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Quantum Algorithms for One-Sided Crossing Minimization

Authors Susanna Caroppo , Giordano Da Lozzo , Giuseppe Di Battista

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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Mathematics of computing → Graph theory
  • Theory of computation → Quantum complexity theory
Keywords
  • One-sided crossing minimization
  • quantum graph drawing
  • quantum dynamic programming
  • quantum divide and conquer
  • exact exponential algorithms

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Abstract

We present singly-exponential quantum algorithms for the One-Sided Crossing Minimization (OSCM) problem. We show that OSCM can be viewed as a set problem amenable for exact algorithms with a quantum speedup with respect to their classical counterparts. First, we exploit the quantum dynamic programming framework of Ambainis et al. [Quantum Speedups for Exponential-Time Dynamic Programming Algorithms. SODA 2019] to devise a QRAM-based algorithm that solves OSCM in 𝒪^*(1.728ⁿ) time and space. Second, we use quantum divide and conquer to obtain an algorithm that solves OSCM without using QRAM in 𝒪^*(2ⁿ) time and polynomial space.

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Susanna Caroppo, Giordano Da Lozzo, and Giuseppe Di Battista. Quantum Algorithms for One-Sided Crossing Minimization. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 20:1-20:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.GD.2024.20

Author Details

Susanna Caroppo
  • Roma Tre University, Rome, Italy
Giordano Da Lozzo
  • Roma Tre University, Rome, Italy
Giuseppe Di Battista
  • Roma Tre University, Rome, Italy

Funding

This research was supported, in part, by MUR of Italy (PRIN Project no. 2022ME9Z78 - NextGRAAL and PRIN Project no. 2022TS4Y3N - EXPAND).

Acknowledgements

We acknowledge the CINECA award under the ISCRA initiative, for the availability of high-performance computing resources and support

References

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