...  In view of Theorem 5, Step (4) has linear time complexity which implies that Algorithm has also linear time complexity.  ... 
doi:10.1007/3-540-63507-6_201 fatcat:lmadhfzupfgndk62cyv3igrdf4

Stability of self-similar solutions for van der Waals driven thin film rupture

Thomas P. Witelski, Andrew J. Bernoff
1999 Physics of Fluids  
Of these, the dynamically stable similarity solutions produce observable rupture behavior as localized, finite-time singularities in the models of the flow.  ...  In this letter we describe a systematic technique for calculating such solutions and determining their linear stability.  ...  ACKNOWLEDGMENTS We are indebted to Wendy Zhang and John Lister for sharing a preprint 2 of their work with us, and to Andrea Bertozzi for enlightening conversations about thin films and self-similarity  ... 
doi:10.1063/1.870138 fatcat:jeew5bh4bfgg3e444kzatpxhna

EEG source localization by multi-planar analytic sensing

D. Kandaswamy, T. Blu, L. Spinelli, C. Michel, D. Van De Ville
2008 2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro  
The estimation of the projection on each plane of the dipoles' positions, which is a non-linear problem, is reduced to polynomial root finding.  ...  Source localization from EEG surface measurements is an important problem in neuro-imaging. We propose a new mathematical framework to estimate the parameters of a multidipole source model.  ...  Each 2-D localization provides us with the projection of the dipoles' positions and moments onto the respective plane. The paper is organized as follows. In Sect. 2, we introduce the problem setting.  ... 
doi:10.1109/isbi.2008.4541186 dblp:conf/isbi/KandaswamyBSMV08 fatcat:5dyqvqdhcbbsvgcvaaytoykw54

Subject Index

2006 Journal of Discrete Algorithms  
algorithms for weighted problems in sparse graphs, 588 Minimum-weight independent set Distributed algorithms for weighted problems in sparse graphs, 588 Monotonic Linear time isotonic and unimodal  ...  The strength of weak proximity, 384 VLSI design Delay optimization of linear depth boolean cir- cuits with prescribed input arrival times, 526 Weighted flow time Online weighted flow time and deadline  ... 
doi:10.1016/s1570-8667(06)00094-3 fatcat:e5in7ez4svbdlcjyzzev4xkzhm

Checking the convexity of polytopes and the planarity of subdivisions

Olivier Devillers, Giuseppe Liotta, Franco P. Preparata, Roberto Tamassia
1998 Computational geometry  
In particular, we design simple optimal checkers for convex polytopes in two and higher dimensions, and for various types of planar subdivisions, such as triangulations, Delaunay triangulations, and convex  ...  This paper considers the problem of verifying the correctness of geometric structures.  ...  Acknowledgements We would like to thank Giuseppe Di Battista, Michael Goodrich, David Kirkpatrick and Luca Vismara for useful discussions.  ... 
doi:10.1016/s0925-7721(98)00039-x fatcat:y3eox33r2rfolf4qeri63hrire

Checking the convexity of polytopes and the planarity of subdivisions (extended abstract) [chapter]

O. Devillers, G. Liotta, F. P. Preparata, R. Tamassia
1997 Lecture Notes in Computer Science  
In particular, we design simple optimal checkers for convex polytopes in two and higher dimensions, and for various types of planar subdivisions, such as triangulations, Delaunay triangulations, and convex  ...  This paper considers the problem of verifying the correctness of geometric structures.  ...  Acknowledgments We w ould like to thank Giuseppe Di Battista, Michael Goodrich, David Kirkpatrick, and Luca Vismara for useful discussions.  ... 
doi:10.1007/3-540-63307-3_59 fatcat:lbpnbl3qbjefbgq7uyuvwx2wai

Connectivity check in 3-connected planar graphs with obstacles

Bruno Courcelle, Cyril Gavoille, Mamadou Moustapha Kanté, Andrew Twigg
2008 Electronic Notes in Discrete Mathematics  
Such embeddings can be constructed in linear time by Schnyder's algorithm [9] (see also [6, 7] ).  ...  A connectivity query asks whether there exists in the given graph a path linking u and v that avoids a set F of edges and a set X of vertices.  ...  Thorup [10] shows that a planar digraph can be preprocessed in near-linear time, producing a near-linear space oracle that can answer reachability queries in constant time.  ... 
doi:10.1016/j.endm.2008.06.030 fatcat:iwpmuccqobfkjcmqqyyimavhcy

Dichotomy Results for Fixed-Point Existence Problems for Boolean Dynamical Systems [article]

Sven Kosub
2008 arXiv   pre-print
The following dichotomy theorems are shown: (1) If F contains the self-dual functions and G contains the planar graphs then the fixed-point existence problem for (F, G)-systems with local transition function  ...  existence problem for (F, G)-systems with local transition function given by formulas or circuits is NP-complete; otherwise, it is decidable in polynomial time.  ...  Mayr (TU München) for careful proofreading and pointing out an error in earlier versions of this paper.  ... 
arXiv:0801.3802v2 fatcat:c4o6mzrkojdahhz3pp6hlmtkii

Page 5635 of Mathematical Reviews Vol. , Issue 96i [page]

1996 Mathematical Reviews  
“Variational principles are applied to generate numerical solu- tions to the full non-linear problems.  ...  This is another interesting paper by the author in which he proves the blow-up and asymptotics of thermal runaway in the non-local problem u; = uxx +Af(u)/(f', f(u)dx)?  ... 
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