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V. A. Mikhailyuk, “General Approach to Estimating the Complexity of Postoptimality Analysis for Discrete Optimization Problems,” Cybernetics and Systems Analysis, Vol. 46, No. 2, 2010, pp. 290-295. doi:10.1007/s10559-010-9206-1

has been cited by the following article:

• TITLE: Optimal Approximation Algorithms for Reoptimization of Constraint Satisfaction Problems

  AUTHORS: Victor Alex Mikhailyuk

  KEYWORDS: C-Approximation Algorithm; Reoptimization; Approximation Resistant Predicates; Integrality Gap; Unique Games Conjecture (UGC)

  JOURNAL NAME: American Journal of Operations Research, Vol.3 No.2, March 28, 2013

  ABSTRACT: The purpose of reoptimization using approximation methods—application of knowledge about the solution of the initial instance I, provided to achieve a better quality of approximation (approximation ratio) of an algorithm for determining optimal or close to it solutions of some “minor” changes of instance I. To solve the problem Ins-Max-EkCSP-P (reoptimization of Max-EkCSP-P with the addition of one constraint) with approximation resistant predicate P exists a polynomial threshold (optimal) -approximation algorithm, where the threshold “random” approximation ratio of P). When the unique games conjecture (UGC) is hold there exists a polynomial threshold (optimal) -approximation algorithm (where and the integrality gap of semidefinite relaxation of Max-EkCSP-P problem Z) to solve the problem Ins-Max-EkCSP-P.