H. Huang, A. W. Richa, and M. Segal. Approximation Algorithms for the Mobile Piercing Set Problem with Applications to Clustering in Ad-hoc Networks. In International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (DIAL-M), pages 52--61, 2002.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....seven disks form a minimum cardinality covering. Figure 1 (a) shows PN(D; 2; 2) where q = x; y) is the center of the unit disk D. The coordinates of the six other points are (x ; y ) x; y ) This completes the proof of Lemma 1 (a more formal proof of this lemma can be found in [22]) Lemma 1 The neighborhood piercing number is equal to 2 for d dimensional space under L 1 and L1 norm. The neighborhood piercing number for 2 dimension and L 2 is equal to 7. For L 2 norm in , we were only able to place an upper bound on the number of unit disks needed to cover a ....

....to cover a disk of diameter 2, hence placing an upper bound on N(3; 2) A simple argument suces to verify that the 20 unit disks centered at the points listed in Table 4 plus a unit disk D centered at the origin cover a disk G of diameter two also centered at the origin. Hence we have N(3; 2) 21 [22]. It remains an open problem to compute the exact value of N(3; 2) The neighborhood piercing number for L 2 is closely related to the sphere packing and sphere covering problems described in [8] When compared to the known results in the literature, the approximation factors based on the ....

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H. Huang, A. W. Richa, and M. Segal. Approximation algorithms for the mobile piercing set problem with applications to clustering. Technical report, 2001. CSE, Arizona State University.

.... unit disk D, the Cartesian coordinates of the six other points are (x ; y 4 ) x; y 2 ) For L 2 norm in , we were only able to place an upper bound on the number of unit disks needed to cover a disk of diameter 2, hence placing an upper bound on N(3; 2) A simple argument [22] suces to verify that 20 unit disks centered at some evenly spaced points on the surface of G plus a unit disk D centered at the origin cover a disk G of diameter two also centered at the origin. Hence we have N(3; 2) 21. It remains an open problem to compute the exact value of N(3; 2) The ....

....respective centralized algorithms. The problem of computing N for other L p metrics is more involved and may not have many practical applications. A method to estimate an upper bound on N and compute the corresponding set of neighborhood piercing points for arbitrary L p metrics is discussed in [22] for completeness. 4 Better Approximation Factors In this section we present a family of constant factor fully distributed (decentralized) approximation algorithms for the piercing set problem, which at least match the best known approximation factors of 12 centralized algorithms for the ....

H. Huang, A. W. Richa, and M. Segal. Approximation algorithms for the mobile piercing set problem with applications to clustering. Technical Report TR-01-007, Dept. of Computer Sci. and Eng., Arizona State University, Tempe, AZ, 2001.

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H. Huang, A. W. Richa, and M. Segal. Approximation Algorithms for the Mobile Piercing Set Problem with Applications to Clustering in Ad-hoc Networks. In International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (DIAL-M), pages 52--61, 2002.

No context found.

H. Huang, A. W. Richa, and M. Segal. Approximation Algorithms for the Mobile Piercing Set Problem with Applications to Clustering in Ad-hoc Networks. In International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (DIAL-M), pages 52--61, 2002.

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