Conict-free coloring of intersection graphs of geometric objects

Chaya Keller, Shakhar Smorodinsky

نتاج البحث: فصل من :كتاب / تقرير / مؤتمرمنشور من مؤتمرمراجعة النظراء

6 اقتباسات (Scopus)

ملخص

In FOCS'2002, Even et al. introduced and studied the notion of conflict-free colorings of geometrically defined hypergraphs. They motivated it by frequency assignment problems in cellular networks. This notion has been extensively studied since then. A conflict-free coloring of a graph is a coloring of its vertices such that the neighborhood (pointed or closed) of each vertex contains a vertex whose color differs from the colors of all other vertices in that neighborhood. In this paper we study conflictfree colorings of intersection graphs of geometric objects. We show that any intersection graph of n pseudo-discs in the plane admits a conflict-free coloring with O(log n) colors, with respect to both closed and pointed neighborhoods. We also show that the latter bound is asymptotically sharp. Using our methods, we obtain the following strengthening of the two main results of Even et al.: Any family F of n discs in the plane can be colored with O(log n) colors in such a way that for any disc B in the plane, the set of discs in F that intersect B contains a uniquely-colored element. Moreover, such a coloring can be computed deterministically in polynomial time. In view of the original motivation to study such colorings, this strengthening suggests further applications to frequency assignment in wireless networks. Finally, we present bounds on the number of colors needed for conflict-free colorings of other classes of intersection graphs, including intersection graphs of axis-parallel rectangles and of ?-fat objects in the plane.

اللغة الأصليةالإنجليزيّة
عنوان منشور المضيف29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
المحررونArtur Czumaj
الصفحات2397-2411
عدد الصفحات15
رقم المعيار الدولي للكتب (الإلكتروني)9781611975031
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - 2018
منشور خارجيًانعم
الحدث29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 - New Orleans, الولايات المتّحدة
المدة: ٧ يناير ٢٠١٨١٠ يناير ٢٠١٨

سلسلة المنشورات

الاسمProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

!!Conference

!!Conference29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
الدولة/الإقليمالولايات المتّحدة
المدينةNew Orleans
المدة٧/٠١/١٨١٠/٠١/١٨

بصمة

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