Data Correcting Approaches in Combinatorial Optimization
Springer Science & Business Media, Oct 10, 2012 - Mathematics - 114 pages
Data Correcting Approaches in Combinatorial Optimization focuses on algorithmic applications of the well known polynomially solvable special cases of computationally intractable problems. The purpose of this text is to design practically efficient algorithms for solving wide classes of combinatorial optimization problems. Researches, students and engineers will benefit from new bounds and branching rules in development efficient branch-and-bound type computational algorithms. This book examines applications for solving the Traveling Salesman Problem and its variations, Maximum Weight Independent Set Problem, Different Classes of Allocation and Cluster Analysis as well as some classes of Scheduling Problems. Data Correcting Algorithms in Combinatorial Optimization introduces the data correcting approach to algorithms which provide an answer to the following questions: how to construct a bound to the original intractable problem and find which element of the corrected instance one should branch such that the total size of search tree will be minimized. The PC time needed for solving intractable problems will be adjusted with the requirements for solving real world problems.
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Chapter 2 Maximization of Submodular Functions Theory and Algorithms
Chapter 3 Data Correcting Approach for the Maximization of Submodular Functions
Chapter 4 Data Correcting Approach for the Simple Plant Location Problem
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applied average calculation branching rule Cherenin’s excluding rules clients combinatorial optimization combinatorial optimization problems component computational experiments computational results Corollary 2.3 corresponding data correcting algorithm Data Correcting Approaches DC algorithm DCA(PPAr deﬁned dense graphs diagonal dominance dichotomy algorithm distance matrix Erlenkotter bound example feasible solutions G T\S global maximum Goldengorin greedy algorithm Hammer–Beresnev function Hasse diagram heuristic interval S,T Khachaturov–Minoux bound Lemma linear local maximum Max-Cut maxima nonlinear terms NP-hard number of vertices optimal solution optimal value Pardalos plant location problem PMSF polynomially solvable special postcondition PP-function PPAr preprocessing rules prescribed accuracy preservation rules Proof proximity measure QCP instances QZOP reduce reduction procedure rules of order Sect simple plant location solve SPLP instance subinterval submodular function submodularfunction subsets supermodular supermodular function Table Theorem 3.2 transportation costs Traveling Salesman Problem upper bound