TY - GEN
T1 - Line segment covering of cells in arrangements
AU - Korman, Matias
AU - Poon, Sheung Hung
AU - Roeloffzen, Marcel
N1 - Funding Information:
M. Korman—Partially supported by the ELC project (MEXT KAKENHI No. 24106008).
Publisher Copyright:
© Springer International Publishing Switzerland 2015.
PY - 2015
Y1 - 2015
N2 - Given a collection L of line segments, we consider its arrangement and study the problem of covering all cells with line segments of L. That is, we want to find a minimum-size set L′ of line segments such that every cell in the arrangement has a line from L′ defining its boundary. We show that the problem is NP-hard, even when all segments are axis-aligned. In fact, the problem is still NP-hard when we only need to cover rectangular cells of the arrangement. For the latter problem we also show that it is fixed parameter tractable with respect to the size of the optimal solution. Finally we provide a linear time algorithm for the case where cells of the arrangement are created by recursively subdividing a rectangle using horizontal and vertical cutting segments.
AB - Given a collection L of line segments, we consider its arrangement and study the problem of covering all cells with line segments of L. That is, we want to find a minimum-size set L′ of line segments such that every cell in the arrangement has a line from L′ defining its boundary. We show that the problem is NP-hard, even when all segments are axis-aligned. In fact, the problem is still NP-hard when we only need to cover rectangular cells of the arrangement. For the latter problem we also show that it is fixed parameter tractable with respect to the size of the optimal solution. Finally we provide a linear time algorithm for the case where cells of the arrangement are created by recursively subdividing a rectangle using horizontal and vertical cutting segments.
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U2 - 10.1007/978-3-319-26626-8_12
DO - 10.1007/978-3-319-26626-8_12
M3 - Conference contribution
AN - SCOPUS:84951927772
SN - 9783319266251
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 152
EP - 162
BT - Combinatorial Optimization and Applications - 9th International Conference, COCOA 2015, Proceedings
A2 - Kim, Donghyun
A2 - Wu, Weili
A2 - Du, Ding-Zhu
A2 - Lu, Zaixin
A2 - Li, Wei
PB - Springer Verlag
T2 - 9th International Conference on Combinatorial Optimization and Applications, COCOA 2015
Y2 - 18 December 2015 through 20 December 2015
ER -