Quantum algorithms for one-sided crossing minimization

IF 1 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS
Susanna Caroppo, Giordano Da Lozzo, Giuseppe Di Battista
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引用次数: 0

Abstract

We present singly-exponential quantum algorithms for the One-Sided Crossing Minimization (OSCM) problem. Given an n-vertex bipartite graph G=(U,V,EU×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.
单侧交叉最小化的量子算法
提出了单侧交叉最小化问题的单指数量子算法。给定一个n点二部图G=(U,V,E U×V),用一个线性有序πU:U↔{1,…,|U|}和一个线性有序πV:V↔{1,…,|V|}来描述G的一个2级图(πU,πV)。对于一个固定的线性有序πU, OSCM问题寻求找到一个线性有序πV,该πV产生一个边交叉数最少的G的2级图(πU,πV)。我们表明,OSCM可以被看作是V上的一个集合问题,适用于具有量子加速的精确算法,相对于它们的经典对应物。首先,我们利用Ambainis等人的量子动态规划框架[指数时间动态规划算法的量子加速]。SODA 2019]设计了一种基于qram的算法,该算法在O * (1.728n)的时间和空间中求解OSCM。其次,我们使用量子分而治之的方法,在O (2n)的时间和多项式空间中,获得了一种不使用QRAM解决OSCM的算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Theoretical Computer Science
Theoretical Computer Science 工程技术-计算机:理论方法
CiteScore
2.60
自引率
18.20%
发文量
471
审稿时长
12.6 months
期刊介绍: Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.
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