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The quantity is devoted to Boris Mirkin at the party of his seventieth birthday. as well as his startling PhD leads to summary automata conception, Mirkin’s flooring breaking contributions in a variety of fields of determination making and information research have marked the fourth area of the 20 th century and past. Mirkin has performed pioneering paintings in staff selection, clustering, information mining and data discovery aimed toward discovering and describing non-trivial or hidden structures—first of all, clusters, orderings and hierarchies—in multivariate and/or community data.
This quantity includes a number of papers reflecting contemporary advancements rooted in Mirkin’s basic contribution to the cutting-edge in staff selection, ordering, clustering, facts mining and information discovery. Researchers, scholars and software program engineers will reap the benefits of new wisdom discovery suggestions and alertness directions.
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Extra info for Clusters, Orders, and Trees: Methods and Applications: In Honor of Boris Mirkin's 70th Birthday
Meyer When constraints are allowed, the functions appearing in the ratio are generally assumed to be linear. Problems that have been considered include the minimum ratio spanning-tree problem, the maximum profit-to-time ratio cycle problem, the minimum mean cycle problem, the maximum mean cut problem and the fractional 0–1 knapsack problem: see  for references to these problems. See also Correa et al. , Ursulenko . 1 The Parametric Approach Almost every solution method developed for fractional programming since the seminal work of Dinkelbach  introduces the following auxiliary problem: FPaux.
Program. 124(1–2, Ser. B), 255–269 (2010) 13. : Fractional Programming. Helderman Verlag, Berlin (1988) 14. : On submodular function minimization. Combinatorica 5(3), 185–192 (1985) 15. : GENNCLUS: new models for general nonhierarchical clustering analysis. Psychometrika 47(4), 449–475 (1982) 16. : On nonlinear fractional programming. Manag. Sci. 13, 492–498 (1967) 17. : Mathematical techniques for efficient record segmentation in large shared databases. J. Assoc. Comput. Mach. 23(4), 619–635 (1976) 18.
X // which shows that x k is an optimal solution of problem (CFP). A Polynomial Algorithm for a Class of 0–1 Fractional Programming Problems. . 33 Proposition 10. x/ 0 and let x be an optimal solution of problem (CFP). CFP/: Proof. x k / holds. x k 1 / implies that x k 1 is an optimal solution of problem (CFP). x k 1 /. x k 1 //. x k 1 // optimal solution of problem (CFP). x k 1 / or x k 1 is an optimal solution of problem (CFP). In the following we assume that the former is true. Since ˆ. x k 1 / we conclude that k ˆ.