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IEEE/ACM Transactions on Networking (TON)
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Journal of the ACM (JACM)
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IEEE/ACM Transactions on Networking (TON)
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Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
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Two Algorithms for Three Dimensional Orthogonal Graph Drawing
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Hardness of Approximating Problems on Cubic Graphs
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
Energy-efficient broadcasting in ad-hoc networks: combining MSTs with shortest-path trees
PE-WASUN '04 Proceedings of the 1st ACM international workshop on Performance evaluation of wireless ad hoc, sensor, and ubiquitous networks
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Theoretical Computer Science
Asymptotic critical total power for k-connectivity of wireless networks
IEEE/ACM Transactions on Networking (TON)
Symmetric range assignment with disjoint MST constraints
Proceedings of the fifth international workshop on Foundations of mobile computing
Journal of Discrete Algorithms
Range assignment problem on the Steiner tree based topology in ad hoc wireless networks
Mobile Information Systems - Advances in Wireless Networks
Low-energy fault-tolerant bounded-hop broadcast in wireless networks
IEEE/ACM Transactions on Networking (TON)
Range assignment and λ-proximity in wireless sensor networks with a realistic physical layer
Proceedings of the 6th ACM symposium on Performance evaluation of wireless ad hoc, sensor, and ubiquitous networks
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WCNC'09 Proceedings of the 2009 IEEE conference on Wireless Communications & Networking Conference
Analysis of the bounded-hops converge-cast distributed protocol in ad-hoc networks
ALGOSENSORS'07 Proceedings of the 3rd international conference on Algorithmic aspects of wireless sensor networks
On alarm protocol in wireless sensor networks
ADHOC-NOW'10 Proceedings of the 9th international conference on Ad-hoc, mobile and wireless networks
Connecting a set of circles with minimum sum of radii
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
A distributed protocol for the bounded-hops converge-cast in ad-hoc networks
ADHOC-NOW'06 Proceedings of the 5th international conference on Ad-Hoc, Mobile, and Wireless Networks
Minimum energy broadcast and disk cover in grid wireless networks
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Low degree connectivity in ad-hoc networks
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Survivable network design problems in wireless networks
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On the hardness of range assignment problems
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Wireless communication in random geometric topologies
ALGOSENSORS'06 Proceedings of the Second international conference on Algorithmic Aspects of Wireless Sensor Networks
Optimal gossiping in directed geometric radio networks in presence of dynamical faults
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Topology Control in Cooperative Ad Hoc Wireless Networks
Electronic Notes in Theoretical Computer Science (ENTCS)
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Given a finite set S of points (i.e. the stations of a radio network) on a d-dimensional Euclidean space and a positive integer 1 ≤ h ≤ |S| - 1, the MIN d D h-RANGE ASSIGNMENT problem consists of assigning transmission ranges to the stations so as to minimize the total power consumption, provided that the transmission ranges of the stations ensure the communication between any pair of stations in at most h hops.Two main issues related to this problem are considered in this paper: the trade-off between the power consumption and the number of hops; the computational complexity of the MIN dD h-RANGE ASSIGNMENT problem.As for the first question, we provide a lower bound on the minimum power consumption of stations on the plane for constant h. The lower bound is a function of |S|, h and the minimum distance over all the pairs of stations in S. Then, we derive a constructive upper bound as a function of |S|, h and the maximum distance over all pairs of stations in S (i.e. the diameter of S). It turns out that when the minimum distance between any two stations is "not too small" (i.e. well spread instances) the upper bound matches the lower bound. Previous results for this problem were known only for very special 1-dimensional configurations (i.e., when points are arranged on a line at unitary distance) [Kirousis, Kranakis, Krizanc and Pelc, 1997].As for the second question, we observe that the tightness of our upper bound implies that MIN 2D h-RANGE ASSIGNMENT restricted to well spread instances admits a polynomial time approximation algorithm. Then, we also show that the same approximation result can be obtained for random instances. On the other hand, we prove that for h=|S|-1 (i.e. the unbounded case) MIN 2D h-RANGE ASSIGNMENT is NP-hard and MIN 3D h-RANGE ASSIGNMENT is APX-complete.