Graphs and Algorithms in Communication Networks on Seven League Boots
1.6 Emerging Applications in Communication Networks
1.6.2 Wireless and Ad Hoc Networks
The part on wireless and ad hoc networks starts with a study on Wireless Local Area Network (WLAN) planning. Chapter 11, coordinated by Di Yuan, considers the op-timization of such networks, taking into account performance measures like deploy-ment cost, coverage, capacity, interference, data throughput, and radio resource uti-lization. Both individual models and an integrated model for placing access points and channel assignment are presented. Computational results are reported on the basis of real-life data.
Broadcasting is a basic network communication task, where a message initially held by a source node has to be disseminated to all other nodes in the network.
Broadcasting in radio networks is studied in Chapter 12. David Peleg and Tomasz Radzik review the literature on time-efficient algorithms under a variety of models and assumptions. They also illustrate the basic techniques to prove the obtained results.
Chapter 13 studies similar problems from the energy consumption perspective. In wireless networks energy is a scarce resource since many network nodes do not have a fixed infrastructure (e.g., notebooks, PDAs, etc.). In this chapter, two problems are studied. The aim of minimum energy broadcast routing is to route a message from a given source to all other nodes with minimum overall energy usage. In the Multi-interface Networks, the energy consumption is minimized by the choice of activated interfaces on devices with multiple interfaces (e.g., Bluetooth, WiFi, etc.).
The leading author of the chapter was Alfredo Navarra.
In contrast to broadcasting, in data gathering information provided or collected by the network nodes has to be gathered in a specific node. Due to interference, simultaneous data communication is limited and has to be carried out in a number of rounds. Hence, minimization of the number of rounds or similar objectives have to be accounted for. In Chapter 14, Ralf Klasing and his coauthors consider different interference models and discuss recent complexity results as well as approximation algorithms.
Chapter 15, by J´erˆome Galtier, focuses on another aspect of WLANs: protocols for Medium Access Control (MAC). The transmission of a packet might fail due to the collision with simultaneously sent packets (from other sources). To achieve a good network performance, protocols are needed to handle the retransmission of the packet. In this chapter, mathematical evidence is presented that the selective tourna-ments protocol is asymptotically tight. Moreover, it is shown that in the context of WiFi and WiMAX networks a collision reduction of 14% to 21% can be achieved compared to the best known methods.
Finally, Chapter 16, coordinated by Lenka Carr-Motyckova and Walter Unger), discusses topology control and routing in ad hoc networks. Mobile entities with
the ability to communicate via radio signals may form an ad hoc network. Special problems arising for these ad hoc networks are considered briefly: range control, the reduction of interferences, regulation of power consumption, and localization.
Acknowledgements This chapter was supported by EU COST action 293 – Graphs and Algo-rithms in Communication Networks. The first author was supported by the Centre for Discrete Mathematics and its Applications (DIMAP), University of Warwick, EPSRC award EP/D063191/1.
References
1. Aardal, K. I., Hoesel, C. P. M. v.: Polyhedral techniques in combinatorial optimization I:
theory. Statistica Neerlandica 50(1), 3–26 (1996)
2. Aardal, K. I., Hoesel, C. P. M. v.: Polyhedral techniques in combinatorial optimization II:
applications and computations. Statistica Neerlandica 53(2), 131–177 (1999)
3. Aardal, K. I., Hoesel, C. P. M. v., Koster, A. M. C. A., Mannino, C., Sassano, A.: Models and solution techniques for the frequency assignment problem. Annals of Operations Research 153, 79–129 (2007). URLhttp://dx.doi.org/10.1007/s10479-007-0178-0 4. Aarts, E. H. L., Lenstra, J. K. (eds.): Local Search in Combinatorial Optimization. Wiley,
Chichester (1997)
5. Achterberg, T.: SCIP: solving constraint integer programs. Mathematical Programming Com-putation 1(1), 1–41 (2009). URLhttp://scip.zib.de/
6. Agrawal, A., Klein, P., Ravi, R.: When Trees Collide: An Approximation Algorithm for the Generalized Steiner Problem on Networks. SIAM Journal on Computing 24, 440–456 (1995) 7. Ahuja, R. K., Magnanti, T. L., Orlin, J. B.: Network Flows: Theory, Algorithms, and
Applica-tions. Prentice Hall, New Jersey (1993)
8. Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.:
Complexity and approximation: combinatorial optimization problems and their approximabil-ity properties. Springer-Verlag (1999)
9. Bang-Jensen, J., Gutin, G.: Digraphs: Theory, Algorithms and Applications, 2 edn. Springer-Verlag (2008).http://www.cs.rhul.ac.uk/books/dbook/
10. Bansal, N., Khandekar, R., Nagarajan, V.: Additive guarantees for degree bounded directed network design. In: Proceedings of the 40th annual ACM symposium on Theory of computing, STOC 2008, pp. 769–778 (2008)
11. Barnhart, C., Hane, C. A., Vance, P. H.: Using branch-and-price-and-cut to origin-destination integer multi-commodity flow problems. Operations Research 48, 318–326 (2000)
12. Bazaraa, M. S., Shetty, C. M.: Nonlinear programming: Theory and algorithms. John Wiley
& Sons (1979)
13. Belady, L. A.: A study of replacement algorithms for a virtual-storage computer. IBM Systems Journal 5(2), 78–101 (1966)
14. Bellare, M., Goldreich, O., Sudan, M.: Free bits, pcps and non-approximability – towards tight results. SIAM Journal on Computing 27, 804–915 (1998)
15. Bermond, J. C., Delorme, C., Quisquater, J. J.: Strategies for interconnection networks: some methods from graph theory. Graphs and Combinatorics 5, 107–123 (1989)
16. Bertsekas, D. P.: Nonlinear Programming, 2nd edn. Athena Scientific (1999)
17. Bhandari, R.: Survivable Networks: Algorithms for Diverse Routing. Kluwer Academic Pub-lishers (1999)
18. Bienstock, D., Bley, A.: Capacitated network design with mulicast commodities. In: Proceed-ings of 8th International Conference on Telecommunication Systems. Nashville, TN (2000).
URLhttp://www.zib.de/Publications/abstracts/ZR-00-14/
19. Bienstock, D., Chopra, S., G¨unl¨uk, O., Tsai, C. Y.: Minimum cost capacity installation for multicommodity network flows. Mathematical Programming 81, 177–199 (1998)
20. Bixby, R.: Solving real-world linear programs: A decade and more of progress. Operations Research 50(1), 3–15 (2002)
21. Bixby, R. E., Fenelon, M., Gu, Z., Rothberg, E., Wunderling, R.: Mixed-Integer Programming:
A Progress Report. In: M. Gr¨otschel (ed.) The Sharpest Cut: The Impact of Manfred Padberg and His Work, MPS-SIAM Series on Optimization, vol. 4, pp. 309–326. SIAM (2004) 22. Bondy, J. A., Murty, U. S. R.: Graph Theory with Applications. North-Holland (1976).
http://www.ecp6.jussieu.fr/pageperso/bondy/books/gtwa/gtwa.html 23. Bornd¨orfer, R., Eisenbl¨atter, A., Gr¨otschel, M., Martin, A.: Frequency assignment in cellular
phone networks. Annals of Operations Research 76, 73–94 (1998)
24. Br´elaz, D.: New methods to color the vertices of a graph. Communications of the ACM 22, 251–256 (1979)
25. Chartrand, G., Lesniak, L.: Graphs & Digraphs. Wadsworth & Brooks (1986)
26. Chopra, S., Gilboa, I., Sastry, S.: Source sink flows with capacity installation in batches.
DAMATH: Discrete Applied Mathematics and Combinatorial Operations Research and Com-puter Science 85 (1998)
27. Chopra, S., Rao, M. R.: The Steiner tree problem I: Formulations, compositions and extension of facets. Mathematical Programming 64, 209–229 (1994)
28. Chung, F. R. K., Coffman, E. G., Reiman, M. I., Simon, B.: On the capacity and forwarding index of communication networks. IEEE Trans. on Information Theory 33, 244–232 (1987) 29. Chv´atal, V.: Linear Programming. W. H. Freeman and Company, New York (1983)
30. Clos, C.: A study of non-blocking switching networks. Bell System Technical Journal (1953) 31. Cook, W.: Fifty-plus years of combinatorial integer programming (2009). URL
http://www2.isye.gatech.edu/˜wcook/ip50/ip50.pdf
32. Cook, W. J., Cunningham, W. H., Pulleybank, W. R., Schrijver, A.: Combinatorial Optimiza-tion. Series in Discrete Mathematics and OptimizaOptimiza-tion. Wiley-Interscience (1998)
33. Cost action 293 – graphs and algorithms in communication networks.
http://www.cost293.org/
34. Coudert, D., Ferreira, A., Mu˜noz, X.: A multihop-multi-OPS optical interconnection network.
IEEE/OSA Journal of Lightwave Technology 18(12), 2076–2085 (2000)
35. Coudert, D., Mu˜noz, X.: Graph theory and traffic grooming in WDM rings. In: Recent Re-search Developments in Optics, 3, chap. 37, pp. 759–778. ReRe-search Signpost. Kerala, India (2003)
36. Dantzig, G. B.: Linear Programming and Extensions. Princeton University Press (1998). Orig-inally published in 1963
37. Dantzig, G. B., Fulkerson, D. R.: On the max-flow min-cut theorem of networks. In: H. W.
Kuhn, A. W. Tucker (eds.) Linear Inequalities and Related Systems, Annals of Mathematics Series, vol. 38, pp. 215–221. Princeton University Press, Princeton, New Jersey (1956)
38. Diestel, R.: Graph Theory, Graduate Texts in
Mathemat-ics, vol. 173, 3 edn. Springer-Verlag, Heidelberg (2005).
http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/
39. Dijkstra, E. W.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)
40. Dolev, D., Halpern, J., Simons, B., Strong, H.: A new look at fault tolerant network routing.
Information and Computation 72, 180–196 (1987)
41. Eisenbl¨atter, A.: Frequency assignment in GSM networks: Models, heuristics, and lower bounds. Ph.D. thesis, Technische Universit¨at Berlin, Berlin, Germany (2001)
42. Eisenbl¨atter, A.: The semidefinite relaxation of the k-partition polytope is strong. In: W. J.
Cook, A. S. Schulz (eds.) Proceedings of the 9th Conference on Integer Programming and Combinatorial Optimization (IPCO’02), Lecture Notes in Computer Science, vol. 2337, pp.
273–290. Springer-Verlag, Berlin Heidelberg (2002)
43. Eisenbl¨atter, A., Gr¨otschel, M., Koster, A. M. C. A.: Frequency planning and ramifications of coloring. Discussiones Mathematicae Graph Theory 22(1), 51–88 (2002)
44. Eisenbl¨atter, A., Koster, A. M. C. A.: FAP web – A website devoted to frequency assignment.
URL: http://fap.zib.de (2000–2008)
45. F`abrega, J., Fiol, M. A.: Maximally connected digraphs. Journal of Graph Theory 13, 657–668 (1989)
46. Ferreira, A., P´erennes, S., Richa, A. W., Rivano, H., Moses, N. S.: Models, Complexity and Algorithms for the Design of Multifiber WDM Networks. Telecommunication Systems 24, 123–138 (2003)
47. Fiat, A., Karp, R. M., Luby, M., McGeoch, L. A., Sleator, D. D., Young, N. E.: Competitive paging algorithms. Journal of Algorithms 12(4), 685–699 (1991)
48. Fortz, B., Labb´e, M.: Design of survivable networks. In: M. G. C. Resende, P. M. Pardalos (eds.) Handbook of Optimization in Telecommunications, chap. 15, pp. 367–389. Springer (2006)
49. Garey, M. R., Johnson, D. S.: The rectilinear Steiner tree problem is NP-complete. SIAM Journal on Applied Mathematics 32, 826–834 (1977)
50. Garey, M. R., Johnson, D. S.: Computers and intractability: a guide to the theory ofNP -completeness. Freeman and Company, N. Y. (1979)
51. Goemans, M. X.: Minimum bounded degree spanning trees. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2006, pp. 273–282 (2006)
52. Gr¨otschel, M., Krumke, S. O., Rambau, J. (eds.): Online Optimization of Large Scale Systems.
Springer (2001)
53. Gr¨otschel, M., Lov´asz, L., Schrijver, A.: The ellipsoid method and its consequences in com-binatorial optimization. Combinatorica 1, 169–197 (1981)
54. Gr¨otschel, M., Lov´asz, L., Schrijver, A.: Corrigendum to our paper “the ellipsoid method and its consequences in combinatorial optimization”. Combinatorica 4, 291–295 (1984) 55. Gr¨otschel, M., Lov´asz, L., Schrijver, A.: Geometric Algorithms and Combinatorial
Optimiza-tion. No. 2 in Algorithms and Combinatorics. Springer-Verlag (1988)
56. Gr¨otschel, M., Monma, C. L., Stoer, M.: Facets for polyhedra arising in the design of com-munication networks with low-connectivity constraints. SIAM Journal on Optimization 2(3), 474–504 (1992)
57. Gr¨otschel, M., Monma, C. L., Stoer, M.: Design of Survivable Networks. In: M. O. Ball, T. L.
Magnanti, C. L. Monma, G. L. Nemhauser (eds.) Network Models, Handbooks in Operations Research and Management Science, vol. 7, pp. 617–672. North-Holland (1995)
58. Gr¨otschel, M., Monma, C. L., Stoer, M.: Polyhedral and Computational Investigations for Designing Communication Networks with High Survivability Requirements. Operations Re-search 43(6), 1012–1024 (1995)
59. Grover, W. D.: Mesh-based Survivable Networks: Options and Strategies for Optical, MPLS, SONET and ATM Networking. Prentice Hall (2003)
60. Henningsson, M., Holmberg, K., Yuan, D.: Ring network design. In: M. G. C. Resende, P. M.
Pardalos (eds.) Handbook of Optimization in Telecommunications, chap. 12, pp. 291–311.
Springer (2006)
61. Heydemann, M. C., Meyer, J. C., Sotteau, D.: On forwarding indices of networks. Discrete Applied Mathematics 23, 103–123 (1989)
62. Holmberg, K., R¨onnqvist, M., Yuan, D.: An exact algorithm for the capacitated facility lo-cation problems with single sourcing. European Journal of Operational Research 113(3), 544–559 (1999)
63. Hromkovic, J., Klasing, R., Monien, B., Peine, R.: Dissemination of information in intercon-nection networks (broadcasting and gossiping) (1996)
64. ILOG: CPLEX version 11.1 (2008).http://www.ilog.com/products/cplex 65. Karmarkar, N.: A new polynomial-time algorithm for linear programming. Combinatorica
4(4), 373–395 (1984)
66. Karp, R. M.: Reducibility among combinatorial problems. In: R. E. Miller, J. W. Thatcher (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press, New York (1972) 67. Klee, V., Minty, G. J.: How good is the Simplex algorithm? In: O. Shisha (ed.) Inequalities,
III, pp. 159–175. Academic Press, New York, NY (1972)
68. Koch, T., Martin, A., Voß, S.: SteinLib: An updated library on Steiner tree problems in graphs.
Tech. Rep. ZIB-Report 00-37, Konrad-Zuse-Zentrum f¨ur Informationstechnik Berlin, Takustr.
7, Berlin (2000). URLhttp://elib.zib.de/steinlib
69. Kruskal Jr., J. B.: On the shortest spanning tree of a graph and the traveling salesman problem.
Proceedings of the American Mathematical Society 7, 48–50 (1956)
70. LEMON: A C++ Library for Efficient Modelling and Optimization in Networks.
http://lemon.cs.elte.hu
71. Lindberg, P.: Network optimisation with successive smooth approximation. In: 11th Nordic Teletraffic Seminar. Stockholm (1993)
72. Lynch, N.: Distributed Algorithms. Morgan Kaufmann Publishers (1996)
73. Marsden, G., Marchand, P., Harvey, P., Esener, S.: Optical transpose interconnection system architectures. OSA Optics Letters 18(13), 1083–1085 (1993)
74. Martello, S., Toth, P.: Knapsack Problems – Algorithms and Computer Implementations.
Wiley-Interscience Series in Discrete Mathematics and Optimization. John Wiley & Sons (1990). URLhttp://www.or.deis.unibo.it/kp.html
75. Metzger, B. H.: Spectrum management technique (Fall 1970). Presentation at 38th National ORSA meeting (Detroit, MI)
76. Nemhauser, G. L., Wolsey, L. A.: Integer and Combinatorial Optimization. Wiley, N. Y. (1988) 77. Orlowski, S., Pi´oro, M., Tomaszewski, A., Wess¨aly, R.: SNDlib 1.0–Survivable Network De-sign Library. In: Proceedings of International Network Optimization Conference (INOC2007) (2007).http://sndlib.zib.de
78. Peleg, D.: Distributed Computing – A Locality-Sensitive Approach. Monographs in Discrete Mathematics and Applications. SIAM (2000)
79. Pi´oro, M., Medhi, D.: Routing, Flow, and Capacity Design in Communication and Computer Networks. Morgan Kaufmann (2004)
80. Polzin, T.: Algorithms for the Steiner problem in networks. Ph.D. thesis, Universit¨at des Saarlandes (2003)
81. Prim, R. C.: Shortest connection networks and some generalizations. The Bell System Tech-nical Journal 36, 1389–1401 (1957)
82. Schrijver, A.: Theory of linear and integer programming. Wiley, New York (1986)
83. Schrijver, A.: Combinatorial Optimization – Polyhedra and Efficiency. No. 24 in Algorithms and Combinatorics. Springer (2003)
84. Sleator, D. D., Tarjan, R. E.: Amortized efficiency of list update and paging rules. Communi-cations of the ACM 28(2), 202–208 (1985)
85. Stidsen, T., Petersen, B., Rasmussen, K. B., Spoorendonk, S., Zachariasen, M., Rambach, F., Kiese, M.: Optimal routing with single backup path protection. In: Proceedings International Network Optimization Conference (INOC 2007). Spa, Belgium (2007)
86. Suurballe, J. W.: Disjoint paths in a network. Networks 4(2), 125–145 (1974) 87. Tel, G.: Introduction to Distributed Algorithms. Cambridge University Press (1994) 88. Vanderbei, R. J.: Linear Programming: Foundations and Extensions, International Series in
Operations Research & Management Science, vol. 114, 3 edn. Springer-Verlag (2008) 89. Vo¨s, S.: Steiner tree problems in telecommunications. In: M. G. C. Resende, P. M. Pardalos
(eds.) Handbook of Optimization in Telecommunications, chap. 18, pp. 459–515. Springer (2006)
90. Wess¨aly, R.: DImensioning Survivable Capacitated NETworks. Ph.D. thesis, Technische Uni-versit¨at Berlin (2000)
91. West, D. B.: Introduction to Graph Theory, 2 edn. Prentice Hall (2001)
92. Wolsey, L. A.: Integer Programming. Series in Discrete Mathematics and Optimization.
Wiley-Interscience (1998)
93. Zymolka, A.: Design of survivable optical networks by mathematical optimization. Ph.d.
thesis, TU Berlin (2007)
94. Zymolka, A., Koster, A. M. C. A., Wess¨aly, R.: Transparent optical network design with sparse wavelength conversion. In: Proceedings of ONDM 2003, pp. 61–80. The 7th IFIP Working Conference on Optical Network Design & Modelling, Budapest, Hungary (2003)