相关论文: Quantum Max-Flow Min-Cut theorem

The classical Okamura-Seymour theorem states that for an edge-capacitated, multi-commodity flow instance in which all terminals lie on a single face of a planar graph, there exists a feasible concurrent flow if and only if the cut…

Optimizing parameterized quantum circuits promises efficient use of near-term quantum computers to achieve the potential quantum advantage. However, there is a notorious tradeoff between the expressibility and trainability of the parameter…

The Langberg-M\'edard multiple unicast conjecture claims that for any strongly reachable $k$-pair network, there exists a multi-flow with rate $(1,1,\dots,1)$. In a previous work, through combining and concatenating the so-called elementary…

We consider the standard first passage percolation model on Z^d with a distribution G on R+ that admits an exponential moment. We study the maximal flow between a compact convex subset A of R^d and infinity. The study of maximal flow is…

We show a deterministic constant-time local algorithm for constructing an approximately maximum flow and minimum fractional cut in multisource-multitarget networks with bounded degrees and bounded edge capacities. Locality means that the…

Given a set of source-sink pairs, the maximum multiflow problem asks for the maximum total amount of flow that can be feasibly routed between them. The minimum multicut, a dual problem to multiflow, seeks the minimum-cost set of edges whose…

In this paper we study minimum cut and maximum flow problems on planar graphs, both in static and in dynamic settings. First, we present an algorithm that given an undirected planar graph computes the minimum cut between any two given…

Despite the pursuit of quantum advantages in various applications, the power of quantum computers in neural network computations has mostly remained unknown, primarily due to a missing link that effectively designs a neural network model…

In the present paper, we apply the network simplex algorithm for solving the minimum cost flow problem, to the maximum flow problem. Then we prove that the cycling phenomenon which causes the infinite loop in the algorithm, does not occur…

The capacity (or maximum flow) of an unicast network is known to be equal to the minimum s-t cut capacity due to the max-flow min-cut theorem. If the topology of a network (or link capacities) is dynamically changing or unknown, it is not…

In measurement-based quantum computing (MBQC), computation is carried out by a sequence of measurements and corrections on an entangled state. Flow, and related concepts, are powerful techniques for characterising the dependence of the…

In this paper we provide an algorithm which given any $m$-edge $n$-vertex directed graph with integer capacities at most $U$ computes a maximum $s$-$t$ flow for any vertices $s$ and $t$ in $m^{4/3+o(1)}U^{1/3}$ time. This improves upon the…

Rapid advances in image acquisition and storage technology underline the need for algorithms that are capable of solving large scale image processing and computer-vision problems. The minimum cut problem plays an important role in…

Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different…

Minimum cut/maximum flow (min-cut/max-flow) algorithms solve a variety of problems in computer vision and thus significant effort has been put into developing fast min-cut/max-flow algorithms. As a result, it is difficult to choose an ideal…

We consider high dimensional variants of the maximum flow and minimum cut problems in the setting of simplicial complexes and provide both algorithmic and hardness results. By viewing flows and cuts topologically in terms of the simplicial…

In this paper we provide an algorithm which given any $m$-edge $n$-vertex directed graph with integer capacities at most $U$ computes a maximum $s$-$t$ flow for any vertices $s$ and $t$ in $m^{11/8+o(1)}U^{1/4}$ time with high probability.…

Quantum information theory, particularly its entropic formulations, has made remarkable strides in characterizing quantum systems and tasks. However, a critical dimension remains underexplored: computational efficiency. While classical…

We study irreducible representations of Rees cones and characterize the max-flow min-cut property of clutters in terms of the normality of Rees algebras and the integrality of certain polyhedra. Then we present some applications to…

We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed…