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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...

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

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...

Stabbing Pairwise Intersecting Disks by Five Points

69978 , Israel 4 Department of Computer Science, University of Illinois , Urbana, IL 61801, USA , USA 5 Sariel Har-Peled 6 School of Computer Science, Tel Aviv