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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...

Conflict-Free Coloring of Points and Simple Regions in the Plane

Discrete Comput Geom Geometry Discrete & Computational Sariel Har-Peled 0 Shakhar Smorodinsky 1 0 Department of Computer Science, University of Illinois , 201 N. Goodwin Avenue, Urbana, IL 61801

Edge Estimation with Independent Set Oracles

. Aronov and S. Har-Peled . On Approximating the Depth and Related Problems . SIAM J. Comput. , 38 ( 3 ): 899 - 921 , 2008 . Paul Beame , Sariel Har-Peled, Sivaramakrishnan Natarajan Ramamoorthy, Cyrus

Finding a Guard that Sees Most and a Shop that Sells Most

Discrete Comput Geom Geometry Discrete & Computational Otfried Cheong 2 Alon Efrat 1 Sariel Har-Peled 0 0 Department of Computer Science, University of Illinois , 201 N. Goodwin Avenue, Urbana ... , The School of Information Technology, KAIST, and that by Sariel Har-Peled was partially supported by NSF CAREER award CCR-0132901. - We consider two problems where our goal is to find a point x such

From Proximity to Utility: A Voronoi Partition of Pareto Optima

We present an extension of Voronoi diagrams where not only the distance to the site is taken into account when considering which site the client is going to use, but additional attributes (i.e., prices or weights) are also considered. A cell in this diagram is then the loci of all clients that consider the same set of sites to be relevant. In particular, the precise site a client...

Optimally Cutting a Surface into a Disk

DMR-0121695. Sariel Har-Peled was partially supported by NSF CAREER Award CCR-0132901. of a sphere, where the texture is also embedded on a sphere.) Of course, when cutting the surface, one would like

Robust Shape Fitting via Peeling and Grating Coresets

Let P be a set of n points in ℝ d . A subset \(\mathcal {S}\) of P is called a (k,ε)-kernel if for every direction, the directional width of \(\mathcal {S}\) ε-approximates that of P, when k “outliers” can be ignored in that direction. We show that a (k,ε)-kernel of P of size O(k/ε (d−1)/2) can be computed in time O(n+k 2/ε d−1). The new algorithm works by repeatedly “peeling...

Shortest Path in a Polygon using Sublinear Space

We resolve an open problem due to Tetsuo Asano, showing how to compute the shortest path in a polygon, given in a read only memory, using sublinear space and subquadratic time. Specifically, given a simple polygon P with n vertices in a read only memory, and additional working memory of size m, the new algorithm computes the shortest path (in P) in O(n^2 / m) expected time...

Stabbing Pairwise Intersecting Disks by Five Points

69978 , Israel 4 Department of Computer Science, University of Illinois , Urbana, IL 61801, USA https://orcid.org/0000-0003-2638-9635 , USA 5 Sariel Har-Peled 6 School of Computer Science, Tel Aviv