Abstract Milling with Turn Costs

M. Fellows; P. Giannopoulos; C. Knauer; C. Paul; F. Rosamond; S. Whitesides; N. Yu

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arXiv · 0912.1050

Abstract Milling with Turn Costs

M. Fellows·P. Giannopoulos·C. Knauer·C. Paul·F. Rosamond·S. Whitesides·N. Yu

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Abstract

The Abstract Milling problem is a natural and quite general graph-theoretic model for geometric milling problems. Given a graph, one asks for a walk that covers all its vertices with a minimum number of turns, as specified in the graph model by a 0/1 turncost function fx at each vertex x giving, for each ordered pair of edges (e,f) incident at x, the turn cost at x of a walk that enters the vertex on edge e and departs on edge f. We describe an initial study of the parameterized complexity of the problem. Our main positive result shows that Abstract Milling, parameterized by: number of turns, treewidth and maximum degree, is fixed-parameter tractable, We also show that Abstract Milling parameterized by (only) the number of turns and the pathwidth, is hard for W[1] -- one of the few parameterized intractability results for bounded pathwidth.

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BibTeX RIS

M. Fellows, P. Giannopoulos, C. Knauer, C. Paul, F. Rosamond, S. Whitesides, N. Yu. 2009-12-05. Abstract Milling with Turn Costs. https://arxiv.org/abs/0912.1050

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