On the complexity of scheduling incompatible jobs with unit-times
We consider scheduling problems in a multiprocessor system with incompatibile jobs of unit-time length where two incompatible jobs can not be processed on the same machine. Given a deadline κ′ and a number of κ machines, the problem is to find a feasible assignment of the jobs to the machines. We prove the computational complexity of this scheduling problem restricted to different graph classes, arbitary and constant numbers κ and κ′.
Unable to display preview. Download preview PDF.
- 1.Corneil, D.G., Perl, Y., Stewart, L.K.: A linear recognition algorithm for cographs. SIAM Journal of Computing 4 (1985) 926–934Google Scholar
- 2.Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)Google Scholar
- 3.Golumbic, M.C.: Algorithmic graph theory and perfect graphs. Academic Press, New York (1980)Google Scholar
- 4.Gupta, U.I., Lee, D.T., Leung, J.Y.-T.: Efficient algorithms for interval graphs and circular arc graphs. Networks 12 (1982) 459–467Google Scholar
- 5.Karp, R.M.: Reducibility among combinatorial problems. In: Miller, Thatcher (eds.): Complexity of computer computations, Plenum Press (1972) 85–104Google Scholar
- 6.Lonc, Z.: On complexity of some chain and antichain partition problems. WG Conference, LNCS (1991) 97–104Google Scholar
- 7.Papadimitriou, C.H., Yannakakis, M.: Scheduling interval-ordered tasks. SIAM Journal of Computing 8 (1979) 405–409Google Scholar
- 8.Scinsche, D.: On a property of the class of n-colorable graphs. Journal of Combinatoral Theory B 16 (1974) 191–193Google Scholar