TY - GEN
T1 - Online Range Assignment Problems
AU - Carmi, Paz
AU - Katz, Matthew J.
AU - Tomer, Idan
N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
PY - 2025/1/1
Y1 - 2025/1/1
N2 - We study two online range assignment problems. In the first problem, introduced by de Berg et al. [4], P is a growing set of transceivers, initially consisting of a single transceiver p1. Upon the arrival of a new transceiver pi, one needs to (re)assign a range to at most one of the ‘previous’ transceivers, so that pi is covered by at least one of them. We adopt the common rule that a transceiver’s range (which is initially 0) can never decrease over time. The cost of such an online range assignment is ∑i=1nρ(pi), where ρ(pi) is the final range assigned to pi, and we wish to compare it with the cost of an optimal offline assignment which satisfies the intermediate coverage requirements. We present several results for this problem, which improve some of the previous results of de Berg et al. [4]. We also introduce a new problem, in which we have a set T of stationary transmitters and an initially-empty set S of mobile receivers. Upon the arrival of a new receiver s, it must first specify its intended route, after which one needs to (re)assign a range to at most one of the transmitters in T, so that s’s route is fully covered by at least one of them. We consider the case where the routes of the receivers are unit line segments and prove a constant factor upper bound on the competitive ratio of our range assignment algorithm.
AB - We study two online range assignment problems. In the first problem, introduced by de Berg et al. [4], P is a growing set of transceivers, initially consisting of a single transceiver p1. Upon the arrival of a new transceiver pi, one needs to (re)assign a range to at most one of the ‘previous’ transceivers, so that pi is covered by at least one of them. We adopt the common rule that a transceiver’s range (which is initially 0) can never decrease over time. The cost of such an online range assignment is ∑i=1nρ(pi), where ρ(pi) is the final range assigned to pi, and we wish to compare it with the cost of an optimal offline assignment which satisfies the intermediate coverage requirements. We present several results for this problem, which improve some of the previous results of de Berg et al. [4]. We also introduce a new problem, in which we have a set T of stationary transmitters and an initially-empty set S of mobile receivers. Upon the arrival of a new receiver s, it must first specify its intended route, after which one needs to (re)assign a range to at most one of the transmitters in T, so that s’s route is fully covered by at least one of them. We consider the case where the routes of the receivers are unit line segments and prove a constant factor upper bound on the competitive ratio of our range assignment algorithm.
KW - broadcast
KW - competitive analysis
KW - online algorithms
KW - range assignment
UR - http://www.scopus.com/inward/record.url?scp=105006793401&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-92932-8_5
DO - 10.1007/978-3-031-92932-8_5
M3 - Conference contribution
SN - 9783031929311
T3 - Lecture Notes in Computer Science
SP - 68
EP - 82
BT - Algorithms and Complexity - 14th International Conference, CIAC 2025, Proceedings
A2 - Finocchi, Irene
A2 - Georgiadis, Loukas
PB - Springer Science and Business Media Deutschland GmbH
T2 - 14th International Conference on Algorithms and Complexity, CIAC 2025
Y2 - 10 June 2025 through 12 June 2025
ER -