TY - GEN

T1 - Balanced line separators of unit disk graphs

AU - Carmi, Paz

AU - Chiu, Man Kwun

AU - Katz, Matthew J.

AU - Korman, Matias

AU - Okamoto, Yoshio

AU - Van Renssen, André

AU - Roeloffzen, Marcel

AU - Shiitada, Taichi

AU - Smorodinsky, Shakhar

N1 - Funding Information:
Chiu, van Renssen and Roeloffzen were supported by JST ERATO Grant Number JPMJER1305, Japan. Korman was supported in part by KAKENHI Nos. 12H00855 and 17K12635. Katz was partially supported by grant 1884/16 from the Israel Science Foundation. Okamoto was partially supported by KAKENHI Grant Numbers JP24106005, JP24220003 and JP15K00009, JST CREST Grant Number JPMJCR1402, and Kayamori Foundation for Informational Science Advancement. Smorodinsky’s research was partially supported by Grant 635/16 from the Israel Science Foundation.
Publisher Copyright:
© Springer International Publishing AG 2017.

PY - 2017

Y1 - 2017

N2 - We prove a geometric version of the graph separator theorem for the unit disk intersection graph: for any set of n unit disks in the plane there exists a line ℓ such that ℓ intersects at most O(Formula presented) disks and each of the halfplanes determined by ℓ contains at most 2n/3 unit disks from the set, where m is the number of intersecting pairs of disks. We also show that an axis-parallel line intersecting O(Formula presented) disks exists, but each halfplane may contain up to 4n/5 disks. We give an almost tight lower bound (up to sublogarithmic factors) for our approach, and also show that no line-separator of sublinear size in n exists when we look at disks of arbitrary radii, even when m = 0. Proofs are constructive and suggest simple algorithms that run in linear time. Experimental evaluation has also been conducted, which shows that for random instances our method outperforms the method by Fox and Pach (whose separator has size O(Formula presented m)).

AB - We prove a geometric version of the graph separator theorem for the unit disk intersection graph: for any set of n unit disks in the plane there exists a line ℓ such that ℓ intersects at most O(Formula presented) disks and each of the halfplanes determined by ℓ contains at most 2n/3 unit disks from the set, where m is the number of intersecting pairs of disks. We also show that an axis-parallel line intersecting O(Formula presented) disks exists, but each halfplane may contain up to 4n/5 disks. We give an almost tight lower bound (up to sublogarithmic factors) for our approach, and also show that no line-separator of sublinear size in n exists when we look at disks of arbitrary radii, even when m = 0. Proofs are constructive and suggest simple algorithms that run in linear time. Experimental evaluation has also been conducted, which shows that for random instances our method outperforms the method by Fox and Pach (whose separator has size O(Formula presented m)).

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U2 - 10.1007/978-3-319-62127-2_21

DO - 10.1007/978-3-319-62127-2_21

M3 - Conference contribution

AN - SCOPUS:85025160302

SN - 9783319621265

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 241

EP - 252

BT - Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings

A2 - Ellen, Faith

A2 - Kolokolova, Antonina

A2 - Sack, Jorg-Rudiger

PB - Springer Verlag

T2 - 15th International Symposium on Algorithms and Data Structures, WADS 2017

Y2 - 31 July 2017 through 2 August 2017

ER -