Fine-grained complexity meets IP = PSPACE
Name
1805.02351.pdf
Description
Submitted version
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565.69 KB
Format
Adobe PDF
Checksum (MD5)
70dc8c6e2bc508f72ff61ce0b797f697
Author(s)
Chen, Lijie
Goldwasser, Shafrira
Date Issued
January 2019
Journal
Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Publisher
Society for Industrial and Applied Mathematics
Citation
Chen, Lijie et al. “Fine-grained complexity meets IP = PSPACE.” Paper in the Proceedings of the 2019 Annual ACM-SIAM Symposium on Discrete Algorithms, San Diego, CA, January 6-9 2019, Society for Industrial and Applied Mathematics: ix + 2972 © 2019 The Author(s)
Version
Original manuscript
Abstract
In this paper we study the fine-grained complexity of finding exact and approximate solutions to problems in P. Our main contribution is showing reductions from an exact to an approximate solution for a host of such problems. As one (notable) example, we show that the Closest-LCS-Pair problem (Given two sets of strings A and B, compute exactly the maximum LCS(a, b) with (a, b) ∈ A × B) is equivalent to its approximation version (under near-linear time reductions, and with a constant approximation factor). More generally, we identify a class of problems, which we call BP-Pair-Class, comprising both exact and approximate solutions, and show that they are all equivalent under near-linear time reductions. Exploring this class and its properties, we also show: • Under the NC-SETH assumption (a significantly more relaxed assumption than SETH), solving any of the problems in this class requires essentially quadratic time. • Modest improvements on the running time of known algorithms (shaving log factors) would imply that NEXP is not in non-uniform NC1. • Finally, we leverage our techniques to show new barriers for deterministic approximation algorithms for LCS. A very important consequence of our results is that they continue to hold in the data structure setting. In particular, it shows that a data structure for approximate Nearest Neighbor Search for LCS (NNSLCS) implies a data structure for exact NNSLCS and a data structure for answering regular expression queries with essentially the same complexity. At the heart of these new results is a deep connection between interactive proof systems for bounded-space computations and the fine-grained complexity of exact and approximate solutions to problems in P. In particular, our results build on the proof techniques from the classical IP = PSPACE result.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1137/1.9781611975482.1
