Abstract
We consider the mixed graph coloring problem which is used for formulating scheduling problems where both incompatibility and precedence constraints can be present. We give an O(n 3.376 logn) algorithm for finding an optimal schedule for a collection of jobs whose constraint relations form a mixed series-parallel graph.
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References
Abdel-Wahab, H.M., Kameda, T.: Scheduling to minimize maximum cumulative cost subject to series-parallel precedence constraints. Operations Research 26(1), 141–158 (1978)
Bender, M.A., Rabin, M.O.: Online scheduling of parallel programs on heterogeneous systems with applications to cilk. Theory of Computing Systems 35(3), 289–304 (2002)
Burns, R.N., Steiner, G.: Single machine scheduling with series-parallel precedence constraints. Operations Research 29(6), 1195–1207 (1981)
Coppersmith, D., Winograd, S.: Matrix multiplication via arithmetic progressions. Journal of Symbolic Computation 9, 251–280 (1990)
Finta, L., Liu, Z., Milis, I., Bampis, E.: Scheduling UET-UCT series-parallel graphs on two processors. Theoretical Computer Science 162(2), 323–340 (1996)
Hansen, P., Kuplinsky, J., de Werra, D.: Mixed graph colorings. Mathematical Methods of Operations Research 45, 145–160 (1997)
Hedetniemi, S.T., Laskar, R., Pfaff, J.: Linear algorithms for independent domination in series-parallel graphs. Congressus Numerantium 45, 71–82 (1984)
Kikuno, T., Yoshida, N., Kakuda, Y.: A linear algorithm for the domination number of a series-parallel graph. Discrete Applied Mathematics 5, 299–311 (1983)
Möhring, R.H., Schäffter, M.W.: Scheduling series-parallel orders subject to 0/1-communication delays. Parallel Computing 25(1), 23–40 (1999)
Ries, B.: Coloring some classes of mixed graphs. Discrete Applied Mathematics 155, 1–6 (2007)
Ries, B., de Werra, D.: On two coloring problems in mixed graphs. Electronic Journal of Combinatorics (to appear)
Roy, B., Sussmann, B.: Les problems d’ordonnancement avec constraintes disjonctives, Node DS No. 9 Bis, SEMA (1964)
Sotskov, Y.N.: Scheduling via mixed graph coloring. In: Operations Research Proceedings, pp. 414–418. Otto-von-Guericke Univeristy (2000)
Sotskov, Y.N., Dolgui, A., Werner, F.: Mixed graph coloring for unit-time job-shop scheduling. International Journal of Mathematical Algorithms 2(4), 289–323 (2001)
Sotskov, Y.N., Tanaev, V.S., Werner, F.: Scheduling problems and mixed graph colorings. Optimization 51(3), 597–624 (2002)
Sotskov, Y.N., Tanaev, V.S.: Chromatic polynomial of a mixed graph. Vestsi Akademii Navuk BSSR, Seriya Fiz.-Mat. Navuk 6, 597–624 (1976)
Valdes, J., Tarjan, R.E., Lawler, E.L.: The recognition of series parallel digraphs. SIAM Journal on Computing 11, 189–201 (1979)
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Furmańczyk, H., Kosowski, A., Żyliński, P. (2008). Scheduling with Precedence Constraints: Mixed Graph Coloring in Series-Parallel Graphs. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2007. Lecture Notes in Computer Science, vol 4967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68111-3_106
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DOI: https://doi.org/10.1007/978-3-540-68111-3_106
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