Book Review: Discrete Analysis and operation Research

Alesksei D. Korshunov(ed.), Discrete Analysis and Operations Research, Kluwer AcademicPublishers,Dordrecht/Boston/London, 1996. This book contains translations ofpapers from the first volume of the new Russianlanguage journal edited at the Sobolev Institute of Mathematics (siberian Branch of the Russian Academy of Sciences, Novosibirsk) since 1994. Thejournal started with the title SibirskiI Zhurnal Issledovaniya Operatsii. Then, the title is changed to Diskretnyi Analiz i Issledovanie Operatsii (Discrete Analysis and Operations Research) since 1995. The discrete optimization (or combinatorial optimization) is the first one in the list of topics covered by this journal. This book contains twenty one articles. Ten of them study combinatorial optimization problems. They are as follows: E.Kh. Gimadi, N.I. Glebov, and A.I. Serdyukov, An Approximation Algorithm for the Traveling Salesman Problem and Its Probabilistic Analysis. N.I. Glebov and A.Y Kostochhka, On Minimum Independent Dominating Sets in Graphs. A.A. Kolokolov, Regular Partitions and Cuts in Integer Programming. A.D. Koshunov, Complexity of Covering of Number Sets by Arithmetical Programming. E. Sh. Kospanov, Circuit Realization of the Sorting Problem. A.Y Kostochka, A Refinement of the Frunk-Sebo-Tardos Theorem and Its Applications. A.V Kastochka and N. Tulai, On the length of the Chinese Postman Tour in Regular Graphs. N.N. Kuzyurin, An Integer Linear Programming Algorithm Polynomial in the Average Case. S.V Sevast’yanov, Efficient Scheduling in Open Shop. S.Y Sevast’ yanov, Nonstrict Vector Summation in Scheduling Problems. These ten articles cover a wide range of optimization problems motivated from applications or theoretical study. Other eleven articles deal with graph and circuit problems. From this book, the reader may learn what Russian mathematician do in discrete mathematics. It is a good reference book for researchers in discrete mathematics, especially in combinatorial optimization.