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Using Graph Algorithms to Pretrain Graph Completion Transformers
Jonathan Pilault, Michael Galkin, Bahare Fatemi, Perouz Taslakian, David Vasquez, Christopher Pal
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The four bars problem
A four-bar linkage is a mechanism consisting of four rigid bars which are joined by their endpoints in a polygonal chain and which can …
Alexandre Mauroy, Perouz Taslakian, Stefan Langerman, Raphaël Jungers
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Necklaces, Convolutions, and X + Y
We give subquadratic algorithms that, given two necklaces each with $n$ beads at arbitrary positions, compute the optimal rotation of …
David Bremner, Timothy M. Chan, Erik D. Demaine, Jeff Erickson, Ferran Hurtado, John Iacono, Stefan Langerman, Mihai P̌atraşcu, Perouz Taslakian
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New and Improved Spanning Ratios for Yao Graphs
For a set of points in the plane and a fixed integer $k > 0$, the Yao graph $Y_k$ partitions the space around each point into $k$ …
Luis Barba, Prosenjit Bose, Mirela Damian, Rolf Fagerberg, Wah Loon Keng, Joseph O'Rourke, André van Renssen, Perouz Taslakian, Sander Verdonschot, Ge Xia
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Theta-3 is connected
In this paper, we show that the $Θ$-graph with three cones is connected. We also provide an alternative proof of the connectivity of …
Oswin Aichholzer, Sang Won Bae, Luis Barba, Prosenjit Bose, Matias Korman, André van Renssen, Perouz Taslakian, Sander Verdonschot
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Coloring and Guarding Arrangements
Given a simple arrangement of lines in the plane, what is the minimum number c of colors required so that we can color all lines in a …
Prosenjit Bose, Jean Cardinal, Sébastien Collette, Ferran Hurtado, Matias Korman, Stefan Langerman, Perouz Taslakian
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Non-crossing Matchings of Points with Geometric Objects
Greg Aloupis, Jean Cardinal, Sébastien Collette, Erik D. Demaine, Martin L. Demaine, Muriel Dulieu, Ruy Fabila-Monroy, Vi Hart, Ferran Hurtado, Stefan Langerman, Maria Saumell, Carlos Seara, Perouz Taslakian
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Transversals in Trees
A transversal in a rooted tree is any set of nodes that meets every path from the root to a leaf. We let c(T,k) denote the number of …
Victor Campos, Văsek Chvátal, Luc Devroye, Perouz Taslakian
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Colorful Strips
Given a planar point set and an integer $k$, we wish to color the points with $k$ colors so that any axis-aligned strip containing …
Greg Aloupis, Jean Cardinal, Sébastien Collette, Shinji Imahori, Matias Korman, Stefan Langerman, Oded Schwartz, Shakhar Smorodinsky, Perouz Taslakian
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The Distance Geometry of Music
We demonstrate relationships between the classic Euclidean algorithm and many other fields of study, particularly in the context of …
Erik D. Demaine, Francisco Gomez-Martin, Henk Meijer, David Rappaport, Perouz Taslakian, Godfried T. Toussaint, Terry Winograd, David R. Wood
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