NDLI: Lower Bounds for Geometrical and Physical Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Sellen, Jrgen
Copyright Year	1996
Abstract	Motion planning involving arbitrarily many degrees of freedom is known to be PSPACE-hard. In this paper, we examine the complexity of generalized motion-planning problems for planar mechanisms consisting of independently movable objects.Our constructions constitute a general framework for reducing problems in information processing to motion planning, leading to easy proofs of known PSPACE-hardness results and to exponential lower bounds for geometrical problems related to motion planning. Particulalrly, we show that the problem of deciding whether a given mechanism A can always avoid a collision with another mechanism B is EXPSPACE-hard.New lower bounds are also obtained for the problem of planning under given physical side conditions. We consider the case that certain motions require forces, e.g., to subdue friction, and ask for motions that stay under a given energy limit. Within our framework, we show that such shortest-path problems are EXPTIME-hard if we use number representations by mantissa and exponent, and even undecidable if we allow that some motions require no force or an infinite amount. The proof consists of a simulation of Turing machines with infinite tape and shows that the notion of Turing computability can be interpreted in purely geometrical terms. The geometrical model obtained is capable of expressing a variety of physical-planning problems.
Starting Page	1231
Ending Page	1253
Page Count	23
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539793243338
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	6
Volume Number	25
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-31
Access Restriction	Subscribed
Subject Keyword	Models of computation collision-avoidability problem Analysis of algorithms and problem complexity motion planning dynamic problems Computer graphics; computational geometry Turing machines and related notions Complexity of computation kinematic problems geometrical problems lower bounds
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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