Handbook of Optimization in Telecommunications pp 865-890 | Cite as

# Graph Domination, Coloring and Cliques in Telecommunications

## Abstract

This chapter aims to provide a detailed survey of existing graph models and algorithms for important problems that arise in different areas of wireless telecommunication. In particular, applications of graph optimization problems such as minimum dominating set, minimum vertex coloring and maximum clique in multihop wireless networks are discussed. Different forms of graph domination have been used extensively to model clustering in wireless ad hoc networks. Graph coloring problems and their variants have been used to model channel assignment and scheduling type problems in wireless networks. Cliques are used to derive bounds on chromatic number, and are used in models of traffic flow, resource allocation, interference, etc. In this chapter we survey the solution methods proposed in the literature for these problems and some recent theoretical results that are relevant to this area of research in wireless networks.

## Keywords

Dominating sets independent sets cliques coloring wireless networks## Preview

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## Bibliography

- J. Abello, P.M. Pardalos, and M.G.C. Resende. On maximum clique problems in very large graphs. In J. Abello and J. Vitter, editors,
*External Memory Algorithms*, volume 50 of*DIMACS Series on Discrete Mathematics and Theoretical Computer Science*, pages 119–130. American Mathematical Society, 1999.Google Scholar - J. Abello, M.G.C. Resende, and S. Sudarsky. Massive quasi-clique detection.
*Lecture Notes in Computer Science*, 2286:598–612, 2002.CrossRefMathSciNetGoogle Scholar - G. Agnarsson and M. M. Halldórsson. Coloring powers of planar graphs.
*SIAM Journal on Discrete Mathematics*, 16(4):651–662, 2003.zbMATHCrossRefMathSciNetGoogle Scholar - N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem.
*Journal of Algorithms*, 7:567–583, 1986.zbMATHCrossRefMathSciNetGoogle Scholar - K. M. Alzoubi, P.-J. Wan, and O. Frieder. Distributed heuristics for connected dominating sets in wireless ad hoc networks.
*Journal of Communications and Networks*, 4:22–29, 2002a.Google Scholar - K. M. Alzoubi, P.-J. Wan, and O. Frieder. Message-optimal connected dominating sets in mobile ad hoc networks. In
*Proceedings of the Third ACM International Symposium on Mobile Ad Hoc Networking and Computing*, pages 157–164, 2002b.Google Scholar - K. M. Alzoubi, P.-J. Wan, and O. Frieder. A simple parallel algorithm for the maximal independent set problem.
*International Journal of Foundations of Computer Science*, 14(2):287–303, 2003a.zbMATHCrossRefMathSciNetGoogle Scholar - K. M. Alzoubi, P.-J. Wan, and O. Frieder. Weakly-connected dominating sets and sparse spanners in wireless ad hoc networks. In
*Proceedings of the 23rd International Conference on Distributed Computing Systems*, page 96. IEEE Computer Society, 2003b.Google Scholar - A. Amis, R. Prakash, T. Vuong, and D. Huynh. Max-min d-cluster formation in wireless ad hoc networks. In
*Proceedings of IEEE INFOCOM*, 2000.Google Scholar - B. An and S. Papavassiliou. A mobility-based clustering approach to support mobility management and multicast routing in mobile ad-hoc wireless networks.
*Intl. J. Network Management*, 11(6):387–395, 2001.CrossRefGoogle Scholar - K. Appel and W. Haken. Every planar map is four colourable. part I: Discharging.
*Illinois Journal of Mathematics*, 21:429–490, 1977.zbMATHMathSciNetGoogle Scholar - K. Appel, W. Haken, and J. Koch. Every planar map is four colourable. part II: Reducibility.
*Illinois Journal of Mathematics*, 21:491–567, 1977.zbMATHMathSciNetGoogle Scholar - E. Arikan. Some complexity results about packet radio networks.
*IEEE Transactions on Information Theory*, IT-30:910–918, 1984.MathSciNetGoogle Scholar - D. J. Baker and A. Ephremides. The architectural organization of a mobile radio network via a distributed algorithm.
*IEEE Trans. on Communications*, COM-29(11): 1694–1701, November 1981.CrossRefGoogle Scholar - B. Balasundaram, S. Butenko, and S. Trukhanov. Novel approaches for analyzing biological networks.
*Journal of Combinatorial Optimization*, 10:23–39, 2005.zbMATHCrossRefMathSciNetGoogle Scholar - S. Bannerjee and S. Khuller. A clustering scheme for hierarchical control in wireless networks. In
*Proceedings of IEEE INFOCOM*, pages 1–12, 2001.Google Scholar - S. Basagni. Distributed clustering for ad hoc networks. In
*Proceedings of the 1999 International Symposium on Parallel Architectures, Algorithms and Networks (ISPAN’ 99)*, page 310, 1999.Google Scholar - S. Basagni. Finding a maximal weighted independent set in wireless networks.
*Telecommunication Systems*, 18(1–3): 155–168, 2001.zbMATHCrossRefGoogle Scholar - S. Basagni, M. Conti, S. Giordano, and I. Stojmenovic, editors.
*Mobile Ad Hoc Networking*. Wiley-IEEE Press, 2004.Google Scholar - R. Battiti, A. A. Bertossi, and M. A. Bonuccelli. Assigning codes in wireless networks: bounds and scaling properties.
*Wireless Networks*, 5:195–209, 1999.CrossRefGoogle Scholar - R. Battiti and M. Protasi. Reactive local search for the maximum clique problem.
*Algorithmica*, 29:610–637, 2001.zbMATHCrossRefMathSciNetGoogle Scholar - A. A. Bertossi and M. A. Bonuccelli. Code assignment for hidden terminal interference avoidance in multihop packet radio networks.
*IEEE/ACM Trans. Netw.*, 3(4): 441–449, 1995.CrossRefGoogle Scholar - I. M. Bomze, M. Budinich, P. M. Pardalos, and M. Pelillo. The maximum clique problem. In D.-Z. Du and P. M. Pardalos, editors,
*Handbook of Combinatorial Optimization*, pages 1–74. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.Google Scholar - M. A. Bonuccelli and S. Leonardi. On scheduling variable length broadcasts in wireless networks.
*Telecommunication Systems*, 8:211–227, 1997.CrossRefGoogle Scholar - D. Brélaz. New methods to color the vertices of a graph.
*Communications of the ACM*, 22(4):251–256, 1979.zbMATHCrossRefGoogle Scholar - H. Breu and D. G. Kirkpatrick. Unit disk graph recognition is NP-hard. Technical Report 93-27, Department of Computer Science, University of British Columbia, 1993.Google Scholar
- R. L. Brooks. On coloring the nodes of a network.
*Proc. Cambridge Philos. Soc.*, 37: 194–197, 1941.CrossRefMathSciNetGoogle Scholar - S. Butenko, X. Cheng, D.-Z. Du, and P. Pardalos. On the construction of virtual backbone for ad hoc wireless networks. In S. Butenko, R. Murphey, and P.M Pardalos, editors,
*Cooperative Control: Models, Applications and Algorithms*, pages 43–54. Kluwer Academic Publisher, 2003.Google Scholar - S. Butenko, X. Cheng, C.A.S Oliveira, and P.M. Pardalos. A new heuristic for the minimum connected dominating set problem on ad hoc wireless networks. In R. Murphey and P.M Pardalos, editors,
*Cooperative Control and Optimization*, pages 61–73. Kluwer Academic Publisher, 2004a.Google Scholar - S. Butenko, C. W. Commander, and P. M. Pardalos. A greedy randomized adaptive search procedure for the broadcast scheduling problem.
*Submitted to Journal of Combinatorial Optimization*, 2004b.Google Scholar - M. Cardei, X. Cheng, X. Cheng, and D. Z. Du. Connected domination in multihop ad hoc wireless networks. In H. J. Caulfield, S. H. Chen, H. D. Cheng, R. J. Duro, V. Honavar, E. E. Kerre, M. Lu, M. G. Romay, T. K. Shih, D. V., P. P. Wang, and Y. Yang, editors,
*Proceedings of the 6th Joint Conference on Information Science*, pages 251–255. JCIS / Association for Intelligent Machinery, Inc., 2002.Google Scholar - Y. Caro, D. B. West, and R. Yuster. Connected domination and spanning trees with many leaves.
*SIAM J. Discret. Math.*, 13(2):202–211, 2000.CrossRefMathSciNetGoogle Scholar - G. J. Chang and G. L. Nemhauser. The k-domination and k-stability problems on sunfree chordal graphs.
*SIAM Journal on Algebraic and Discrete Methods*, 5:332–345, 1984.zbMATHCrossRefMathSciNetGoogle Scholar - M. Chatterjee, S. Das, and D. Turgut. WCA: A weighted clustering algorithm for mobile ad hoc networks.
*Journal of Cluster Computing*, 5:193–204, 2002.CrossRefGoogle Scholar - Y. P. Chen and A. L. Liestman. Approximating minimum size weakly connected dominating sets for clustering mobile ad hoc networks. In
*Proceedings of the Third ACM International Symposium on Mobile Ad Hoc Networking and Computing*, pages 165–172, 2002.Google Scholar - Y. P. Chen and A. L. Liestman. A zonal algorithm for clustering ad hoc networks.
*International Journal of Foundations of Computer Science*, 14(2):305–322, 2003.zbMATHCrossRefGoogle Scholar - Y. P. Chen, A. L. Liestman, and J. Liu. Clustering algorithms for ad hoc wireless networks. In Y. Pan and Y. Xiao, editors,
*Ad Hoc and Sensor Networks*, volume 2 of*Wireless Networks and Mobile Computing*, chapter 7. Nova Science Publishers, 2005.Google Scholar - X. Cheng, X. Huang, and D.-Z. Du, editors.
*Ad Hoc Wireless Networking*. Kluwer Academic Publisher, The Netherlands, 2003a.Google Scholar - X. Cheng, X. Huang, D. Li, W. Wu, and D. Z. Du. A polynomial-time approximation scheme for the minimum-connected dominating set in ad hoc wireless networks.
*Networks*, 42(4):202–208, 2003b.zbMATHCrossRefMathSciNetGoogle Scholar - I. Chlamtac, M. Conti, and J. J.-N. Liu. Mobile ad hoc networking: imperatives and challenges.
*Ad Hoc Networks*, 1:13–64, 2003.CrossRefGoogle Scholar - I. Chlamtac and S. Kutten. On broadcasting in radio networks-problem analysis and protocol design.
*IEEE Transactions on Communications*, 33(12): 1240–1246, 1985a.zbMATHCrossRefGoogle Scholar - I. Chlamtac and S. Kutten. A spatial reuse TDMA/FDMA for mobile multi-hop radio networks. In
*Proceedings of the IEEE INFOCOM*, 1985b.Google Scholar - I. Chlamtac and A. Lerner. A link allocation protocol for mobile multihop networks. In
*Proceedings of the IEEE Globecom*, 1985.Google Scholar - I. Chlamtac and S. S. Pinter. Distributed nodes organization algorithm for channel access in a multihop dynamic radio network.
*IEEE Transactions on Computers*, 36(6):728–737, 1987.CrossRefGoogle Scholar - I. Cidon and M. Sidi. Distributed assignment algorithms for multihop packet radio networks.
*IEEE Trans. Comput.*, 38(10): 1353–1361, 1989.CrossRefGoogle Scholar - B. Clark, C. Colbourn, and D. Johnson. Unit disk graphs.
*Discrete Mathematics*, 86: 165–177, 1990.zbMATHCrossRefMathSciNetGoogle Scholar - E. J. Cockayne, B. Gamble, and B. Shepherd. An upper bound for the k-domination number of a graph.
*Journal of Graph Theory*, 9(4):533–534, 1985.zbMATHCrossRefMathSciNetGoogle Scholar - C. W. Commander, S. Butenko, and P. M. Pardalos. On the performance of heuristics for broadcast scheduling. In D. Grundel, R. Murphey, and P. Pardalos, editors,
*Theory and Algorithms for Cooperative Systems*, pages 63–82. World Scientific, 2004.Google Scholar - M. B. Cozzens and F. S. Roberts. T-colorings of graphs and the channel assignment problem.
*Congressus Numerantium*, 35:191–208, 1982.MathSciNetGoogle Scholar - B. Das and V. Bharghavan. Routing in ad-hoc networks using minimum connected dominating sets. In
*IEEE International Conference on Communications (ICC’ 97)*, pages 376–380, 1997.Google Scholar - B. Das, R. Sivakumar, and V. Bharghavan. Routing in ad-hoc networks using a virtual backbone. In
*Proceedings of the International Conference on Computers and Communication Networks (IC3N)*, pages 1–20, 1997.Google Scholar - J.S. Deogun, D. Kratsch, and G. Steiner. An approximation algorithm for clustering graphs with dominating diametral path.
*Information Processing Letters*, 61:121–127, 1997.CrossRefMathSciNetGoogle Scholar - DIMACS. Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge. http://dimacs.rutgers.edu/Challenges/, 1995. Accessed November 2004.
- D. Dubhashi, A. Mei, A. Panconesi, J. Radhakrishnan, and A. Srinivasan. Fast distributed algorithms for (weakly) connected dominating sets and linear-size skeletons. In
*Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms*, pages 717–724, 2003.Google Scholar - P. Duchet and H. Meyniel. On Hadwiger’s number and stability numbers.
*Annals of Discrete Mathematics*, 13:71–74, 1982.zbMATHMathSciNetGoogle Scholar - W. Duckworth and B. Mans. Randomized algorithms for finding small weakly-connected dominating sets of regular graphs. In R. Petreschi, G. Persiano, and R. Silvestri, editors,
*Proceedings of the Fifth Conference on Algorithms and Complexity*, pages 83–95, 2003.Google Scholar - J. E. Dunbar, J.W. Grossman, J. H. Hattingh, S. T. Hedetniemi, and A. A. McRae. On weakly connected domination in graphs.
*Discrete Mathematics*, 167–168:261–269, 1997.CrossRefMathSciNetGoogle Scholar - A. Ephremides and T. V. Truong. Scheduling broadcasts in multihop radio networks.
*IEEE Transactions on Communications*, 38:456–461, 1990.CrossRefGoogle Scholar - S. Even, O. Goldreich, S. Moran, and P. Tong. On the NP-completeness of certain network testing problems.
*Networks*, 14:1–24, 1984.zbMATHCrossRefMathSciNetGoogle Scholar - Z. Fang and B. Bensaou. Fair bandwidth sharing algorithms based on game theory frameworks for wireless ad-hoc networks. In
*Proceedings of the IEEE Infocom*, 2004.Google Scholar - T. A. Feo and M. G. C. Resende. A greedy randomized adaptive search procedure for maximum independent set.
*Operations Research*, 42:860–878, 1994.zbMATHCrossRefGoogle Scholar - T. A. Feo and M. G. C. Resende. Greedy randomized adaptive search procedures.
*Journal of Global Optimization*, 6:109–133, 1995.zbMATHCrossRefMathSciNetGoogle Scholar - Y. Fernandess and D. Malkhi. K-clustering in wireless ad hoc networks. In
*Proceedings of the Second ACM International Workshop on Principles of Mobile Computing*, pages 31–37, 2002.Google Scholar - P. Festa and M.G.C. Resende. GRASP: An annotated bibliography. In P. Hansen and C.C. Ribeiro, editors,
*Essays and Surveys on Metaheuristics*, pages 325–367. Kluwer Academic Publishers, 2001.Google Scholar - M. R. Garey and D. S. Johnson.
*Computers and Intractability: A Guide to the Theory of NP-completeness*. W.H. Freeman and Company, New York, 1979.zbMATHGoogle Scholar - M. Gerla and J. T. C. Tsai. Multicluster, mobile, multimedia radio network.
*Wireless Networks*, 1(3):255–265, 1995.CrossRefGoogle Scholar - F. Glover. Tabu search-part I.
*ORSA J. Comput.*, 1:190–260, 1989.zbMATHMathSciNetGoogle Scholar - F. Glover. Tabu search-part II.
*ORSA J. Comput.*, 2:4–32, 1990.zbMATHGoogle Scholar - F. Glover and M. Laguna.
*Tabu Search*. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997.zbMATHGoogle Scholar - M. Goldberg and T. Spencer. A new parallel algorithm for the maximal independent set problem.
*SIAM Journal on Computing*, 18(2):419–427, 1989.zbMATHCrossRefMathSciNetGoogle Scholar - A. Gräf, M. Stumpf, and G. Weißenfels. On coloring unit disk graphs.
*Algorithmica*, 20(3):277–293, 1998.zbMATHCrossRefMathSciNetGoogle Scholar - S. Guha and S. Khuller. Approximation algorithms for connected dominating sets.
*Algorithmica*, 20:374–387, 1998.zbMATHCrossRefMathSciNetGoogle Scholar - R. Gupta and J. Walrand. Approximating maximal cliques in ad-hoc networks. In
*Proceedings of the PIMRC 2004*, September 2004.Google Scholar - B. Hajek and G. Sasaki. Link scheduling in polynomial time.
*IEEE Transactions on Information Theory*, 34:910–917, 1988.CrossRefMathSciNetGoogle Scholar - W. K. Hale. Frequency assignment: theory and applications.
*Proceedings of the IEEE*, 68(12): 1497–1514, 1980.CrossRefGoogle Scholar - J. Håstad. Clique is hard to approximate within
*n*^{1−ɛ}.*Acta Mathematica*, 182:105–142, 1999.zbMATHCrossRefMathSciNetGoogle Scholar - T. W. Haynes, S. T. Hedetniemi, and P.J. Slater.
*Fundamentals of Domination in Graphs*. Marcel Dekker Inc., 1998a.Google Scholar - T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, editors.
*Domination in Graphs: Advanced Topics*. Marcel Dekker Inc., 1998b.Google Scholar - S. T. Hedetniemi and R. C. Laskar. Bibliography on domination in graphs and some basic definitions of domination parameters.
*Discrete Mathematics*, 86(1–3):257–277, 1997.MathSciNetGoogle Scholar - J. J. Hopfield. Neural networks and physical systems with emergent collective computational abilities.
*Proceedings of the National Academy of Sciences*, 79:2554–2558, 1982.CrossRefMathSciNetGoogle Scholar - J. J. Hopfield and D. W. Tank. “Neural” computation of decisions in optimization problems.
*Biological Cybernetics*, 52:141–152, 1985.zbMATHMathSciNetGoogle Scholar - E. Hossain, R. Palit, and P. Thulasiraman. Clustering in mobile wireless ad hoc networks: issues and approaches. In
*Wireless Communications Systems and Networks*, pages 383–424. Plenum Publishing Corporation, New York, 2004.CrossRefGoogle Scholar - T. C. Hou and T. J. Tsai. An access-based clustering protocol for multihop wireless ad hoc networks.
*IEEE Journal on Selected Areas in Commnications*, 19(7):1201–1210, 2001.CrossRefGoogle Scholar - I. Hoyler. The NP-completeness of edge-coloring.
*SIAM Journal on Computing*, 10: 718–720, 1981.CrossRefMathSciNetGoogle Scholar - H. Huang, A. W. Richa, and M. Segal. Approximation algorithms for the mobile piercing set problem with applications to clustering in ad-hoc networks.
*Mobile Networks and Applications*, 9(2):151–161, 2004.CrossRefGoogle Scholar - F. Ingelrest, D. Simplot-Ryl, and I. Stojmenovic. A dominating sets and target radius based localized activity scheduling and minimum energy broadcast protocol for ad hoc and sensor networks. In
*Proceedings of the 3rd IFIP Mediterranean Ad Hoc Networking Workshop (MED-HOC-NET)*, pages 351–359, 2004.Google Scholar - S. Jendrol’ and Z. Skupień. Local structures in plane maps and distance colorings.
*Discrete Mathematics*, 236(1–3): 167–177, 2001.zbMATHCrossRefMathSciNetGoogle Scholar - L. Jia, R. Rajaraman, and T. Suel. An efficient distributed algorithm for constructing small dominating sets.
*Distributed Computing*, 15(4): 193–205, 2002.CrossRefGoogle Scholar - J. Kalvenes, J. Kennington, and E. V. Olinick. Hierarchical cellular network design with channel allocation.
*To appear in European Journal of Operational Research*, 160(1):3–18, 2005.zbMATHGoogle Scholar - I. Katzela and M. Naghshineh. Channel assignment schemes for cellular mobile telecommunications: A comprehensive survey.
*IEEE Personal Communications*, pages 10–31, 1996.Google Scholar - P. Krishna, N, Vaidya, M. Chatterjee, and D. Pradhan. A cluster-based approach for routing in dynamic networks. In
*ACM SIGCOMM Computer Communication Review*, pages 49–65, 1997.Google Scholar - B. Krishnamachari, S. Wicker, R. Béjar, and C. Fernandez. On the complexity of distributed self-configuration in wireless networks.
*Telecommunication Systems*, 22(1–4):33–59, 2003.CrossRefGoogle Scholar - S. O. Krumke, M. V. Marathe, and S. S. Ravi. Models and approximation algorithms for channel assignment in radio networks.
*Wireless Networks*, 7(6):575–584, 2001.zbMATHCrossRefGoogle Scholar - F. Kuhn and R. Wattenhofer. Constant-time distributed dominating set approximation. In
*Proceedings of the Twenty Second Annual Symposium on Principles of Distributed Computing*, pages 25–32. ACM Press, 2003.Google Scholar - S. Kutten and D. Peleg. Fast distributed construction of small k-dominating sets and applications.
*J. Algorithms*, 28(1):40–66, 1998.zbMATHCrossRefMathSciNetGoogle Scholar - M. Laguna and R. Martí. A GRASP for coloring sparse graphs.
*Computational Optimization and Applications*, 19(2): 165–178, 2001.zbMATHCrossRefMathSciNetGoogle Scholar - C. R. Lin and M. Gerla. Adaptive clustering for mobile wireless networks.
*IEEE Journal of Selected Areas in Communications*, 15(7): 1265–1275, 1991.CrossRefGoogle Scholar - E. L. Lloyd and S. Ramanathan. On the complexity of distance-2 coloring. In W. W. Koczkodaj, P. E. Lauer, and A. A. Toptsis, editors,
*Computing and Information-ICCI’92, Fourth International Conference on Computing and Information, Toronto, Ontario, Canada, May 28–30, 1992, Proceedings*, pages 71–74. IEEE Computer Society, 1992.Google Scholar - M. Luby. A simple parallel algorithm for the maximal independent set problem.
*SIAM Journal on Computing*, 15(4): 1036–1055, 1986.zbMATHCrossRefMathSciNetGoogle Scholar - C. Lund and M. Yannakakis. On the hardness of approximating minimization problems.
*Journal of the ACM*, 41(5):960–981, 1994.zbMATHCrossRefMathSciNetGoogle Scholar - M. V. Marathe, H. Breu, H. B. Hunt III, S. S. Ravi, and D. J. Rosenkrantz. Simple heuristics for unit disk graphs.
*Networks*, 25:59–68, 1995.zbMATHCrossRefMathSciNetGoogle Scholar - S. T. McCormick. Optimal approximation of sparse hessians and its equivalence to a graph coloring problem.
*Mathematical Programming*, 26:153–171, 1983.zbMATHCrossRefMathSciNetGoogle Scholar - T. Minn and K.-Y. Siu. Dynamic assignment of orthogonal variable spreading factor codes in W-CDMA.
*IEEE Journal on Selected Areas in Communications*, 18(8): 1429–1440, 2000.CrossRefGoogle Scholar - R. J. Mokken. Cliques, clubs and clans.
*Quality and Quantity*, 13:161–173, 1979.CrossRefGoogle Scholar - R. Montemanni, D. H. Smith, and S. M. Allen. Lower bounds for fixed spectrum frequency assignment.
*Annals of Operations Research*, 107:237–250, 2001.zbMATHCrossRefMathSciNetGoogle Scholar - T. Moscibroda and R. Wattenhofer. Efficient computation of maximal independent sets in unstructured multi-hop radio networks. In
*Proceedings of the First International Conference on Mobile Ad-hoc and Sensor Systems (MASS)*, 2004.Google Scholar - R. A. Murphey, P. M. Pardalos, and M. G. C. Resende. Frequency assignment problems. In D.-Z Du and P.M. Pardalos, editors,
*Handbook of Combinatorial Optimization*. Kluwer Academic Publishers, 1999.Google Scholar - F. Nocetti, J. Gonzalez, and I. Stojmenovic. Connectivity-based k-hop clustering in wireless networks.
*Telecommunication Systems*, 22(1–4):205–220, 2003.CrossRefGoogle Scholar - R. Ogier. A decomposition method for optimal link scheduling. In
*Proceedings of the 24th Allerton Conference*, pages 822–823, 1986.Google Scholar - S. Parthasarathy and R. Gandhi. Fast distributed well connected dominating sets for ad hoc networks. Technical Report CS-TR-4559, University of Maryland, Computer Science Department, 2004.Google Scholar
- L. D. Penso and V. C. Barbosa. A distributed algorithm to find k-dominating sets.
*Discrete Applied Mathematics*, 141:243–253, 2004.zbMATHCrossRefMathSciNetGoogle Scholar - C. E. Perkins, editor.
*Ad Hoc Networking*. Addison-Wesley, 2001.Google Scholar - A. Puri. Optimizing traffic flow in fixed wireless networks. In
*Proceedings of the Wireless Communications and Networking Conference, WCNC 2002*, volume 2, pages 904–907, 2002.CrossRefGoogle Scholar - S. Ramanathan. Scheduling algorithms for multihop radio networks.
*IEEE/ACM Transactions on Networking*, 1(2): 166–172, 1993.CrossRefMathSciNetGoogle Scholar - S. Ramanathan. A unified framework and algorithm for channel assignment in wireless networks.
*Wireless Networks*, 5(2):81–94, 1999.CrossRefGoogle Scholar - R. Ramaswami and K. K. Parhi. Distributed scheduling of broadcasts in a radio network. In
*Proceedings of the INFOCOM*, 1989.Google Scholar - M.G.C. Resende and C.C. Ribeiro. Greedy randomized adaptive search procedures. In F. Glover and G. Kochenberger, editors,
*Handbook of Metaheuristics*. Kluwer Academic Publishers, 2003.Google Scholar - M.G.C. Resende and C.C. Ribeiro. GRASP with path-relinking: Recent advances and applications. In T. Ibaraki, K. Nonobe, and M. Yagiura, editors,
*Metaheuristics: Progress as Real Problem Solvers*. Kluwer Academic Publishers, 2005.Google Scholar - N. Robertson, D. Sanders, P. Seymour, and R. Thomas. The four-color theorem.
*Journal of Combinatorial Theory*, 70(1):2–44, 1997.zbMATHCrossRefMathSciNetGoogle Scholar - S. Salcedo-Sanz, C. Buso no Calzón, and A. R. Figueiral-Vidal. Mixed neural-genetic algorithm for the broadcast scheduling problem.
*IEEE Transactions on Wireless Communications*, 2(2):277–283, 2003.CrossRefGoogle Scholar - A. Saxena. Polyhedral studies in domination graph theory (I). http://littlehurt.gsia.cmu.edu/gsiadoc/WP/2003-E80.pdf, 2003. Accessed November 2004.
- A. Sen and M. L. Huson. A new model for scheduling packet radio networks.
*Wireless Networks*, 3:71–82, 1997.CrossRefGoogle Scholar - R. Sivakumar, B. Das, and V. Bharghavan. Spine routing in ad hoc networks.
*Cluster Computing*, 1(2):237–248, 1998.CrossRefGoogle Scholar - S. Sivavakeesar and G. Pavlou. A prediction-based clustering algorithm to achieve quality of service in mulithop ad hoc networks. In
*Proceedings of the London Communications Symposium (LCS), London, UK*, pages 17–20, 2002.Google Scholar - I. Stojmenovic, editor.
*Handbook of Wireless Networks and Mobile Computing*. Wiley InterScience, 2002.Google Scholar - I. Stojmenovic, M. Seddigh, and J. Zunic. Dominating sets and neighbor elimination-based broadcasting algorithms in wireless networks.
*IEEE Transactions on Parallel and Distributed Systems*, 13(1): 14–25, 2002.CrossRefGoogle Scholar - L. Tassiulas and A. Ephremides. Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks.
*IEEE Transactions on Automatic Control*, 37(12): 1936–1948, 1992.zbMATHCrossRefMathSciNetGoogle Scholar - J. A. Telle. Complexity of domination-type problems in graphs.
*Nordic J. of Computing*, 1(1): 157–171, 1994.MathSciNetGoogle Scholar - J. van den Heuvel and S. McGuinness. Coloring the square of a planar graph.
*Journal of Graph Theory*, 42(2):110–124, 2003.zbMATHCrossRefMathSciNetGoogle Scholar - T. H. P. Vuong and D. T. Huynh. Adapting broadcasting sets to topology changes in packet radio networks. In
*Proceedings of the Eight International Conference on Computer Communications and Networks*, pages 263–268, 1999.Google Scholar - P.-J. Wan. Lecture notes on wireless networking: OVSF-CDMA code assignment in wireless ad hoc networks. http://www.cs.iit.edu/wan/lecture10.pdf, 2004. Accessed October 2004.
- P.-J. Wan, K. M. Alzoubi, and O. Frieder. A simple heuristic for minimum connected dominating set in graphs.
*International Journal of Foundations of Computer Science*, 14(2):323–333, 2003.zbMATHCrossRefMathSciNetGoogle Scholar - P.-J. Wan, K. M. Alzoubi, and O. Frieder. Distributed construction of connected dominating set in wireless ad hoc networks.
*Mobile Networks and Applications*, 9(2): 141–149, 2004.CrossRefGoogle Scholar - G. Wang and N. Ansari. Optimal broadcast scheduling in packet radio networks using mean field annealing.
*IEEE Journal on Sleceted Areas in Communications*, 15(2): 250–260, 1997.CrossRefGoogle Scholar - Y. Watanabe, N. Mizuguchi, and Y. Fujii. Solving optimization problems by using a hopfield neural network and genetic algorithm combination.
*Syst. Comput. Japan*, 29(10):68–73, 1998.CrossRefGoogle Scholar - J. Wu. Extended dominating-set-based routing in ad hoc wireless networks with unidirectional links.
*IEEE Transactions on Parallel and Distributed Computing*, 22(1–4):327–340, 2002.Google Scholar - J. Wu and H. Li. A dominating-set-based routing scheme in ad hoc wireless networks.
*Telecommunication Systems*, 18(1–3): 13–36, 2001.zbMATHCrossRefGoogle Scholar - J. Wu, B. Wu, and I. Stojmenovic. Power-aware broadcasting and activity scheduling in ad hoc wireless networks using connected dominating sets.
*Wireless Communications and Mobile Computing*, 4(1):425–438, 2003.CrossRefGoogle Scholar - Y. Xue, B. Li, and K. Nahrstedt. Price-based resource allocation in wireless ad-hoc networks. In
*Proc. IWQoS 2003*, 2003.Google Scholar - J. Yeo, H. Lee, and S. Kim. An efficient broadcast scheduling algorithm for TDMA ad hoc networks.
*Computers and Operations Research*, 29:1793–1806, 2002.CrossRefGoogle Scholar