**Reference**:- Erik D. Demaine, MohammadTaghi Hajiaghayi, and Dániel Marx, “Minimizing Movement: Fixed-Parameter Tractability”,
*ACM Transactions on Algorithms*, volume 11, number 2, November 2014, Paper 14. **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 setup: 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 paper is also available as arXiv.org:1205.6960 of the Computing Research Repository (CoRR).
**Length**:- The paper is 27 pages.
**Availability**:- The paper is available in PostScript (927k), gzipped PostScript (415k), and PDF (506k).
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**Related papers**:- MovementFPT_ESA2009 (Minimizing Movement: Fixed-Parameter Tractability)

See also other papers by Erik Demaine.

Last updated January 4, 2022 by Erik Demaine.