TAILIEUCHUNG - On some interconnections between combinatorial optimization and extremal graph theory

The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set. While in combinatorial optimization the point is in developing efficient algorithms and heuristics for solving specified types of problems, the extremal graph theory deals with finding bounds for various graph invariants under some constraints and with constructing extremal graphs. | Yugoslav Journal of Operations Research 14 (2004), Number 2, 147-154 ON SOME INTERCONNECTIONS BETWEEN COMBINATORIAL OPTIMIZATION AND EXTREMAL GRAPH THEORY Dragoš CVETKOVIĆ Faculty of Electrical Engineering, University of Belgrade, Belgrade, Serbia and Montenegro, ecvetkod@ Pierre HANSEN GERAD and École des Hautes Études Commerciales, Montréal H3T 2A7, Canada Vera KOVAČEVIĆ-VUJČIĆ Faculty of Organizational Sciences, University of Belgrade, Belgrade, Serbia and Montenegro verakov@ Received: March 2004 / Accepted: August 2004 The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set. While in combinatorial optimization the point is in developing efficient algorithms and heuristics for solving specified types of problems, the extremal graph theory deals with finding bounds for various graph invariants under some constraints and with constructing extremal graphs. We analyze by examples some interconnections and interactions of the two theories and propose some conclusions. Keywords: Combinatorial optimization, extremal graph theory, variable neighborhood search, mathematical programming. 148 D. Cvetković, P. Hansen, V. Kovačević-Vujčić / On Some Interconnections 1. INTRODUCTION We list a few details from Mathematics Subject Classification 2000 which are relevant for our discussion. 05 Combinatorics 05C Graph Theory 05C35 Extremal Problems 05C90 Graph Algorithms 90 Operations Research, Mathematical Programming 90C Mathematical Programming 90C27 Combinatorial Optimization 90C35 Programming Involving Graphs and Networks 90C22 Semidefinite Programming 68 Computer Science 68R Discrete Mathematics in Relation to Computer Science 68R10 Graph Theory 68W Algorithms 68W05 Non-numerical Algorithms We shal discuss some relations between combinatoral optimization (90C27) and extremal problems in graph theory or .

• Toán học
• Combinatorial optimization
• Extremal graph theory
• Variable neighborhood search
• Mathematical programming
• Efficient algorithms
• Ecosystem management
• Combinatorial optimization techniques
• Meta heuristic
• Economical values
• Probabilistic Combinatorial Optimization
• Probabilistic Graph problems
• Probabilistic Minimum Coloring
• The Probabilistic Longest Path
• Probabilistic Minimum Vertex
• the Probabilistic Maximum Independen
• Efficient transformations
• Generalized combinatorial optimization problems
• Integer programming
• Graph into node sets
• Information sciences
• Multiobjective combinatorial optimization problems
• Well spread set
• Well spread non dominated points
• State of the art
• Ebook Linear optimization
• Linear optimization
• Linear extensions
• Projective algorithms
• Ellipsoid algorithms
• Optimization software
• Minimum cost network flow problem
• Optimization software packages
• Meta–Heuristic methods
• Swarm intelligence
• Scheduling problems
• Foraging habits of honeybees
• Center location problems
• Reverse optimization
• Tree graphs
• Time complexity
• Hamming norms
• Gaussian variable neighborhood search
• File transfer scheduling problem
• Optimization problems
• Báo cáo sinh học hay
• cách trình bày báo cáo
• báo cáo sinh học
• công trình nghiên cứu sinh học
• tài liệu về sinh học
• Dynamic memory allocation Ppblem
• Regarding quality
• Metaheuristic approach
• Transportation problem
• Bottleneck transportation problem
• Bi criteria transportation problem
• Efficient points
• Salesman problem
• System of vertexr equisitions
• Local search
• Efficient point
• Evolutionary algorithms
• Runtime analysis
• Fitness level
• Strong metric dimension
• Graph problems
• Computational approaches
• Historical and scientific framework
• Music generation
• Evolutionary approach
• Algorithm composing
• Music compositions
• Genetic Algorithm
• Optimal Recombination Problem
• Boolean Linear Programming
• Optimal recombination
• Maximum Diverse Grouping
• Extensive computational
• Diversity problem
• Operations research
• Exteriorpoint simplex type
• Network dual simplex algorithm
• Electromagnetism like metaheuristic
• Maximum set splitting problem
• Steiner triple systems
• Fast implementation
• Evolutionary computation
• Graph coloring problem
• Bandwidth multicoloring problem
• Bandwidth coloring problem
• Quadratic assignment problem
• Modified genetic operators
• Weighted graphs
• Minimal branching
• Asymetric weight matrix
• Minimal s branching