Skip to main content

Algorithms and Methods for Solving Scheduling Problems and Other Extremum Problems on Large-Scale Graphs


We consider a large-scale directed graph G = (V, E) whose edges are endowed with a family of characteristics. A subset of vertices of the graph, V′ ⊂ V, is selected and some additional conditions are imposed on these vertices. An algorithm for reducing the optimization problem on the graph G to an optimization problem on the graph G′ = (V′, E′) of a lower dimension is developed. The main steps of the solution and some methods for constructing an approximate solution to the problem on the transformed graph G′ are presented.

This is a preview of subscription content, access via your institution.


  1. 1.

    T. H. Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms, McGraw-Hill, New York (1990).

    Google Scholar 

  2. 2.

    M. Thorup, “Undirected single-source shortest paths with positive integer weights in linear time,” J. ACM, 46, No.3, 362–394 (1999).

    Article  Google Scholar 

  3. 3.

    J. W. J. Williams, “Heapsort,” Commun. ACM, 7, No.6 (June), 347–348 (1964).

    Google Scholar 

  4. 4.

    A. V. Inyukhin, E. V. Pankratiev, A. M. Chepovskiy, and S. V. Chernyshev, “Using the T-system for transforming the road graph in the problem of route optimization,” in: High-Efficient Computations and Their Applications, Proceedings of All-Russia scientific conference (Chernogolovka, October 30–November 2, 2000), Mosk. Gos. Univ., Moscow (2000), pp. 220–223.

    Google Scholar 

  5. 5.

    E. V. Pankratiev, A. M. Chepovskiy, E. A. Cherepanov, and S. V. Chernyshev, “Determining collections of optimal routes on large-scale road networks of geoinformational systems,” Proceedings of the 10th International Conference on Problems of Data Transmitting and Processing in Telecommunication Networks and Systems, Ryazan’, 2001, Ryazanskaya Gos. Radiotekhnicheskaya Akademiya, Ryazan (2001), pp. 240–241.

    Google Scholar 

Download references

Author information



Additional information


Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 235–251, 2003.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Pankratiev, E.V., Chepovskiy, A.M., Cherepanov, E.A. et al. Algorithms and Methods for Solving Scheduling Problems and Other Extremum Problems on Large-Scale Graphs. J Math Sci 128, 3487–3495 (2005).

Download citation


  • Approximate Solution
  • Schedule Problem
  • Additional Condition
  • Directed Graph
  • Main Step