Programming in Networks and Graphs: On the Combinatorial Background and Near-Equivalence of Network Flow and Matching Algorithms
Ulrich Derigs · OpenGrey (Institut de l'Information Scientifique et Technique) · 2014
Preliminaries.- Terminology.- Linear Programming.- Combinatorial Optimization.- The Class of General Matching Problems.- Three Cornerstone Problems.- Important Subclasses.- Network Flow Algorithms Revisited.- Prologue: Two Apparently Easier Network Flow Problems.- Approaches to Min-Cost Flow Problems.- Near Equivalence of Network Flow Algorithms.- Bipartite Matching Problems.- The Cardinality Matching Problem in Bipartite Graphs.- The Assignment Problem.- The Hitchcock Transportation Problem.- The 1-Matching Problem.- The Cardinality Matching Problem.- The Min-Cost Perfect Matching Problem.- The b-Matching Problem.- Basic Structures and Operations.- b-Matching Algorithms.