Abstract
The Hierarchical Chinese Postman Problem is finding a shortest traversal of all edges of a graph respecting precedence constraints given by a partial order on classes of edges. We show that the special case with connected classes is NP-hard even on orders decomposable into a chain and an incomparable class. For the case with linearly ordered (possibly disconnected) classes, we get 5/3-approximations and fixed-parameter algorithms by transferring results from the Rural Postman Problem.
Highlights
IntroductionThe following NP-hard arc routing problem arises in snow plowing, garbage collection, flame and laser cutting [8, 23]
The following NP-hard arc routing problem arises in snow plowing, garbage collection, flame and laser cutting [8, 23].Problem 1.1 (Hierarchical Chinese Postman Problem, HCPP)
To get 5/3-approximations for HCPP(l), we use the construction from Section 4 and show a 5/3-approximation algorithm for s-t-Rural Postman Problem (RPP) analogously to that for s-t-Travelling Salesman Problem (TSP) [17]
Summary
The following NP-hard arc routing problem arises in snow plowing, garbage collection, flame and laser cutting [8, 23]. This contrasts TSP in temporal graphs, which is not better than 2-approximable unless P = NP [26]. To get 5/3-approximations for HCPP(l), we use the construction from Section 4 and show a 5/3-approximation algorithm for s-t-RPP analogously to that for s-t-TSP [17]. When the edge weights are polynomially bounded, one can even obtain randomized fixed-parameter algorithms with respect to c
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