A sublinear query quantum algorithm for s-t minimum cut on dense simple graphs

• URL: http://arxiv.org/abs/2110.15587v2
• Date: Mon, 5 Feb 2024 01:45:51 GMT
• Title: A sublinear query quantum algorithm for s-t minimum cut on dense simple graphs
• Authors: Simon Apers, Arinta Auza, Troy Lee
• Abstract summary: An $soperatorname-t$ minimum cut in a graph corresponds to a minimum weight subset of edges whose removal disconnects $s$ and $t$. In this work we describe a quantum algorithm for the minimum $soperatorname-t$ cut problem on undirected graphs.
• Score: 1.0435741631709405
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: An $s{\operatorname{-}}t$ minimum cut in a graph corresponds to a minimum weight subset of edges whose removal disconnects vertices $s$ and $t$. Finding such a cut is a classic problem that is dual to that of finding a maximum flow from $s$ to $t$. In this work we describe a quantum algorithm for the minimum $s{\operatorname{-}}t$ cut problem on undirected graphs. For an undirected graph with $n$ vertices, $m$ edges, and integral edge weights bounded by $W$, the algorithm computes with high probability the weight of a minimum $s{\operatorname{-}}t$ cut after $\widetilde O(\sqrt{m} n^{5/6} W^{1/3})$ queries to the adjacency list of $G$. For simple graphs this bound is always $\widetilde O(n^{11/6})$, even in the dense case when $m = \Omega(n^2)$. In contrast, a randomized algorithm must make $\Omega(m)$ queries to the adjacency list of a simple graph $G$ even to decide whether $s$ and $t$ are connected.

Related papers

• The Communication Complexity of Approximating Matrix Rank [50.6867896228563]
  We show that this problem has randomized communication complexity $Omega(frac1kcdot n2log|mathbbF|)$. As an application, we obtain an $Omega(frac1kcdot n2log|mathbbF|)$ space lower bound for any streaming algorithm with $k$ passes.
  arXiv  Detail & Related papers  (2024-10-26T06:21:42Z)
• Optimal Sketching for Residual Error Estimation for Matrix and Vector Norms [50.15964512954274]
  We study the problem of residual error estimation for matrix and vector norms using a linear sketch. We demonstrate that this gives a substantial advantage empirically, for roughly the same sketch size and accuracy as in previous work. We also show an $Omega(k2/pn1-2/p)$ lower bound for the sparse recovery problem, which is tight up to a $mathrmpoly(log n)$ factor.
  arXiv  Detail & Related papers  (2024-08-16T02:33:07Z)
• Graph Unfolding and Sampling for Transitory Video Summarization via Gershgorin Disc Alignment [48.137527345353625]
  User-generated videos (UGVs) uploaded from mobile phones to social media sites like YouTube and TikTok are short and non-repetitive. We summarize a transitory UGV into several discs in linear time via fast graph sampling based on Gershgorin disc alignment (GDA) We show that our algorithm achieves comparable or better video summarization performance compared to state-of-the-art methods, at a substantially reduced complexity.
  arXiv  Detail & Related papers  (2024-08-03T20:08:02Z)
• Efficient Continual Finite-Sum Minimization [52.5238287567572]
  We propose a key twist into the finite-sum minimization, dubbed as continual finite-sum minimization. Our approach significantly improves upon the $mathcalO(n/epsilon)$ FOs that $mathrmStochasticGradientDescent$ requires. We also prove that there is no natural first-order method with $mathcalOleft(n/epsilonalpharight)$ complexity gradient for $alpha 1/4$, establishing that the first-order complexity of our method is nearly tight.
  arXiv  Detail & Related papers  (2024-06-07T08:26:31Z)
• A quantum algorithm for learning a graph of bounded degree [1.8130068086063336]
  We present an algorithm that learns the edges of $G$ in at most $tildeO(d2m3/4)$ quantum queries. In particular, we present a randomized algorithm that, with high probability, learns cycles and matchings in $tildeO(sqrtm)$ quantum queries.
  arXiv  Detail & Related papers  (2024-02-28T21:23:40Z)
• Sketching Algorithms and Lower Bounds for Ridge Regression [65.0720777731368]
  We give a sketching-based iterative algorithm that computes $1+varepsilon$ approximate solutions for the ridge regression problem. We also show that this algorithm can be used to give faster algorithms for kernel ridge regression.
  arXiv  Detail & Related papers  (2022-04-13T22:18:47Z)
• Finding the KT partition of a weighted graph in near-linear time [1.572727650614088]
  Kawarabayashi and Thorup gave a near-trivial time deterministic algorithm for minimum cut in a simple graph $G = (V,E)$. We give a near-linear time randomized algorithm to find the $(1+varepsilon)$-KT partition of a weighted graph.
  arXiv  Detail & Related papers  (2021-11-02T05:26:10Z)
• Fast Graph Sampling for Short Video Summarization using Gershgorin Disc Alignment [52.577757919003844]
  We study the problem of efficiently summarizing a short video into several paragraphs, leveraging recent progress in fast graph sampling. Experimental results show that our algorithm achieves comparable video summarization as state-of-the-art methods, at a substantially reduced complexity.
  arXiv  Detail & Related papers  (2021-10-21T18:43:00Z)
• Local classical MAX-CUT algorithm outperforms $p=2$ QAOA on high-girth regular graphs [0.0]
  We show that for all degrees $D ge 2$ of girth $> 5$, QAOA$ has a larger expected cut fraction than QAOA$$ on $G$. We conjecture that for every constant $p$, there exists a local classical MAX-CUT algorithm that performs as well as QAOA$_p$ on all graphs.
  arXiv  Detail & Related papers  (2021-01-14T09:17:20Z)
• Quantum complexity of minimum cut [0.2538209532048867]
  We characterize the quantum query and time complexity of the minimum cut problem in the adjacency matrix model. Our algorithm uses a quantum algorithm for graph sparsification by Apers and de Wolf (FOCS 2020) and results on the structure of near-minimum cuts by Kawarabayashi and Thorup (STOC 2015) and Rubinstein, Schramm and Weinberg (ITCS 2018)
  arXiv  Detail & Related papers  (2020-11-19T13:51:49Z)
• Quantum algorithms for graph problems with cut queries [17.149741568581096]
  We show that a quantum algorithm can learn a graph with maximum degree $d$ after $O(d log(n)2)$ many cut queries. We also show that a quantum algorithm can learn a general graph with $O(sqrtm log(n)3/2)$ many cut queries.
  arXiv  Detail & Related papers  (2020-07-16T12:21:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.