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Topology Control Problems 1911. We show that if the diameter constraint cannot be violated, the 〈Undir, Diameter,TotalP〉 problem cannot be approximated to within an Ω(log n)factor unless P = NP. This result holds even when the diameter boundD = 2. (Note that the problem is trivial when D = 1.)2. We show that using any (α, β)-approximation algorithm for the Mctdcproblem, one can devise a (2α, 2(1− 1/n) β)-approximation algorithm for〈Undir, Diameter, TotalP〉 problem. This result is based on a generalframework presented in [10] for approximating the total power objective.Utilizing this general framework and known bicriteria approximations forthe Mctdc problem, we obtain several bicriteria approximation algorithmsfor the 〈Undir, Diameter, TotalP〉 problem. (See Section 4.2.)3. For every fixed integer ∆ ≥ 2, we show that the 〈Undir, Deg LB, TotalP〉problem is NP-complete. Also, we present an approximation algorithm witha performance guarantee of 2(∆+1)(1−1/n) for the problem. This algorithmproduces a power assignment that induces a connected graph in which eachnode has degree at least ∆. The performance guarantee is with respect to theoptimal total power value. (Details regarding these results will be includedin a complete version of this paper.)4. While the above results are under the symmetric power threshold model, weconsider the 〈Undir, Connected, TotalP〉 problem under the asymmetricpower threshold model. We show that the problem cannot be approximatedto within an Ω(log n) factor unless P = NP. We also presentan O(log n) approximation algorithm for the problem.3.2 Related WorkReference [10] provides a general approach that leads to an approximation frameworkfor minimizing total power. Using that framework, two new approximationalgorithms for 〈Undir, 2-Node Connected, TotalP〉 and 〈Undir, 2-Edge Connected, TotalP〉 with an asymptotic approximation ratio of 8 arepresented in [10]. Both of the approximation ratios are improved to 4 in [6]. Reference[3] shows that the 〈Dir, Strongly Connected, TotalP〉 problem isNP-complete and presents a 2-approximation algorithm for the problem. Calinescuet al. [4] improve the approximation ratio to (1+ln 2). The approximationratio is further improved to 5/3 in a journal submission based on [4].4 Results for Diameter Problems4.1 Lower Bound on ApproximationThe following theorem can be proven using an approximation preserving reductionfrom the Minimum Set Cover (Msc) problem. The proof is omitted dueto space constraint.
192 S.O. Krumke et al.1. From the given problem instance, construct the undirected complete edge weightedgraph G c(V,E c), where the weight of each edge {u, v} in E c is equal to the powerthreshold value p(u, v).2. Use any approximation algorithm A for the Mctdc problem on graph G c(V,E c)with diameter bound 2D, and obtain a spanning tree T (V,E T )ofG c.3. For each node (transceiver) u, assign a power value f(u) equal to the weight of thelargest edge incident on u in T .Fig. 1. Outline of Heuristic Gen-Diameter-Total-PowerTheorem 1. Let n denote the number of nodes in an instance of the〈Undir, Diameter, TotalP〉 problem. There is a constant δ 1 , 0
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Lecture Notes in Computer Science 2
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Samuel Pierre Michel BarbeauEvangel
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PrefaceAd Hoc Networks are wireless
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Program CommitteeG. Alonso, ETHZ, S
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XTable of ContentsResisting Malicio
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2 H. Dubois-Ferrière, M. Grossglau
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10 H. Dubois-Ferrière, M. Grossgla
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SAFAR: An Adaptive Bandwidth-Effici
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14 J. Doshi and P. Kilambiour proto
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16 J. Doshi and P. Kilambipacket th
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18 J. Doshi and P. Kilambibandwidth
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20 J. Doshi and P. Kilambi5 Simulat
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22 J. Doshi and P. Kilambiquery its
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24 J. Doshi and P. Kilambi4. David
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26 P. Narayan and V.R. SyrotiukThe
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28 P. Narayan and V.R. Syrotiuk2.2
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30 P. Narayan and V.R. Syrotiukrand
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32 P. Narayan and V.R. Syrotiukenti
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34 P. Narayan and V.R. SyrotiukDSRA
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36 P. Narayan and V.R. Syrotiuk7. A
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38 L. Qin and T. Kunzthese two prot
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40 L. Qin and T. Kunzsidered broken
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42 L. Qin and T. KunzP = Prdlog( )
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46 L. Qin and T. KunzFig. 5. Averag
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48 L. Qin and T. Kunz6. J. Broch et
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50 M. Diha and S. Pierrethe propose
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52 M. Diha and S. Pierre3. All proc
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54 M. Diha and S. Pierre3.3 Perform
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56 M. Diha and S. PierreCmip/Cprop0
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58 M. Diha and S. PierreThe tunneli
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Proactive QoS Routing in Ad Hoc Net
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62 Y. Ge, T. Kunz, and L. LamontFig
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64 Y. Ge, T. Kunz, and L. Lamontits
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66 Y. Ge, T. Kunz, and L. Lamonttha
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68 Y. Ge, T. Kunz, and L. Lamontwhi
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70 Y. Ge, T. Kunz, and L. Lamontver
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Delivering Messagesin Disconnected
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74 R. Shah and N.C. Hutchinson3.1 T
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76 R. Shah and N.C. Hutchinsonset c
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78 R. Shah and N.C. HutchinsonTable
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80 R. Shah and N.C. HutchinsonOracl
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82 R. Shah and N.C. Hutchinsonthe r
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Extending Seamless IP Multicast Edg
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86 P.M. Ruiz et al.Section 4 presen
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88 P.M. Ruiz et al.Access NetworkCo
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90 P.M. Ruiz et al.Access NetworkR
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92 P.M. Ruiz et al.MIGAccess Networ
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94 P.M. Ruiz et al.10.90.81-hop-750
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A Uniform Continuum Model for Scali
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98 E.W. Grundke and A.N. Zincir-Hey
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100 E.W. Grundke and A.N. Zincir-He
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102 E.W. Grundke and A.N. Zincir-He
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Probabilistic Protocols for Node Di
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106 G. Alonso et al.A node discover
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108 G. Alonso et al.frequency alloc
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110 G. Alonso et al.- D is a diagon
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112 G. Alonso et al.and therefore,
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114 G. Alonso et al.complicated. Fo
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Towards Adaptive WLAN Frequency Man
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118 F. Gamba, J.-F. Wagen, and D. R
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Analyzing Split Channel Medium Acce
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130 J. Deng, Y.S. Han, and Z.J. Haa
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242 G. Calinescu and P.-J. Wan5 Alg
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244 G. Calinescu and P.-J. WanThe n
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246 G. Calinescu and P.-J. Wan9. A.
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248 C.J. Colbourn, V.R. Syrotiuk, a
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260 S. Bhadra and A. Ferreirathe mo
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262 S. Bhadra and A. FerreiraIn thi
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264 S. Bhadra and A. FerreiraDefini
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266 S. Bhadra and A. FerreiraThis s
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268 S. Bhadra and A. FerreiraTheore
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270 S. Bhadra and A. Ferreira4. T.
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272 M.K. Denko and Q.H. MahmoudAn i
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274 M.K. Denko and Q.H. Mahmoud3.1
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276 M.K. Denko and Q.H. Mahmoud5. D
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278 B. Macabéo, S. Pierre, and A.
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280 B. Macabéo, S. Pierre, and A.
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282 A. Benslimane and A. BachirIn [
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284 A. Benslimane and A. BachirFig.
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286 A. Benslimane and A. Bachir5 Co
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288 L. Hughes, K. Shumon, and Y. Zh
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3BerlinHeidelbergNew YorkHong KongL
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Series EditorsGerhard Goos, Karlsru
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Organizing CommitteeConference Co-c
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Table of ContentsSpace-Time Routing
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Author IndexAlonso, G. 104Bachir, A
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