Book:Bernhard H. Korte/Combinatorial Optimization: Theory and Algorithms

Subject Matter

 * Combinatorial Optimization

Contents

 * 1 $\quad$Introduction
 * 1.1 $\quad$ Enumeration
 * 1.2 $\quad$ Running Time of Algorithms
 * 1.3 $\quad$ Linear Optimization Problems
 * 1.4 $\quad$ Sorting
 * Exercises
 * References


 * 2 $\quad$Graphs
 * 2.1 $\quad$ Basic Definitions
 * 2.2 $\quad$ Trees, Circuits, and Cuts
 * 2.3 $\quad$ Connectivity
 * 2.4 $\quad$ Eulerian and Bipartite Graphs
 * 2.5 $\quad$ Planarity
 * 2.6 $\quad$ Planar Duality
 * Exercises
 * References


 * 3 $\quad$Linear Programming
 * 3.1 $\quad$ Polyhedra
 * 3.2 $\quad$ The Simplex Algorithm
 * 3.3 $\quad$ Implementation of the Simplex Algorithm
 * 3.4 $\quad$ Duality
 * 3.5 $\quad$ Convex Hulls and Polytopes
 * Exercises
 * References


 * 4 $\quad$Linear Programming Algorithms
 * 4.1 $\quad$ Size of Vertices and Faces
 * 4.2 $\quad$ Continued Fractions
 * 4.3 $\quad$ Gaussian Elimination
 * 4.4 $\quad$ The Ellipsoid Method
 * 4.5 $\quad$ Khachiyan's Theorem
 * 4.6 $\quad$ Separation and Optimization
 * Exercises
 * References


 * 5 $\quad$Integer Programming
 * 5.1 $\quad$ The Integer Hull of a Polyhedron
 * 5.2 $\quad$ Unimodular Transformations
 * 5.3 $\quad$ Total Dual Integrality
 * 5.4 $\quad$ Totally Unimodular Matrices
 * 5.5 $\quad$ Cutting Planes
 * 5.6 $\quad$ Lagrangian Relaxation
 * Exercises
 * References


 * 6 $\quad$Spanning Trees and Arborescences
 * 6.1 $\quad$ Minimum Spanning Tree
 * 6.2 $\quad$ Minimum Weight Arborescences
 * 6.3 $\quad$ Polyhedral Descriptions
 * 6.4 $\quad$ Packing Spanning Trees and Arborescences
 * Exercises
 * References


 * 7 $\quad$Shortest Paths
 * 7.1 $\quad$ Shortest Paths From One Source
 * 7.2 $\quad$ Shortest Paths Between All Pairs of Vertices
 * 7.3 $\quad$ Minimum Mean Cycles
 * 7.4 $\quad$ Shallow-Light Trees
 * Exercises
 * References


 * 8 $\quad$Network Flows
 * 8.1 $\quad$ Max-Flow-Min-Cut Theorem
 * 8.2 $\quad$ Menger's Theorem
 * 8.3 $\quad$ The Edmonds-Karp Algorithm
 * 8.4 $\quad$ Dinic's, Karanoz's, and Fujishige's Algorithm
 * 8.5 $\quad$ The Goldberg-Tarjan Algorithm
 * 8.6 $\quad$ Gomory-Hu Trees
 * 8.7 $\quad$ The Minimum Capacity of a Cut in an Undirected Graph
 * Exercises
 * References


 * 9 $\quad$Minimum Cost Flows
 * 9.1 $\quad$ Problem Formulation
 * 9.2 $\quad$ An Optimality Criterion
 * 9.3 $\quad$ Minimum Mean Cycle-Cancelling Algorithm
 * 9.4 $\quad$ Successive Shortest Path Algorithm
 * 9.5 $\quad$ Orlin's Algorithm
 * 9.6 $\quad$ The Network Simplex Algorithm
 * 9.7 $\quad$ Flows Over time
 * Exercises
 * References


 * 10$\quad$Maximum Matchings
 * 10.1 $\quad$ Bipartite Matchings
 * 10.2 $\quad$ The Tutte Matrix
 * 10.3 $\quad$ Tutte's Theorem
 * 10.4 $\quad$ Ear-Decomposition of Factor-Critical Graphs
 * 10.5 $\quad$ Edmonds' Matching Algorithm
 * Exercises
 * References


 * 11$\quad$Weighted Matching
 * 11.1 $\quad$ The Assignment Problem
 * 11.2 $\quad$ Outline of the Weighted Matching Algorithm
 * 11.3 $\quad$ Implementation of the Weighted Matching Algorithm
 * 11.4 $\quad$ Postoptimality
 * 11.5 $\quad$ The Matching Polytope
 * Exercises
 * References


 * 12$\quad$$\beta$-Matchings and $T$-Joins
 * 12.1 $\quad$ $\beta$-Matchings
 * 12.2 $\quad$ Minimum Weight $T$-Joins
 * 12.3 $\quad$ $T$-Joins and $T$-Cuts
 * 12.4 $\quad$ The Padberg-Rao Theorem
 * Exercises
 * References


 * 13$\quad$Matroids
 * 13.1 $\quad$ Independence Systems and Matroids
 * 13.2 $\quad$ Other Matroid Axioms
 * 13.3 $\quad$ Duality
 * 13.4 $\quad$ The Greedy Algorithm
 * 13.5 $\quad$ Matroid Intersection
 * 13.6 $\quad$ Matroid Partitioning
 * 13.7 $\quad$ Weighted Matroid Intersection
 * Exercises
 * References


 * 14$\quad$Generalizations of Matroids
 * 14.1 $\quad$ Greedoids
 * 14.2 $\quad$ Polymatroids
 * 14.3 $\quad$ Minimizing Submodular Functions
 * 14.4 $\quad$ Schrijver's Algorithm
 * 14.5 $\quad$ Symmetric Submodular Functions
 * 14.6 $\quad$ Submodular Function Maximization
 * Exercises
 * References


 * 15$\quad$$NP$-Completeness
 * 15.1 $\quad$ Turing Machines
 * 15.2 $\quad$ Church's Thesis
 * 15.3 $\quad$ $P$ and $NP$
 * 15.4 $\quad$ Cook's Theorem
 * 15.5 $\quad$ Some Basic $NP$-Complete Problems
 * 15.6 $\quad$ The Class $coNP$
 * 15.7 $\quad$ $NP$-Hard Problems
 * Exercises
 * References


 * 16$\quad$Approximation Algorithms
 * 16.1 $\quad$ Set Covering
 * 16.2 $\quad$ The Max-Cut Problem
 * 16.3 $\quad$ Colouring
 * 16.4 $\quad$ Approximation Schemes
 * 16.5 $\quad$ Maximum Satisfiability
 * 16.6 $\quad$ The $PCP$ Theorem
 * 16.7 $\quad$ L-Reductions
 * Exercises
 * References


 * 17$\quad$The Knapsack Problem
 * 17.1 $\quad$ Fractional Knasak and Weighted Median Problem
 * 17.2 $\quad$ A Pseudopolynomial Algorithm
 * 17.3 $\quad$ A Fully Polynomial Approximation Scheme
 * 17.4 $\quad$ Multi-Dimensional Knapsack
 * 17.5 $\quad$ The Nemhauser-Ullmann Algorithm
 * Exercises
 * References


 * 18$\quad$Bin-Packing
 * 18.1 $\quad$ Greedy Heuristics
 * 18.2 $\quad$ An Asymptotic Approximation Scheme
 * 18.3 $\quad$ The Karmarkar-Karp Algorithm
 * Exercises
 * References


 * 19$\quad$Multicommodity Flows and Edge-Disjoint Paths
 * 19.1 $\quad$ Multicommodity Flows
 * 19.2 $\quad$ Algorithms for Multicommodity Flows
 * 19.3 $\quad$ Sparsest Cut and Max-Flow Min-Cut Ratio
 * 19.4 $\quad$ The Leighton-Rao Theorem
 * 19.5 $\quad$ Directed Edge-Disjoint Paths Problem
 * 19.6 $\quad$ Undirected Edge-Disjoint Paths Problem
 * Exercises
 * References


 * 20$\quad$Network Design Problems
 * 20.1 $\quad$ Steiner Trees
 * 20.2 $\quad$ The Robins-Zelikovsky Algorithm
 * 20.3 $\quad$ Rounding the Directed Component LP
 * 20.4 $\quad$ Survivable Network Design
 * 20.5 $\quad$ A Primal-Dual Approximation Algorithm
 * 20.6 $\quad$ Jain's Algorithm
 * 20.7 $\quad$ The VPN Problem
 * Exercises
 * References


 * 21$\quad$The Traveling Salesman Problem
 * 21.1 $\quad$ Approximation Algorithms for the TSP
 * 21.2 $\quad$ Euclidean TSP
 * 21.3 $\quad$ Local Search
 * 21.4 $\quad$ The Traveling Salesman Polytope
 * 21.5 $\quad$ Lower Bounds
 * 21.6 $\quad$ Branch-and-Bound
 * Exercises
 * References


 * 22$\quad$Facility Location
 * 22.1 $\quad$ The Uncapacitated Facility Location Problem
 * 22.2 $\quad$ Rounding Linear Programming Solutions
 * 22.3 $\quad$ Primal-Dual Algorithms
 * 22.4 $\quad$ Scaling and Greedy Augmentation
 * 22.5 $\quad$ Bounding the Number of Facilities
 * 22.6 $\quad$ Local Search
 * 22.7 $\quad$ Capacitated Facility Location Problems
 * 22.8 $\quad$ Universal Facility Location
 * Exercises
 * References


 * Notation Index


 * Author Index


 * Subject Index