TY - GEN
T1 - Maintenance of a piercing set for intervals with applications
AU - Katz, Matthew J.
AU - Nielsen, Frank
AU - Segal, Michael
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2000.
PY - 2000/1/1
Y1 - 2000/1/1
N2 - We show how to efficiently maintain a minimum piercing set for a set S of intervals on the line, under insertions and deletions to/from S. A linear-size dynamic data structure is presented, which enables us to compute a new minimum piercing set following an insertion or deletion in time O(c(S) log |S|), where c(S) is the size of the new minimum piercing set. We also show how to maintain a piercing set for S of size at most (1+ε)c(S), for 0 < ε ≤ 1, in (formula presented) amortized time per update. We then apply these results to obtain efficient (sometimes improved) solutions to the following three problems: (i) the shooter location problem, (ii) computing a minimum piercing set for arcs on a circle, and (iii) dynamically maintaining a box cover for a d-dimensional point set.
AB - We show how to efficiently maintain a minimum piercing set for a set S of intervals on the line, under insertions and deletions to/from S. A linear-size dynamic data structure is presented, which enables us to compute a new minimum piercing set following an insertion or deletion in time O(c(S) log |S|), where c(S) is the size of the new minimum piercing set. We also show how to maintain a piercing set for S of size at most (1+ε)c(S), for 0 < ε ≤ 1, in (formula presented) amortized time per update. We then apply these results to obtain efficient (sometimes improved) solutions to the following three problems: (i) the shooter location problem, (ii) computing a minimum piercing set for arcs on a circle, and (iii) dynamically maintaining a box cover for a d-dimensional point set.
UR - http://www.scopus.com/inward/record.url?scp=84949810725&partnerID=8YFLogxK
U2 - 10.1007/3-540-40996-3_47
DO - 10.1007/3-540-40996-3_47
M3 - Conference contribution
AN - SCOPUS:84949810725
SN - 3540412557
SN - 9783540412557
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 552
EP - 563
BT - Algorithms and Computation - 11th International Conference, ISAAC 2000, Proceedings
A2 - Lee, D.T.
A2 - Teng, Shang-Hua
A2 - Teng, Shang-Hua
PB - Springer Verlag
T2 - 11th Annual International Symposium on Algorithms and Computation, ISAAC 2000
Y2 - 18 December 2000 through 20 December 2000
ER -