**Reference**:- Erik D. Demaine, MohammadTaghi Hajiaghayi, and Dániel Marx, “Minimizing Movement: Fixed-Parameter Tractability”, in
*Proceedings of the 17th Annual European Symposium on Algorithms (ESA 2009)*, Lecture Notes in Computer Science, volume 5757, Copenhagen, Denmark, September 7–9, 2009, pages 718–729. **Abstract**:- We study an extensive class of movement minimization problems which arise from many practical scenarios but so far have little theoretical study. In general, these problems involve planning the coordinated motion of a collection of agents (representing robots, people, map labels, network messages, etc.) to achieve a global property in the network while minimizing the maximum or average movement (expended energy). The only previous theoretical results about this class of problems are about approximation, and mainly negative: many movement problems of interest have polynomial inapproximability. Given that the number of mobile agents is typically much smaller than the complexity of the environment, we turn to fixed-parameter tractability. We characterize the boundary between tractable and intractable movement problems in a very general set up: it turns out the complexity of the problem fundamentally depends on the treewidth of the minimal configurations. Thus the complexity of a particular problem can be determined by answering a purely combinatorial question. Using our general tools, we determine the complexity of several concrete problems and fortunately show that many movement problems of interest can be solved efficiently.
**Comments**:- The full paper is available as arXiv.org:1205.6960 of the Computing Research Repository (CoRR).
**Copyright**:- Copyright held by the authors.
**Length**:- The paper is 12 pages.
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**Related papers**:- MovementFPT_TALG (Minimizing Movement: Fixed-Parameter Tractability)

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Last updated June 1, 2023 by Erik Demaine.