"The composite graph coloring problem (CGCP) is a generalization of the standard graph coloring problem (SGCP). Associated with each vertex is a positive integer called its chromaticity. The chromaticity of a vertex specifies the number of consecutive colors which must be assigned to it.
An exact algorithm for solving the CGCP is presented. The algorithm is a generalization of the vertex-sequential with dynamic reordering approach for the SGCP. It is shown that the method is as effective on composite graphs as its counterpart is on standard graphs. Let 𝒳̅̅(CGn,p) and 𝒳̅̅(SGn,p) denote, respectively, the mean chromatic number of a sample of random composite and standard graphs of order n and edge density p. It is demonstrated that the ratio 𝒳̅̅(CGn,p) / 𝒳̅̅(SGn,p), depends on p, but, for fixed p, is essentially constant, over the range of values of n for which the algorithms were applied.
Several new heuristic methods for efficiently approximating 𝒳(CGn,p) for large values of n are presented. Of these, the CDsatur and CDsaturI1 algorithms, which are generalizations of the well known Dsatur algorithm, are shown to be very competitive with previously tested procedures.
A known method for calculating probabilistic lower bounds for 𝒳̅̅(SGn,p) is generalized to produce such bounds for 𝒳̅̅(CGn,p). Also, a method for estimating the value of 𝒳̅̅(SGn,p), is shown to produce probabilistic upper bounds for 𝒳̅̅(SGn,p). This procedure is then generalized to a method for calculating probabilistic upper bounds for 𝒳̅̅(CGn,p). The resulting bounds are used to evaluate the actual effectiveness of several heuristic algorithms. It is shown that, for fixed p, although the mean absolute error of the heuristic procedures appears to increase as n is varied from 100 to 1000, the mean relative error remains reasonably constant"--
Abstract, page iii.
Gillett, Billy E.
Ho, C. Y. (Chung You), 1933-1988
Prater, John Bruce, 1932-2002
Rigler, A. K.
Ph. D. in Computer Science
University of Missouri--Rolla
xv, 373 pages
© 1990 Jack L. Oakes, All rights reserved.
Dissertation - Restricted Access
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Electronic access to the full-text of this document is restricted to Missouri S&T users. Otherwise, request this publication directly from Missouri S&T Library or contact your local library.http://merlin.lib.umsystem.edu/record=b2322506~S5
Oakes, Jack L., "Algorithms and probabilistic bounds for the chromatic number of random composite graphs" (1990). Doctoral Dissertations. 794.
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