On the windy postman problem on Eulerian graphs
Mathematical Programming: Series A and B
A cutting plane algorithm for the windy postman problem
Mathematical Programming: Series A and B
Computers and Operations Research
On the complexity of edge traversing
Journal of the ACM (JACM)
Approximation Algorithms for Some Postman Problems
Journal of the ACM (JACM)
The Chinese Postman Problem for Mixed Graphs
WG '80 Proceedings of the International Workshop on Graphtheoretic Concepts in Computer Science
Graph theory: An algorithmic approach (Computer science and applied mathematics)
Graph theory: An algorithmic approach (Computer science and applied mathematics)
Approximation algorithms for the asymmetric postman problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
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The postman problem requires finding a lowest cost tour in a connected graph that traverses each edge at least once. In this paper we first give a brief survey of the literature on postman problems including, the original Chinese postman problem on undirected graphs, the windy Chinese postman problem on graphs where the cost of an arc depends on the direction the arc is transversed, the directed postman problem on graphs with directed edges, and the mixed postman problem on graphs in which there are some directed and some undirected arcs.We show how the mixed postman problem can be solved as an integer program, using the formulation of Gendreau, Laporte and Zhao, by a new row addition branch and bound algorithm, which is a modification of the column subtraction algorithm for set partitioning problems of Harcheand Thompson. Computational experience shows that a “slack variable” heuristic is very effective in finding good solutions that are frequently optimal for these problems.