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Complexity of Connected Components in Evolving Graphs 269the arc is present both at times f a (u j ,v j ) − 1 and f a (u j ,v j ), since w(u j ,v j ) < 1,the packet will reach v j in t uj + w(u j ,v j ). If, however, the arc is not present attime f a (u j ,v j ) − 1, then the transmission process itself starts at the f a (u j ,v j ) thstep (i.e. from time f a (u j ,v j ) − 1 to time f a (u j ,v j )), thus reaching v j by timef a (u j ,v j ) − 1+w(u j ,v j ).We remark that a rooted directed tree can also be computed over an o-SCC V G ′. As a modification for that purpose, V G must be replaced by V G ′ andcorrespondingly, Step 3 of Algorithm 1 should be modified to V G ′ ⊂ V f since thefragment can also contain the h-nodes for the vertices in V G ′ and the loop canstop once all the vertices are covered.Algorithm 1 is a greedy algorithm that always chooses the arc that transmitsin minimum time. The proof of its correctness is the same as the proof of thePrim-Dijkstra algorithm [4]. If the maximum outdegree of each vertex is D, theneach step of increasing the fragment will take O(NDlog T ) time and the fragmentwill increase N times adding up to a total execution time of O(N 2 D log T )steps.5 ConclusionThe two important results in this paper are the intractability of the decompositioninto (open) strongly connected components in FSDN’s and the constructionof DMST’s over an already existing strongly connected components.The first result implies that it is possible to lead a non-strongly connectednetwork towards strong connectedness by adding intermediary agents to serveas hops between two nodes that are out of range from each other. An interestingproblem would be to find a way to add such links so as to minimize the numberof intermediary (helping) nodes. Another way for further research is to designapproximation algorithms for (open) strongly connected components in evolvingdigraphs.AcknowledgmentsThe authors are grateful to Aubin Jarry and Stephane Perennes for very fruitfuldiscussions.References1. A. Borodin and R. El-Yaniv. Online computation and competitive analysis. CambridgeUniversity Press, 1998.2. B. Bui-Xuan, A. Ferreira, and A. Jarry. Computing shortest, fastest, and foremostjourneys in dynamic networks. International Journal of Foundations of ComputerScience, 14(2):267–285, April 2003.3. Y. J. Chu and T. H. Liu. On the shortest arborescence of a directed graph. ScienceSinica, 14:1396–1400, 1965.
270 S. Bhadra and A. Ferreira4. T. Cormen, C. Leiserson, and R. Rivest. Introduction to Algorithms. The MITPress, 1990.5. S.E. Dreyfus. An appraisal of Some Shortest-Path Algorithms. Operations Research,17:269–271, 1969.6. E. Ekici, I. F. Akyildiz, and M. D. Bender. Datagram routing algorithm for LEOsatellite networks. In IEEE Infocom, pages 500–508, 2000.7. A. Faragó and V.R. Syrotiuk. MERIT: A unified framework for routing protocolassessment in mobile ad hoc networks. In Proc. ACM Mobicom 01, pages 53–60.ACM, 2001.8. A. Ferreira, J. Galtier, and P. Penna. Topological design, routing and handover insatellite networks. In I. Stojmenovic, editor, Handbook of Wireless Networks andMobile Computing, pages 473–493. John Wiley and Sons, 2002.9. L.R. Ford and D.R. Fulkerson. Constructing maximal dynamic flows from staticflows. Operations Research, 6:419–433, 1958.10. J. Halpern. Shortest route with time dependent length of edges and limited delaypossibilities in nodes. Zeitschrift für Operations Research, 21:117–124, 1977.11. J. Halpern and I. Priess. Shortest path with time constraints on movement andparking. Networks, 4:241–253, 1974.12. P. A. Humblet. A distributed algorithm for minimum weight directed spanningtrees. IEEE Transactions on Communications, COM-31(6):756–762, 1983.13. E. Köhler, K. Langkau, and M. Skutella. Time-expanded graphs for flow-dependenttransit times. In proc. ESA’02, 2002.14. E. Köhler and M.Skutella. Flows over time with load-dependent transit times. InProc. of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pages174–183, 2002.15. C. Scheideler. Models and techniques for communication in dynamic networks. InIn H. Alt and A. Ferreira, editors, Proceedings of the 19th International Symposiumon Theoretical Aspects of Computer Science, volume 2285, pages 27–49. Springer-Verlag, March 2002.16. I. Stojmenovic, editor. Handbook of Wireless Networks and Mobile Computing.John Wiley & Sons, February 2002.17. V. Syrotiuk and C. J. Colbourn. Routing in mobile aerial networks. In Proceedingsof WiOpt’03 – Modeling and Optimization in Mobile, Ad-Hoc and WirelessNetworks, pages 293–302, Sophia Antipolis, March 2003. INRIA.18. R. E. Tarjan. Finding optimum branchings. Networks, pages 25–35, 1977.19. P.-J. Wan, G. Calinescu, X. Li, and O. Frieder. Minimum-energy broadcast routingin static ad hoc wireless networks. In Proc. IEEE Infocom, pages 1162–1171,Anchorage, Alaska, 2001.20. J. Wieselthier, G. Nguyen, and A. Ephremides. On the construction of energyefficientbroadcast and multicast trees in wireless networks. In Proc. IEEE Infocom,pages 585–594, Tel Aviv, 2000.
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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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78 R. Shah and N.C. HutchinsonTable
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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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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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Preventing Replay Attacks for Secur
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142 J. Zhen and S. SrinivasTraffic
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A New Framework for Building Secure
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166 H.-P. Bischof, A. Kaminsky, and
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176 G. Calinescuof the UDG 2-hops a
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178 G. CalinescuSection 3 describe
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180 G. CalinescuWhen receiving a pa
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182 G. CalinescuRyvxFig. 3. The unn
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184 G. Calinescu< nodeID, pieceID,
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186 G. Calinescu7. Heinz Breu and D
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188 S.O. Krumke et al.desirable in
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190 S.O. Krumke et al.2.2 Bicriteri
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192 S.O. Krumke et al.1. From the g
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194 S.O. Krumke et al.The following
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196 S.O. Krumke et al.1. Let α =6l
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198 S.O. Krumke et al.for any given
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200 S. PatilIDEA uses the concept o
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202 S. PatilAfter flooding the quer
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206 S. PatilAvg. Aggregate Energy C
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208 S. PatilTable 1. Probability of
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210 S. Patilergy consumption of the
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212 T. Chu and I. Nikolaidisenergy
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Page 305 and 306: 3BerlinHeidelbergNew YorkHong KongL
Page 307 and 308: Series EditorsGerhard Goos, Karlsru
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Page 312 and 313: Table of ContentsSpace-Time Routing
Page 314: Author IndexAlonso, G. 104Bachir, A
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