Frequency Assignment: Theory and Applications

Proceedings of the IEEE

Volumn 68, Issue 12, 1980, Pages 1497-1514

  Hale, William K ^a  

^a US Department of Commerce   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

RADIO;

EID: 0019213982     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/PROC.1980.11899     Document Type: Article

References (98)

1. D. M. Jansky, Spectrum Management Techniques, Germantown, MD: Don White Consultants, 1977.
2. JTAC, “Spectrum engineering—The key to progress,” New York: IEEE, 1968.
3. H. Eden, H. W. Fastert, and K. H. Kaltbeitzer, “More recent methods of television network planning and the results obtained,” E.B.U. Rev., no. 60-A, pp. 54–59, Apr. 1960.
4. H. W. Fastert, “The mathematical theory underlying the planning of transmitter networks,” E.B.U. Rev., no. 60-A, pp. 60–69, Apr. 1960.
5. B. H. Metzger, “Spectrum management technique,” presented at 38th Nat. ORSA Meet. (Detroit, MI), Fall 1970.
6. J. J. Pawelec, “An algorithm for assignment of optimum frequencies to homogeneous VHF radio networks,” Telecommun. J., vol. 40, pp. 21–27, 1973.
7. J. Arthur Zoellner, “Frequency assignment games and strategies,” IEEE Trans. on Electromagn. Compat., vol. EMC-15, pp. 191–196, Nov. 1973.
8. C. E. Dadson, J. Durkin, and R. E. Martin, “Computer prediction of field strength in the planning of radio systems,” IEEE Trans. Veh. Technol., vol. VT-24, pp. 1–8, Feb. 1975.
9. R. A. Frazier, “Compatibility and the frequency selection problem,” IEEE Trans. Electromagn. Compat., vol. EMC-17, pp. 248–254, Nov. 1975.
10. S. H. Cameron, “Sequential insertion: An algorithm for conserving spectrum in the assignment of operating frequencies to operating systems,” Annapolis, MD: ECAC, Sept. 1975, (ECAC-TN-75-0023).
11. T. Sakaki, K. Nakashima, and Y. Hattori, “Algorithms for finding in the lump both bounds of the chromatic number of a graph,” Comput. J., vol. 19, no. 4, pp. 329–332, Nov. 1976.
12. R. J. Pennotti and R. R. Boorstyn, “Channel assignments for cellular mobile telecommunications systems,” in Proc. IEEE Nat. Telecommunications Conf. (Dallas, TX), pp. 16.5-1–16.5-5, Nov. 1976.
13. J. A. Zoellner and C. L. Beall, “A breakthrough in spectrum conserving frequency assignment technology,” IEEE Trans. Electromagn. Compat., vol. EMC-19, pp. 313–319, Aug. 1977.
14. C. L. Beall, and M. J. Dash, “An automated frequency assignment system for air voice communication circuits in the frequency band from 225 MHz to 400 MHz,” in Proc. IEEE Int. Symp. Electromagnetic Compatibility (Seattle, WA), pp. 302–304, Aug. 1977.
15. P. A. Major, “A parameter-sensitive frequency-assignment method (PSFAM),” IEEE Trans. Electromagn. Compat., vol. EMC-19, pp. 330–332, Aug. 1977.
16. M. J. Dash and S. R. Green, “Parameter sensitivity analysis: An approach used in the investigation of frequency assignment problems,” in Proc. Conf. Electromagnetic Compatibility (Guildford, England), pp. 55–64, Apr. 1978.
17. F. Box, “A heuristic technique for assigning frequencies to mobile radio nets,” IEEE Trans. Veh. Technol. vol. VT-27, pp. 57–74, May 1978.
18. S. Cameron, and Y. Wu, “A frequency assignment algorithm based on a minimum residual difficulty heuristic,” in Proc. IEEE Int. Symp. EMC '79 (CH 13839 EMC), pp. 350–354, Oct. 1979.
19. S. A. Cook, “The complexity of theorem-proving procedures,” Proc. 3rd ACM Symp. Theory of Computing, pp. 151–158, 1971.
20. R. M. Karp, “Reducibility among combinatorial problems,” in Complexity of Computer Computations, R. E. Miller and J. W. Thatcher, Eds. New York: Plenum Press, pp. 85–104, 1972.
21. M. R. Garey, D. S. Johnson, and L. Stockmeyer, “Some simplified NP-complete problems,” in Proc. 6th ACM Annu. Symp. Theory and Computing, pp. 237–267, 1974.
22. M. R. Garey and D. S. Johnson, “The complexity of near-optimal graph coloring,” J. ACM, vol. 23, no. 1, pp. 43–49, Jan. 1976.
23. —, Computers and Intractability: A Guide to the Theory of NP-Completeness. San Francisco, CA: Freeman, 1979.
24. H. R. Lewis and C. H. Papadimitriou, “The efficiency of algorithms,” Scientific Amer., pp. 96–109, Jan. 1978.
25. R. L. Brooks, “On colouring the nodes of a network,” in Proc. Cambridge Philosophy Society, vol. 37, pp. 194–197, 1941.
26. A. A. Zykov, “On some properties of linear complexes,” Mat. Sbornik, vol. 24/26, p. 163 (in Russian) (Amer. Math. Soc. Translation, No. 79, 1952.)
27. C. Berge, Theory of Graphs and its Applications. Paris, France: Dunod, 1958.
28. F. Harary, Graph Theory. Reading, Ma: Addison-Wesley, 1969.
29. N. Christofides, “An algorithm for the chromatic number of a graph,” Comput. J., vol. 14, no. 1, pp. 38–39, Feb. 1971.
30. F. Gavril, “Algorithms for minimum colouring, maximum clique, minimum covering, by cliques and maximum independent set of a chordal graph,” SIAM J. Comput. vol. 1, no. 2, pp. 180–187, 1972.
31. S. Even and A. Pnueli, “Permutation graphs and transitive graphs,” J. ACM, vol. 19, no. 3, pp. 400–410, July 1972.
32. A. A. Borovikov and V. A. Gorbatov, “A criterion for coloring of the vertices of a graph,” Eng. Cybernetics, vol. 10, no. 4, pp. 683–686, 1972.
33. J. Randall-Brown, “Chromatic scheduling and the chromatic number problems,” Management Sci. vol. 19.4, Part I, pp. 456–463, Dec. 1972.
34. A. C. Tucker, “Perfect graphs and an application to optimizing municipal services,” SIAM Rev., vol. 15, pp. 585–590, 1973.
35. S. I. Roschke and A. L. Furtado, “An algorithm for obtaining the chromatic number and an optimal coloring of a graph,” Inf. Process. Lett. (The Netherlands), vol. 2, no. 2, pp. 34–38, June 1973.
36. D. G. Corneil and B. Graham, “An algorithm for determining the chromatic number of a graph,” SIAM J. Comput., vol. 2, no. 4, pp. 311–318, Dec. 1973.
37. C. C. Wang, “An algorithm for the chromatic number of a graph,” J. ACM vol. 21, no. 3, pp. 385–391, July 1974.
38. A. Tucker, “Coloring a family of circular arcs,” SIAM J. Appl. Math., vol. 29, pp. 493–502, 1975.
39. N. Christofides, Graph Theory: An Algorithmic Approach, New York: Academic Press, pp. 58–78, 1975.
40. E. L. Lawler, “A note on the complexity of the chromatic number problem,” Inf. Process. Lett., (The Netherlands), no. 3, pp. 66–67, Aug. 1976.
41. M. C. Golumbic, “The complexity of comparability graph recognition and coloring,” Computing (Austria), vol. 18, no. 3, pp. 199–208, 1977.
42. S. H. Cameron, “The solution of the graph-coloring problem as a set-covering problem,” IEEE Trans. Electromagn. Compat., vol. ECM-19, no. 3, Pt. 2, pp. 320–322, Aug. 1977.
43. A. M. Walsh and W. A. Burkhard, “Efficient algorithms for (3, 1) graphs,” Inform. Sci., vol. 3, no. 1, pp. 1–10, 1977.
44. P. K. Srimani, B. P. Sinha, and A. K. Choudhury, “A new method to find out the chromatic partition of a symmetric graph,” Int. J. Syst. Sci., vol. 9, no. 12, pp. 1425–1437, Dec. 1978.
45. S. M. Korman, “The graph-colouring problem,” in Combinatorial Optimization, N. Christofides, A. Mingozzi, P. Toth, and C. Sandi, Eds. Chinchester, England: Wiley, pp. 211–235, 1979.
46. C. McDiarmid, “Determining the chromatic number of a graph,” SIAM J. Comput., vol. 8, no. 1, pp. 1–14, Feb. 1979.
47. D. Brelaz, “New methods to color the vertices of a graph,” Commun. ACM, vol. 22, no. 4, pp. 251–256, Apr. 1979.
48. M. R. Garey, D. S. Johnson, G. L. Miller, and C. H. Papadimitriou, “The complexity of coloring circular arcs and chords,” SIAM J. Discrete Algebraic Methods, to be published.
49. 2) algorithm for coloring proper circular arc graphs,” SIAM J. Discrete Algebraic Methods, to be published.
50. J. E. L. Peck and M. R. Williams, “Examination scheduling, algorithm 286,” Commun. ACM, vol. 9, no. 6, pp. 433–434, 1966.
51. D. J. A. Welsh and M. B. Powell, “An upper bound for the chromatic number of a graph and its application to timetabling problems,” Computer J., vol. 10, pp. 85–86, 1967.
52. I. Tomescu, “An algorithm for determining the chromatic number of a finite graph,” Econ. Comput. Cybern. Stud. Res. (Rumania), no. 1, pp. 69–81, 1969.
53. D. C. Wood, “A technique for colouring a graph applicable to large scale timetabling problems,” Comput. J., vol. 12, pp. 317–319, 1968.
54. M. R. Williams, “The colouring of very large graphs,” in Combinatorial Structures and Their Applications, R. K. Guy, H. Hanani, N. Sauer, and J. Schonheim, Eds. New York: Gordon and Breach, 1970, pp. 477–478.
55. R. S. Wilkov and W. H. Kim, “A practical approach to the chromatic partition problem,” J. Franklin Inst., vol. 289, no. 5, pp. 333–349, May 1970.
56. R. A. Draper, “A graph coloring algorithm and a scheduling problem,” M.S. thesis, Naval Postgraduate School Monterey, CA, 1971.
57. A. A. Kalnin'sh, “The coloring of graphs in a linear number of steps,” Cybern., vol. 7, no. 4, pp. 691–700, July–Aug. 1971.
58. D. W. Matula, W. G. Marble and J. D. Isaacson, “Graph coloring algorithms,” in Graph Theory and Computing, R. C. Read, Ed. New York: Academic Press, 1972, pp. 109–122.
59. D. W. Matula, “Bounded color functions on graphs,” Networks, vol. 2, pp. 29–44, 1972.
60. M. R. Williams, “Heuristic procedures (if they work leave them alone),” Software Practice and Experience, vol. 4, no. 3, pp. 237–240, July–Sept. 1974.
61. F. Dunstan, “Greedy algorithms for optimization problems,” presented at Euro I meeting, (Brussels, Belgium) Jan. 1975.
62. A. Tehrani, “Un algorithme de coloration,” Cahiers du centre d'Etudes de Recherche Operationnelle, vol. 17, no. 2–4, pp. 395–398, 1975.
63. D. S. Johnson, “Worst case behavior of graph coloring algorithms,” in Proc. 5th Southeastern Conf. Combinatories, Graph Theory Computing pp. 513–528, 1974. (Winnepeg, Canada: Utilitas Mathematics Publishing.)
64. D. S. Johnson, “Approximation algorithms for combinatorial problems,” J. Comput. Syst. Sci., vol. 9, no. 3, pp. 256–278, 1974.
65. R. Karp and D. W. Matula, “Probabilistic behaviour of a naive coloring algorithm on random graphs,” Bull. Oper. Res. Soc. Amer., vol. 23, suppl. 2, p. 264, Fall 1975.
66. J. Mitchem, “On various algorithms for estimating the chromatic number of a graph,” Comput. J., vol. 19, no. 2, pp. 182–183, May 1976.
67. M. Kubale, and J. Dabrowski, “Empirical comparison of efficiency of some graph colouring algorithms,” Arch. Autom. Telemech. (Poland), vol. 23, no. 1–2, pp. 129–139, 1978.
68. N. K. Mehta, “Performance of selected graph coloring algorithms-empirical results,” presented at the 1980 TIMS/ORSA Conf. (Washington, DC), May 4–7, 1980.
69. A. P. Ershov and G. I. Kozhukhin, “Estimates of the chromatic number of connected graphs,” Dokl. Akad. Nauk, vol. 142, pp. 270–273; and Trans. Soviet Math., vol. 3, pp. 50–53, 1962.
70. H. S. Wilf, “The eigenvalues of a graph and its chromatic number,” J. London Math. Soc., vol. 42, pp. 330–332, 1967.
71. G. Szekeres and H. S. Wilf, “An inequality for the chromatic number of a graph,” J. Comb. Theory, vol. 4, pp. 1–3, 1968.
72. J. H. Folkman, “An upper bound on the chromatic number of a graph,” Rand Corp., California, Rep. RM-5808-PR, NTIS no. AD-684 527, Febr. 1969.
73. P. Holgate, “Majorants of the chromatic number of a random graph,” J. Roy. Statistics Soc. Ser. B, vol. 31, pp. 303–309, 1969.
74. A. J. Hoffman, “On eigenvalues and colorings of graphs,” in Graph Theory and Its Applications, B. Harris, Ed. New York: Academic Press, pp. 79–91, 1970.
75. B. Andrasfai, P. Erdos, and V. T. Sos, “On the connection between chromatic number, maximal clique and minimal degree of a graph,” Discrete Math. (The Netherlands), vol. 8, no. 3, pp. 205–218, May 1974.
76. J. Lawrence, “Covering the vertex set of a graph with subgraphs of smaller degree,” Discrete Math. (The Netherlands), vol. 21, no. 1, pp. 61–68, Jan. 1978.
77. P. A. Catlin, “A bound on the chromatic number of a graph,” Discrete Math. (The Netherlands), vol. 22, no. 1, pp. 81–83, Apr. 1977.
78. —, “Another bound on the chromatic number of a graph,” Discrete Math. (The Netherlands), vol. 24, no. 1, pp. 1–6, Oct. 1978.
79. E. Nordhaus, E. and J. Gaddum, “On complementary graphs coloring,” Amer. Math. Monthly, vol. 63, pp. 175–177, 1956.
80. J. A. Bondy, “Bounds for the chromatic number of a graph,” J. Combin. Theory, vol. 7, pp. 96–98, 1969.
81. B. R. Myers, and R. Liu, “A lower bound on the chromatic number of a graph,” Networks, vol. 1, no. 3, pp. 273–277, 1972.
82. L. C. Middlekamp, “UHF taboos—History and development,” IEEE Trans. Consumer Electron., vol. CE-24, pp. 514–519, Nov. 1978.
83. K. Baker, Introduction to Sequencing and Scheduling, New York: Wiley, 1974.
84. E. G. Coffman, Jr., Computer and Job Shop Scheduling Theory, New York: Wiley, 1976.
85. R. W. Conway, W. L. Maxwell, and L. W. Miller, Theory of Scheduling. Reading, MA: Addison-Wesley, 1967.
86. S. Elmaghraby Ed., Symposium on the Theory of Scheduling. Berlin, Germany: Springer-Verlag, 1973.
87. J. L. Lenstra, Sequencing of Enumerative Methods. Amsterdam, The Netherlands: Mathematisch Centrum, 1976.
88. A. H. G. Rinnooy Kan, Machine Scheduling Problems: Classification, Complexity and Computations. The Hague, The Netherlands: Nijhoff, 1976.
89. W. K. Hale, “Optimal channel assignment and chromatic graph theory,” presented at MAA/AMS/ASL Nat. Meet., Boulder, CO, Mar. 1980.
90. A. M. Odlyzko and N. J. A. Sloane, “New bounds on the number of unit spheres that can touch a unit spere in n dimensions,” J. Combin. Theory Ser. B (USA), vol. 26, no. 3, pp. 276–294, Mar. 1979.
91. A. Tucker, “An efficient test for circular-arc graphs,” SIAM J. Comput., vol. 9, pp. 1–24, Feb. 1980.
92. W. K. Hale, “Spectrum efficiency as a function of frequency distance rules,” presented at ORSA/TIMS Nat. Meet. (Colorado Springs, CO), Nov. 10–12, 1980.
93. P. Armitage, “An overlap problem arising in particle counting,” Biometrika, vol. 36, pp. 257–266, 1949.
94. C. Mack, “The expected number of clumps when convex laminae are placed at random and with random orientation on a plane area,” in Proc. Cambridge Philosophy Society, vol. 50, pp. 581–585, 1954.
95. E. Gilbert, “Random plane networks,” J. Soc. Indust. Appl. Math, vol. 9, no. 4, pp. 533–543, Dec. 1961.
96. —, “The probability of covering a sphere with N circular caps,” Biometrika, vol. 52, nos. 3 and 4, pp. 323–330, 1965.
97. H. DeWitt and M. Krieger, “An efficient algorithm for computing the minimal spanning tree of a graph in a Euclidean-like space,” in Proc. 8th Hawaii Int. Conf. System Sciences, pp. 253–255, 1975.
98. —, “Expected structure of Euclidean graphs,” presented at the 1976 Symp. New Directions and Resent Results in Algorithms and Complexity, Carnegie-Mellon Univ., Pittsburgh, PA, Apr. 7–9, 1976.