This book contains translations of papers from the first volume of the new Russian-language journal published at the Sobolev Institute of Mathematics (Sibe­ rian Branch of the Russian Academy of Sciences, Novosibirsk) since 1994. In 1994 the journal was titled Sibirskil Zhurnal Issledovaniya Operatsil. Since 1995 this journal has the title DiskretnYl Analiz i Issledovanie Operatsil (Discrete Analysis and Operations Research) The aim of this journal is to bring together research papers in different areas of discrete mathematics and computer science. The journal DiskretnYl Analiz i Issledovanie Operatsil covers the following fields: - discrete optimization - synthesis and complexity - discrete structures and - of control systems extremal problems - automata - combinatorics - graphs - control and reliability - game theory and its of discrete devices applications - mathematical models and - coding theory methods of decision making - scheduling theory - design and analysis - functional systems theory of algori thms Contributions presented to the journal can be original research papers and occasional survey articles of moderate length. A. D. Korshunov THE NUMBER OF DISTINCT SUBWORDS OF FIXED LENGTH IN THE MORSE-HEDLUND SEQUENCEt) S. V. Avgustinovich An exact formula is obtained for the number of distinct subwords of length n in the Morse-Hedlund sequence [1), i. e., the sequence in which the initial member is 0 and subsequent members are produced by unlimited application of the operation of substituting 01 for 0 and 10 for 1.

InhaltsangabePreface. The Number of Distinct Subwords of Fixed Length in the Morse-Hedlund Sequence; S.V. Avgustinovich. Locally Isometric Embeddings of Graphs and the Metric Prolongation Property; A.A. Evdokimov. Local Complementations of Simple and Directed Graphs; D.G. Fon-Der-Flaass. An Approximation Algorithm for the Travelling Salesman Problem and Its Probabilistic Analysis; È.Kh. Gimadi, et al. On Minimum Independent Dominating Sets in Graphs; N.I. Glebov, A.V. Kostochka. Regular Partitions and Cuts in Integer Programming; A.A. Kolokolov. Complexity of Coverings of Number Sets by Arithmetical Progressions; A.D. Korshunov. Circuit Realization of the Sorting Problem; È.Sh. Kospanov. A Refinement of the Frank-Sebö-Tardos Theorem and Its Applications; A.V. Kostochka. On the Length of the Chinese Postman Tour in Regular Graphs; A.V. Kostochka, N. Tulai. An Integer Linear Programming Algorithm Polynomial in the Average Case; N.N. Kuzyurin. Projections of the Hypercube on the Line and the Plane; A.A. Levin. Canonical Decomposition of Graphs; V.V. Lozin. Fault Detection in Parts of the Circuits of Functional Element; V.N. Noskov. On the External Stability Number of the Generalized De Bruijn Graphs; V. Nyu. On the Lower Bounds for the Complexity of Serial-Parallel Contact Circuits Realizing Linear Boolean Functions; K.L. Rychkov. Efficient Scheduling in Open Shops; S.V. Sevast'yanov. Nonstrict Vector Summation in Scheduling Problems; S.V. Sevast'yanov. Worst-Case Analysis of Some Algorithms for Solving the Subset-Sum Problem; Yu.V. Shamardin. On the Depth of Conditional Tests for Controlling `Negation' Type Faults in Circuits of Functional Gates; V.I. Shevchenko. Synthesis of Transitive Order Relations Compatible with the Power ofCriteria; L.A. Sholomov. Index.

Preface. The Number of Distinct Subwords of Fixed Length in the Morse-Hedlund Sequence; S.V. Avgustinovich. Locally Isometric Embeddings of Graphs and the Metric Prolongation Property; A.A. Evdokimov. Local Complementations of Simple and Directed Graphs; D.G. Fon-Der-Flaass. An Approximation Algorithm for the Travelling Salesman Problem and Its Probabilistic Analysis; ÿ.Kh. Gimadi, et al. On Minimum Independent Dominating Sets in Graphs; N.I. Glebov, A.V. Kostochka. Regular Partitions and Cuts in Integer Programming; A.A. Kolokolov. Complexity of Coverings of Number Sets by Arithmetical Progressions; A.D. Korshunov. Circuit Realization of the Sorting Problem; ÿ.Sh. Kospanov. A Refinement of the Frank-Sebö-Tardos Theorem and Its Applications; A.V. Kostochka. On the Length of the Chinese Postman Tour in Regular Graphs; A.V. Kostochka, N. Tulai. An Integer Linear Programming Algorithm Polynomial in the Average Case; N.N. Kuzyurin. Projections of the Hypercube on the Line and the Plane; A.A. Levin. Canonical Decomposition of Graphs; V.V. Lozin. Fault Detection in Parts of the Circuits of Functional Element; V.N. Noskov. On the External Stability Number of the Generalized De Bruijn Graphs; V. Nyu. On the Lower Bounds for the Complexity of Serial-Parallel Contact Circuits Realizing Linear Boolean Functions; K.L. Rychkov. Efficient Scheduling in Open Shops; S.V. Sevast''yanov. Nonstrict Vector Summation in Scheduling Problems; S.V. Sevast''yanov. Worst-Case Analysis of Some Algorithms for Solving the Subset-Sum Problem; Yu.V. Shamardin. On the Depth of Conditional Tests for Controlling Negation'' Type Faults in Circuits of Functional Gates; V.I. Shevchenko. Synthesis of Transitive Order Relations Compatible with the Power of Criteria; L.A. Sholomov. Index.