Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Improved methods for approximating node weighted Steiner trees and connected dominating sets
Information and Computation
Performance guarantees for the TSP with a parameterized triangle inequality
Information Processing Letters
Power consumption in packet radio networks
Theoretical Computer Science
Polynomial-time approximation schemes for geometric graphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
On the Complexity of Computing Minimum Energy Consumption Broadcast Subgraphs
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Discrete & Computational Geometry
Minimum-cost coverage of point sets by disks
Proceedings of the twenty-second annual symposium on Computational geometry
Bounded-hop energy-efficient broadcast in low-dimensional metrics via coresets
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Geometric clustering to minimize the sum of cluster sizes
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Symmetric connectivity with directional antennas
Computational Geometry: Theory and Applications
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A fundamental class of problems in wireless communication is concerned with the assignment of suitable transmission powers to wireless devices/stations such that the resulting communication graph satisfies certain desired properties and the overall energy consumed is minimized. Many concrete communication tasks in a wireless network like broadcast, multicast, point-to-point routing, creation of a communication backbone, etc. can be regarded as such a power assignment problem.This paper considers several problems of that kind; the first problem was studied before in [1,6] and aims to select and assign powers to kout of a total of nwireless network stations such that all stations are within reach of at least one of the selected stations. We show that the problem can be (1 + 茂戮驴) approximated by only looking at a small subset of the input, which is of size , i.e. independent of nand polynomial in kand 1/茂戮驴. Here ddenotes the dimension of the space where the wireless devices are distributed, so typically d≤ 3 and describes the relation between the Euclidean distance between two stations and the power consumption for establishing a wireless connection between them. Using this coresetwe are able to improve considerably on the running time of $n^{((\alpha/\epsilon)^{O(d)})}$ for the algorithm by Bilo et al. at ESA'05 ([6]) actually obtaining a running time that is linearin n. Furthermore we sketch how outliers can be handled in our coreset construction.The second problem deals with the energy-efficient, bounded-hop multicast operation: Given a subset Cout of a set of nstations and a designated source node swe want to assign powers to the stations such that every node in Cis reached by a transmission from swithin khops. Again we show that a coreset of size independent of nand polynomial in k, |C|, 1/茂戮驴exists, and use this to provide an algorithm which runs in time linear in n.The last problem deals with a variant of non-metric TSP problem where the edge costs are the squared Euclidean distances; this problem is motivated by data aggregation schemes in wireless sensor networks. We show that a good TSP tour under Euclidean edge costs can be very bad in the squared distance measure and provide a simple constant approximation algorithm, partly improving upon previous results in [5], [4].