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Stabbing Rectangles by Line Segments - How Decomposition Reduces the Shallow-Cell Complexity

://orcid.org/0000-0001-6553-7317 4 Timothy M. Chan University of Illinois at Urbana-Champaign , U.S.A 5 Alexander Wolff Universität Würzburg , Germany https://orcid.org/0000-0001-5872-718X 6 Joachim Spoerhase ... Optimal Set Covers in Finite VCDimension . Discrete Comput. Geom. , 14 ( 4 ): 463 - 479 , 1995 . doi: 10 .1007/BF02570718. Timothy M. Chan and Elyot Grant . Exact Algorithms and APX-hardness Results for

Tree Drawings Revisited

trees. In Proc. 29th Canadian Conference on Computational Geometry (CCCG), pages 232?237, 2017. URL: http://2017.cccg.ca/proceedings/Session6B-paper4.pdf. Timothy M. Chan. A near-linear area bound for ... drawing binary trees. Algorithmica, 34(1):1?13, 2002. doi:10.1007/s00453-002-0937-x. Timothy M. Chan, Michael T. Goodrich, S. Rao Kosaraju, and Roberto Tamassia. Optimizing area and aspect ration in

Approximate Shortest Paths and Distance Oracles in Weighted Unit-Disk Graphs

and n-body potential fields . Journal of the ACM , 42 ( 1 ): 67 - 90 , 1995 . doi: 10 .1145/200836.200853. Timothy M. Chan . A dynamic data structure for 3-d convex hulls and 2-d nearest neighbor ... queries . Journal of the ACM , 57 ( 3 ): 16 : 1 - 16 : 15 , 2010 . doi: 10 .1145/1706591.1706596. Timothy M. Chan and Dimitrios Skrepetos . All-pairs shortest paths in unit-disk graphs in slightly

Subquadratic Encodings for Point Configurations

-2312-0967 6 Timothy M. Chan Department of Computer Science, University of Illinois at Urbana-Champaign Champaign , IL , USA order types that allows efficient query of the orientation of any triple: the

Faster Approximate Diameter and Distance Oracles in Planar Graphs

sum of pairwise distances in planar graphs . CoRR , abs/1702.07815v1, 2017 . Timothy M. Chan . All-pairs shortest paths for unweighted undirected graphs in o(mn) time . ACM Transactions on Algorithms

Orthogonal Range Searching in Moderate Dimensions: k-d Trees and Range Trees Strike Back

Algorithms (SODA) , pages 218 - 230 , 2015 . Peyman Afshani , Timothy M. Chan , and Konstantinos Tsakalidis . Deterministic rectangle enclosure and offline dominance reporting on the RAM . In Proc. 41st Int'l ... Colloq. Automata, Languages, and Programming (ICALP) , Part I , pages 77 - 88 , 2014 . Josh Alman , Timothy M. Chan , and Ryan Williams . Polynomial representation of threshold functions with applications

Applications of Chebyshev Polynomials to Low-Dimensional Computational Geometry

. Josh Alman , Timothy M. Chan , and Ryan Williams . Polynomial representation of threshold functions and algorithmic applications . In Proc. 57th IEEE Symp. Found. Comput. Sci. (FOCS) , pages 467 - 476 ... nearest neighbor searching in fixed dimensions . J. ACM , 45 : 891 - 923 , 1998 . Preliminary version in SODA'94. Sunil Arya and Timothy M. Chan . Better ?-dependencies for offline approximate nearest

Dynamic Streaming Algorithms for Epsilon-Kernels

S o C G Dynamic Streaming Algorithms for ?-Kernels Timothy M. Chan 0 0 Cheriton School of Computer Science, University of Waterloo , Waterloo , Canada Introduced by Agarwal, Har-Peled, and ... on Discrete Algorithms , pages 447 - 452 , 2012 . ACM Trans. Algorithms , to appear. Sunil Arya and Timothy M. Chan . Better ?-dependencies for offline approximate nearest neighbor search, Euclidean

A Clustering-Based Approach to Kinetic Closest Pair

, 1995 . Timothy M. Chan and Zahed Rahmati . Approximating the minimum closest pair distance and nearest neighbor distances of linearly moving points . Computational Geometry , 2016 . Tom?s Feder and

Two Approaches to Building Time-Windowed Geometric Data Structures

17 18 19 20 21 22 23 24 25 26 27 Timothy M. Chan. Dynamic planar convex hull operations in near-logarithmaic amortized time. Journal of the ACM, 48(1):1?12, 2001. doi:10.1145/363647.363652. Timothy M ... . Chan. A fully dynamic algorithm for planar width. In Proceedings of the 17th Annual Symposium on Computational Geometry (SoCG), pages 172?176, 2001. Timothy M. Chan. A dynamic data structure for 3-d

A Simpler Linear-Time Algorithm for Intersecting Two Convex Polyhedra in Three Dimensions

, and Edgar A. Ramos . A randomized algorithm for triangulating a simple polygon in linear time . Discrete and Computational Geometry , 26 ( 2 ): 245 - 265 , 2001 . Timothy M. Chan . Deterministic

Approximation Algorithms for Maximum Independent Set of Pseudo-Disks

We present approximation algorithms for maximum independent set of pseudo-disks in the plane, both in the weighted and unweighted cases. For the unweighted case, we prove that a local-search algorithm yields a PTAS. For the weighted case, we suggest a novel rounding scheme based on an LP relaxation of the problem, which leads to a constant-factor approximation.Most previous...

Dynamic Coresets

Discrete Comput Geom Timothy M. Chan 0 0 T.M. Chan ( ) School of Computer Science, University of Waterloo , Waterloo, Ontario N2L 3G1 , Canada We give a dynamic data structure that can maintain an