The Capacitated Arc Routing Problem (CARP) is a well-known and fundamental vehicle routing problem. A promising exact solution approach to the CARP is to model it as a set covering problem and solve it via branch-cut-and-price. The bottleneck in this approach is the pricing (column generation) routine. In this paper, we note that most CARP instances arising in practical applications are defined...

Most algorithms for solving vehicle routing problems use the criterion of minimizing total travel time in forming their routes. As illustrated in the paper, even in the case of a homogeneous fleet, solutions using other criteria may be preferred to the solution generated by minimizing total travel time. This situation becomes more pronounced when considering a vehicle routing problem where the ...

A well known transformation by Pearn, Assad and Golden reduces a Capacitated Arc Routing Problem (CARP) into an equivalent Capacitated Vehicle Routing Problem (CVRP). However, that transformation is regarded as unpractical, since an original instance with r required edges is turned into a CVRP over a complete graph with 3r + 1 vertices. We propose a similar transformation that reduces this grap...

We study the complexity of two Inverse Shortest Paths (ISP) problems with integer arc lengths and the requirement for uniquely determined shortest paths. Given a collection of paths in a directed graph, the task is to find positive integer arc lengths such that the given paths are uniquely determined shortest paths between their respective terminals. The first problem seeks for arc lengths that...

The concept af virtual channels is extended to multiple, virtual communication systems that provide adaptability and fault tolerance in addition to being deadlock-free. A channel dependency graph is taken as the definition of what connections are possible and any routing function must use only those connections defined by it. Virtual interconnection networks allowing adaptive, deadlock-free rou...

In this work we study the Generalized Arc Routing Problem (GARP) on an undirected graph. In the GARP a given graph is partitioned into clusters and a route is sought that traverses at least one edge of each cluster. Broadly speaking, the GARP is the arc routing counterpart of the Generalized Traveling Salesman Problem (GTSP). In the GTSP the set of vertices of a given graph is partitioned into ...

In this research, we focus on the windy rural postman problem with the additional option to zigzag street segments during certain times of the day. If a street is narrow or traffic is light, it is possible (and often desirable) to service both sides of the street in a single pass by zigzagging. However, if a street is wide or traffic is heavy, we must service the street by two single traversals...

This chapter is devoted to surveying aspects of computational complexity for three central arc routing problems (and their corresponding variants): • Chinese Postman, where one asks for a minimum-cost tour traversing all edges of a graph at least once; • Rural Postman, which generalizes Chinese Postman in the sense that only a subset of the edges has to be visited; • Capacitated Arc Routing, re...