Scheduling theory is an important branch of operations research. Problems studied within the framework of that theory have numerous applications in various fields of human activity. As an independent discipline scheduling theory appeared in the middle of the fifties, and has attracted the attention of researchers in many countries. In the Soviet Union, research in this direction has been mainly related to production scheduling, especially to the development of automated systems for production control. In 1975 Nauka ("Science") Publishers, Moscow, issued two books providing systematic descriptions of scheduling theory. The first one was the Russian translation of the classical book Theory of Scheduling by American mathematicians R. W. Conway, W. L. Maxwell and L. W. Miller. The other one was the book Introduction to Scheduling Theory by Soviet mathematicians V. S. Tanaev and V. V. Shkurba. These books well complement each other. Both. books well represent major results known by that time, contain an exhaustive bibliography on the subject. Thus, the books, as well as the Russian translation of Computer and Job-Shop Scheduling Theory edited by E. G. Coffman, Jr., (Nauka, 1984) have contributed to the development of scheduling theory in the Soviet Union. Many different models, the large number of new results make it difficult for the researchers who work in related fields to follow the fast development of scheduling theory and to master new methods and approaches quickly.

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Preface. Introduction. 1: Elements of Graph Theory and Computational Complexity of Algorithms. 1. Sets, Orders, Graphs. 2. Balanced 2-3-Trees. 3. Polynomial Reducibility of Discrete Problems. Complexity of Algorithms. 4. Bibliography and Review. 2: Polynomially Solvable Problems. 1. Preemption. 2. Deadline-Feasible Schedules. 3. Single Machine. Maximal Cost. 4. Single Machine. Total Cost. 5. Identical Machines. Maximal Completion Time. Equal Processing Times. 6. Identical Machines. Maximal Completion Time. Preemption. 7. Identical Machines. Due Dates. Equal Processing Times. 8. Identical Machines. Maximal Lateness. 9. Uniform and Unrelated Parallel Machines. Total and Maximal Cost. 10. Bibliography and Review. 3: Priority-Generating Functions. Ordered Sets of Jobs. 1. Priority-Generating Functions. 2. Elimination Conditions. 3. Tree-like Order. 4. Series-Parallel Order. 5. General Case. 6. Convergence Conditions. 7. 1-Priority-Generating Functions. 8. Bibliography and Review. 4: NP-Hard Problems. 1. Reducibility of the Partition Problem. 2. Reducibility of the 3-Partition Problem. 3. Reducibility of the Vertex Covering Problem. 4. Reducibility of the Clique Problem. 5. Reducibility of the Linear Arrangement Problem. 6. Bibliographic Notes. Appendix. Approximation Algorithms. References. Additional References. Index.