Quantum algorithms for one-sided crossing minimization

We present singly-exponential quantum algorithms for the One-Sided Crossing Minimization (OSCM) problem. Given an n-vertex bipartite graph G=(U,V,E⊆U×V), a 2-level drawing(πU,πV) of G is described by a linear ordering πU:U↔{1,…,|U|} of U and linear ordering πV:V↔{1,…,|V|} of V. For a fixed linear or...

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Veröffentlicht in:Theoretical computer science Jg. 1052; S. 115424
Hauptverfasser: Caroppo, Susanna, Da Lozzo, Giordano, Di Battista, Giuseppe
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 19.10.2025
Schlagworte:
Exact exponential algorithms
One-sided crossing minimization
Quantum divide and conquer
Quantum dynamic programming
Quantum graph drawing
Theory of computation
Exact exponential algorithms
Quantum divide and conquer
Quantum complexity theory
Quantum dynamic programming
Graph theory
Mathematics of computing
Design and analysis of algorithms
One-sided crossing minimization
Quantum graph drawing
ISSN:0304-3975
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Zusammenfassung:We present singly-exponential quantum algorithms for the One-Sided Crossing Minimization (OSCM) problem. Given an n-vertex bipartite graph G=(U,V,E⊆U×V), a 2-level drawing(πU,πV) of G is described by a linear ordering πU:U↔{1,…,|U|} of U and linear ordering πV:V↔{1,…,|V|} of V. For a fixed linear ordering πU of U, the OSCM problem seeks to find a linear ordering πV of V that yields a 2-level drawing (πU,πV) of G with the minimum number of edge crossings. We show that OSCM can be viewed as a set problem over V 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.
ISSN:0304-3975
DOI:10.1016/j.tcs.2025.115424