Reconfiguration of satisfying assignments and subset sums: Easy to find, hard to connect
Name
1805.04055.pdf
Description
Submitted version
Size
502.26 KB
Format
Adobe PDF
Checksum (MD5)
b02da417c9becb86d9fe1d6df3709c2a
Author(s)
Demaine, Erik D
Date Issued
July 2019
Journal
Theoretical Computer Science
Publisher
Elsevier BV
Citation
Jean Cardinal et al. “Reconfiguration of satisfying assignments and subset sums: Easy to find, hard to connect.” Theoretical Computer Science, 806 (July 2019): 332-343 © 2019 The Author(s)
Version
Original manuscript
Abstract
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 operations, while satisfying the constraints at all times. Such problems appear naturally in many contexts, such as model checking, motion planning, enumeration, 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 of a planar monotone instance of NAE 3-SAT, can one assignment be transformed into the other by a sequence of variable flips such that the formula remains satisfied 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 sets of instances that appear as input to the reconfiguration problems in our reductions 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. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.TCS.2019.05.028
