Reconfiguration of Satisfying Assignments and Subset Sums: Easy to Find, Hard to Connect
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1805.04055.pdf
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Accepted version
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502.26 KB
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Checksum (MD5)
b02da417c9becb86d9fe1d6df3709c2a
Author(s)
Cardinal, Jean
Demaine, Erik D.
Eppstein, David
Hearn, Robert A.
Winslow, Andrew
Date Issued
2018
Publisher
Springer International Publishing
Citation
Cardinal, Jean, Demaine, Erik D., Eppstein, David, Hearn, Robert A. and Winslow, Andrew. 2018. "Reconfiguration of Satisfying Assignments and Subset Sums: Easy to Find, Hard to Connect."
Version
Author's final manuscript
Abstract
© 2018, Springer International Publishing AG, part of Springer Nature. We consider the computational complexity of reconfiguration problems, in which one is given two combinatorial configurations satisfying some constraints, and is asked to transform one into the other using elementary transformations, while satisfying the constraints at all times. Such problems appear naturally in many contexts, such as model checking, motion planning, enumeration and sampling, and recreational mathematics. We provide hardness results for problems in this family, in which the constraints and operations are particularly simple. More precisely, we prove the PSPACE -completeness of the following decision problems: Given two satisfying assignments to a planar monotone instance of Not-All-Equal 3-SAT, can one assignment be transformed into the other by single variable “flips” (assignment changes), preserving satisfiability at every step?Given two subsets of a set S of integers with the same sum, can one subset be transformed into the other by adding or removing at most three elements of S at a time, such that the intermediate subsets also have the same sum?Given two points in {0,1}n contained in a polytope P specified by a constant number of linear inequalities, is there a path in the n-hypercube connecting the two points and contained in P? These problems can be interpreted as reconfiguration analogues of standard problems in NP. Interestingly, the instances of the NP problems that appear as input to the reconfiguration problems in our reductions can be shown to lie in P. In particular, the elements of S and the coefficients of the inequalities defining P can be restricted to have logarithmic bit-length.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1007/978-3-319-94776-1_31
