A unified approach to approximation algorithms for bottleneck problems
Journal of the ACM (JACM)
Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Erratum: generalized selection and ranking: sorted matrices
SIAM Journal on Computing
Approximation algorithms for hitting objects with straight lines
Discrete Applied Mathematics
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Rectilinear and polygonal p-piercing and p-center problems
Proceedings of the twelfth annual symposium on Computational geometry
Multicluster, mobile, multimedia radio network
Wireless Networks
Hierarchically-organized, multihop mobile wireless networks for quality-of-service support
Mobile Networks and Applications - Special issue: mobile multimedia communications
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Data structures for mobile data
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Exact and approximation algorithms for clustering
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Mobile facility location (extended abstract)
DIALM '00 Proceedings of the 4th international workshop on Discrete algorithms and methods for mobile computing and communications
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Dynamic Data Structures for Fat Objects and Their Applications
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Fast Stabbing of Boxes in High Dimensions
Proceedings of the 8th Canadian Conference on Computational Geometry
Distributed Clustering for Ad Hoc Networks
ISPAN '99 Proceedings of the 1999 International Symposium on Parallel Architectures, Algorithms and Networks
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Adaptive clustering for mobile wireless networks
IEEE Journal on Selected Areas in Communications
A mobility-based framework for adaptive clustering in wireless ad hoc networks
IEEE Journal on Selected Areas in Communications
Ad-hoc networks beyond unit disk graphs
DIALM-POMC '03 Proceedings of the 2003 joint workshop on Foundations of mobile computing
Ad hoc networks beyond unit disk graphs
Wireless Networks
Algorithmic models of interference in wireless ad hoc and sensor networks
IEEE/ACM Transactions on Networking (TON)
Algorithms for sensor and ad hoc networks: advanced lectures
Algorithms for sensor and ad hoc networks: advanced lectures
Hi-index | 0.00 |
The main contributions of this paper are two-fold. First, we present a simple, general framework for obtaining efficient constant-factor approximation algorithms for the mobile piercing set (MPS) problem on unit-disks for standard metrics in fixed dimension vector spaces. More specifically, we provide low constant approximations for L1- and L∞-norms on a d-dimensional space, for any fixed d 0, and for the L2-norm on 2- and 3-dimensional spaces. Our framework provides a family of fully-distributed and decentralized algorithms, which adapts (asymptotically) optimally to the mobility of disks, at the expense of a low degradation on the best known approximation factors of the respective centralized algorithms: Our algorithms take O(1) time to update the piercing set maintained, per movement of a disk. We also present a family of fully-distributed algorithms for the MPS problem which either match or improve the best known approximation bounds of centralized algorithms for the respective norms and dimensions.Second, we show how the proposed algorithms can be directly applied to provide theoretical performance analyses for two popular 1-hop clustering algorithms in ad-hoc networks: the lowest-id algorithm and the Least Cluster Change (LCC) algorithm. More specifically, we formally prove that the LCC algorithm adapts in constant time to the mobility of the network nodes, and minimizes (up to low constant factors) the number of 1-hop clusters maintained; we propose an alternative algorithm to the lowest-id algorithm which achieves a better approximation factor without increasing the cost of adapting to changes in the network topology. While there is a vast literature on simulation results for the LCC and the lowest-id algorithms, these had not been formally analysed prior to this work. We also present an O(log n)-approximation algorithm for the mobile piercing set problem for nonuniform disks (i.e., disks that may have different radii), with constant update time.