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Title: Algorithms for Intersection Graphs of t-Intervals and t-Pseudodisks
Intersection graphs of planar geometric objects such as intervals, disks, rectangles and pseudodisks are well-studied. Motivated by various applications, Butman et al. (ACM Trans. Algorithms, 2010) considered algorithmic questions in intersection graphs of $$t$$-intervals. A $$t$$-interval is a union of $$t$$ intervals --- these graphs are also referred to as multiple-interval graphs. Subsequent work by Kammer et al.\ (APPROX-RANDOM 2010) considered intersection graphs of $$t$$-disks (union of $$t$$ disks), and other geometric objects. In this paper we revisit some of these algorithmic questions via more recent developments in computational geometry. For the \emph{minimum-weight dominating set problem} in $$t$$-interval graphs, we obtain a polynomial-time $$O(t \log t)$$-approximation algorithm, improving upon the previously known polynomial-time $t^2$-approximation by Butman et al. In the same class of graphs we show that it is $$\NP$$-hard to obtain a $$(t-1-\epsilon)$$-approximation for any fixed $$t \ge 3$$ and $$\epsilon > 0$$. The approximation ratio for dominating set extends to the intersection graphs of a collection of $$t$$-pseudodisks (nicely intersecting $$t$$-tuples of closed Jordan domains). We obtain an $$\Omega(1/t)$$-approximation for the \emph{maximum-weight independent set} in the intersection graph of $$t$$-pseudodisks in polynomial time. Our results are obtained via simple reductions to existing algorithms by appropriately bounding the union complexity of the objects under consideration.  more » « less
Award ID(s):
1910149
PAR ID:
10348203
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Theory of computing
Volume:
18
ISSN:
1557-2862
Page Range / eLocation ID:
1-18
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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