KR2020Proceedings of the 17th International Conference on Principles of Knowledge Representation and ReasoningProceedings of the 17th International Conference on Principles of Knowledge Representation and Reasoning

Rhodes, Greece. September 12-18, 2020.

Edited by
  1. Diego Calvanese
  2. Esra Erdem
  3. Michael Thielscher

ISSN: 2334-1033
ISBN: 978-0-9992411-7-2

Sponsored by
Published by

Copyright © 2020 International Joint Conferences on Artificial Intelligence Organization

Fine-Grained Complexity of Temporal Problems

  1. Konrad K. Dabrowski(Durham University)
  2. Peter Jonsson(Linköping University)
  3. Sebastian Ordyniak(University of Sheffield)
  4. George Osipov(Linköping University)
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BibTeX
DOI 10.24963/kr.2020/29

Keywords

  1. Computational aspects of knowledge representation-General
  2. Geometric, spatial, and temporal reasoning-General

Abstract

Expressive temporal reasoning formalisms are essential for AI. One family of such formalisms consists of disjunctive extensions of the simple temporal problem (STP). Such extensions are well studied in the literature and they have many important applications.

It is known that deciding satisfiability of disjunctive STPs is NP-hard, while the fine-grained complexity of such problems is virtually unexplored. We present novel algorithms that exploit structural properties of the solution space and prove, assuming the Exponential-Time Hypothesis, that their worst-case time complexity is close to optimal. Among other things, we make progress towards resolving a long-open question concerning whether Allen's interval algebra can be solved in single-exponential time, by giving a 2^{O(nloglog(n))} algorithm for the special case of unit-length intervals.