Inapproximability of the Standard Pebble Game and Hard to Pebble Graphs
Name
1707.06343.pdf
Description
Accepted version
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999.04 KB
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Checksum (MD5)
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Author(s)
Demaine, Erik D
Liu, Quanquan
Alternative Title
Inapproximability of the Standard Pebble Game and Hard to Pebble Graphs
Date Issued
July 2017
Journal
Workshop on Algorithms and Data Structures 2017
Publisher
Springer Nature
Citation
Demaine E.D. and Q.C. Liu. "Inapproximability of the Standard Pebble Game and Hard to Pebble Graphs." Workshop on Algorithms and Data Structures 2017, July-August 2017, St. Johns, Canada, Springer International Publishing, July 2017 © 2017 Springer International Publishing
Version
Author's final manuscript
Abstract
Pebble games are single-player games on DAGs involving placing and moving pebbles on nodes of the graph according to a certain set of rules. The goal is to pebble a set of target nodes using a minimum number of pebbles. In this paper, we present a possibly simpler proof of the result in [4] and strengthen the result to show that it is PSPACE-hard to determine the minimum number of pebbles to an additive n1/3−εterm for all ε > 0, which improves upon the currently known additive constant hardness of approximation [4] in the standard pebble game. We also introduce a family of explicit, constant indegree graphs with n nodes where there exists a graph in the family such that using 0 < k < √n pebbles requires Ω((n/k)k) moves to pebble in both the standard and black-white pebble games. This independently answers an open question summarized in [14] of whether a family of DAGs exists that meets the upper bound of O(nk) moves using constant k pebbles with a different construction than that presented in [1].
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/10.1007/978-3-319-62127-2_27
