D. Blough, M. Leoncini, G. Resta, and P. Santi, "On the symmetric range assignment problem in wireless ad hoc networks," in Proc. of the 2nd IFIP International Conference on Theoretical Computer Science (TCS), 2002. [Online]. Available: citeseer.nj.nec.com/blough02symmetric.html  Home/Search   Document Details and Download   Summary   Related Articles   Check

....and n goes infinity. 2. 3 Literature Review The connectivity of random graphs, especially the geometric graphs and its variations, have been considered in the random graph theory literature [4] in the stochastic geometry literature [7, 20, 21, 22, 23] and the wireless ad hoc network literature [2, 3, 9, 10, 11, 18, 19, 30, 33]. Let s first consider the connectivity problem. Given n nodes V randomly and independently distributed in a unit area disk D, Gupta and Kumar [11] showed that G(V,rn ) is connected almost surely ln n c(n) for any c(n) with c(n) ##as goes infinity. Notice this bound is tight as they ....

D.M.Blough, M.Leoncini, G.Resta, and P.Santi. On the symmetric range assignment problem in wireless ad hoc networks. In Proc. 2nd IFIP Int. Conf. on Theoretical Computer Science, 2002.

....minimum value of r such that the r homogeneous range assignment is connecting. Note that HRA can be equivalently restated as the problem of finding a connecting homogeneous range assignment of minimum energy cost. RA and WSRA have been shown to be NP hard in the two and three dimensional cases [3, 7, 13], while HRA can be easily solved if node positions are known. HRA has been studied also in the case of nodes distributed according to some probability distribution [9, 24] In this paper, we are concerned with the following connectivity problem on the symmetric sub graph of the k neighbors graph. ....

....is questionable. For example, in [17] Marina and Das have shown that the high overhead needed to handle unidirectional links in routing protocols outweighs the benefits that they provide, and better performance can be achieved by simply avoiding unidirectional links; a recent theoretical result [3] has shown that the optimal solution to RA and WSRA have the same energy cost (asymptotically) In other words, starting from a strongly connected graph, obtaining a connected backbone of symmetric edges incurs in no additional (asymptotic) energy cost. Thus, having a connected backbone of ....

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D.M. Blough, M. Leoncini, G. Resta, P. Santi, "On the Symmetric Range Assignment Problem in Wireless Ad Hoc Networks", Proc. IFIP Conf. on Theoretical Computer Science, pp. 71-82, 2002.

....assignment r (S) such that cost(r (S) opt SC (S) where opt SC (S) is the optimal cost. The MstAlg algorithm also works when the input is a generic graph since the quality of the solution relies only on the properties of minimum spanning trees. Strong Connectivity with Symmetry. In [7, 6] another version of the Min Range(SC) problem is proposed. Here, in addition to the strong connectivity property, the communication graph must be symmetric. In the two papers it is observed that the proof of NP hardness in [13] Theorem 3) also holds for the symmetric case. Moreover, in [7] a 15 8 ....

D.M. Blough, M. Leoncini, G.Resta, and P. Santi. On the Symmetric Range Assignment Problem in Wireless Ad Hoc Networks. In Proceedings of the 2nd IFIP International Conference on Theoretical Computer Science (TCS), 2002. to appear.

.... , while the length of the longest edge in the MST is exactly the critical transmitting range [7, 22] The critical transmitting range in ad hoc networks has been studied in [11, 21, 25] The total edge length of the MST is closely related to the cost of the optimal transmitting range assignment [5, 14], while the Voronoi diagram and Delaunay triangulation, or derivation of these graphs, are used to construct spanners for power ecient routing [8] and in the evaluation of sensor networks coverage and exposure [18, 19] Finally, a subdivision of the deployment region into square cells is used, ....

D.M. Blough, M. Leoncini, G. Resta, P. Santi, \On the Symmetric Range Assignment Problem in Wireless Ad Hoc Networks", to appear in Proc. 2nd IFIP International Conference on Theoretical Computer Science, Montreal, August 2002.

....the message reception. Hence, a topology control mechanism which returns a symmetric range assignment is transparent to higher level protocols, which can continue to operate as the range assignment was homogeneous. Further motivations for studying SRA can be found in the full version of the paper [5]. From the discussion above it is clear that the symmetry of the range assignment is a useful property in the design of protocols for wireless ad hoc networks. However, it should be noted that what is really important is the existence of a set of symmetric edges that connect all the nodes in the ....

....SRA and HRA will be denoted c R , c WS , c S and c HR , respectively. By de nition, it is immediate that c R c WS c S c HR . 3. Complexity of SRA Due to space limitations, the proof that SRA (and, consequently, WSRA) for two and three dimensional networks is NP hard is not reported. See [5] for details. 4. Bounds on cWS In this section we investigate the cost of the optimal solution of WSRA and its relation with the cost of the solutions of other versions of the problem. We start by showing that c R and c WS have the same magnitude. Given a set V = fv 1 ; v n g of points in ....

D.M. Blough, M. Leoncini, G. Resta, P. Santi, \On the Symmetric Range Assignment Problem in Wireless Ad Hoc Networks", Tech. Rep. IMC-B4-01-07, Istituto di Matematica Computazionale del CNR, Pisa - Italy, Nov. 2001.

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D. Blough, M. Leoncini, G. Resta, and P. Santi, "On the symmetric range assignment problem in wireless ad hoc networks," in Proc. of the 2nd IFIP International Conference on Theoretical Computer Science (TCS), 2002. [Online]. Available: citeseer.nj.nec.com/blough02symmetric.html

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D.M.Blough, M.Leoncini, G.Resta, and P.Santi, "On the symmetric range assignment problem in wireless ad hoc networks," in Proc. 2nd IFIP International Conference on Theoretical Computer Science, 2002.

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D. Blough, M. Leoncini, G. Resta, and P. Santi. On the Symmetric Range Assignment Problem in Wireless Ad Hoc Networks. In Proceedings of the 2nd IFIP International Conference on Theoretical Computer Science (IFIP-TCS), pages 71--82, 2002.

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D.M. Blough, M. Leoncini, G. Resta, and P. Santi. On the symmetric range assignment problem in wireless ad hoc networks. In 2nd IFIP International Conference on Theoretical Computer Science (TCS 2002.

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D.M.Blough, M.Leoncini, G.Resta, and P.Santi. On the symmetric range assignment problem in wireless ad hoc networks. In Proc. 2nd IFIP Int. Conf. on Theoretical Computer Science, 2002.

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D. Blough, M. Leoncini, G. Resta, and P. Santi, \On the symmetric range assignment problem in wireless ad hoc networks," in 2nd IFIP International Conference on Theoretical Computer Science (TCS 2002). Kluwer Academic Publishers, 2002, pp. 71-82.

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D.M. Blough, M. Leoncini, G. Resta, and P. Santi, On the Symmetric Range Assignment Problem in Wireless Ad Hoc Networks, Proc. 2nd IFIP International Conference on Theoretical Computer Science, Montreal, August 2002.

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