On the cycle polytope of a binary matroid
Journal of Combinatorial Theory Series B
Data Structures and Algorithms
Data Structures and Algorithms
A New Approach to Cactus Construction Applied to TSP Support Graphs
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
On the Undirected Rural Postman Problem: Tight Bounds Based on a New Formulation
Operations Research
Traveling Salesman Problems with Profits
Transportation Science
The Clustered Prize-Collecting Arc Routing Problem
Transportation Science
The undirected capacitated arc routing problem with profits
Computers and Operations Research
An evolutionary approach to the multidepot capacitated arc routing problem
IEEE Transactions on Evolutionary Computation
The Windy Clustered Prize-Collecting Arc-Routing Problem
Transportation Science
A Tabu Search Heuristic for the Prize-collecting Rural Postman Problem
Electronic Notes in Theoretical Computer Science (ENTCS)
The time-dependent prize-collecting arc routing problem
Computers and Operations Research
GRASP and Path Relinking for the Clustered Prize-collecting Arc Routing Problem
Journal of Heuristics
An ILP-refined tabu search for the Directed Profitable Rural Postman Problem
Discrete Applied Mathematics
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In this work we analyze the privatized rural postman problem which is the edge version of the traveling salesman problems with profits.The problem is defined on a undirected graph G(V, E) with a distinguished vertex d, called the Depot. There are two non-negative real functions on the edge set E, which define the value of a cycle in G: one is the profit function, b, and the other one is the cost function, c. They have different meanings when a cycle C traverses an edge e (possibly more than once), because we pay a cost ce every time e is traversed, but we collect the profit be only the first time e is traversed. The privatized rural postman problem is to find a cycle C*, passing through d and not necessarily simple, which maximizes the sum of the values of the edges traversed in C*. That is, maxC {Σe∈C (be - teCe)} where te is the number of times that edge e is traversed in C.We study some properties of the problem: we show that it is NP-hard, its relation with known and new problems, and special cases with good algorithms. We also analyze several integer linear systems of inequalities, which define the polyhedral structure of the problem, and we give dominance and preprocessing conditions. We finish with some remarks and comments about future research.