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About 148 papers for “Blossom algorithm”

Edmonds' Blossom Algorithm Part 1: Cast of Characters

Richard L. Apodaca · Front Matter · 2020

Many problems in business and science can be cast in terms of <em> graph matching </em> . Given an undirected graph, a matching is a subgraph in which every node has a degree of one. It's often important to find a matching that contains the most possible edges. This is the maximum matching problem. Although the concept is easy to understand, algorithms for finding maximum matchings tend to be complex.

Cited by 0Open access

Edmonds' Blossom Algorithm Part 1: Cast of Characters

Richard L. Apodaca · Front Matter · 2020

Many problems in business and science can be cast in terms of <em> graph matching </em> . Given an undirected graph, a matching is a subgraph in which every node has a degree of one. It's often important to find a matching that contains the most possible edges. This is the maximum matching problem. Although the concept is easy to understand, algorithms for finding maximum matchings tend to be complex.

Cited by 0Open access

A Formal Correctness Proof of Edmonds’ Blossom Shrinking Algorithm

Mohammad Abdulaziz, Kurt Mehlhorn · Journal of Automated Reasoning · 2026

Abstract We present the first formal correctness proof of Edmonds’ blossom shrinking algorithm for maximum cardinality matching in general graphs. We focus on formalising the mathematical structures and properties that allow the algorithm to run in worst-case polynomial running time. We formalise Berge’s lemma, blossoms and their properties, and a mathematical model of the algorithm, showing that it is totally correct. We provide the first detailed proofs of many of the facts underlying the algorithm’s correctness.

Cited by 0Open access

A distributed blossom algorithm for minimum-weight perfect matching

Eric C. Peterson, Peter J. Karalekas · arXiv (Cornell University) · 2022

We describe a distributed, asynchronous variant of Edmonds's exact algorithm for producing perfect matchings of minimum weight. The development of this algorithm is driven by an application to online error correction in quantum computing, first envisioned by Fowler; we analyze the performance of our algorithm as applied to this domain in a sequel.

Cited by 2Open access

A 1‐matching blossom‐type algorithm for edge covering problems

Katta G. Murty, Clovis Perin · Networks · 1982

Abstract We discuss an efficient primal‐dual algorithm for finding a minimum cost edge cover in an undirected network G with n nodes and m edges, which is based on the blossom algorithm for 1‐matching problems. We establish that its worst case computational complexity is O ( n 3 ), the same as that for blossom or primal algorithms for 1‐matching problems.

Cited by 27

Blossom Harmonic Algorithm (BHA) A Zero-Drift Framework for Scalable Quantum Architecture

Carolina Johnson · Zenodo (CERN European Organization for Nuclear Research) · 2025

Blossom Harmonic Algorithm (BHA) This paper introduces the Blossom Harmonic Algorithm, a quantum architecture that prevents error propagation through tier-gated validation. Unlike traditional error correction that reacts to errors after they occur, BHA blocks them at the source by verifying zero drift before allowing any computation to advance. The result is a 100x reduction in qubit overhead, deterministic reliability, and linear scalability. The framework is built on harmonic shell theory and can be implemented on existing quantum hardware through software changes.

Cited by 0Open access

Towards the Acceleration of the Sparse Blossom Algorithm for Quantum Error Correction

M. Vénere, Valentino Guerrini, Beatrice Branchini et al. · 2024

Quantum computing is a new computing paradigm that exploits laws of quantum mechanics to achieve an exponential speedup compared to classical logic. However, noise strongly limits current quantum hardware, reducing achievable performance. Quantum Error Correction (QEC) techniques are a valuable approach to reduce the effects of noise. Nevertheless, the high computational complexity of QEC algorithms is incompatible with the tight time constraints of quantum devices. Thus, hardware acceleration is paramount to achieving real-time QEC. This work represents the first step in the FPGA acceleration of the Sparse Blossom Algorithm (SBA), a state-of-the-art decoding algorithm for QEC. We provide a performance profiling and a design methodology for the hardware development of the SBA. We evaluate the execution time, and energy efficiency of our solution, attaining up to 2.75× speedup and 9.59× improvement in energy efficiency compared to the software baseline.

Cited by 2

Blossom Harmonic Algorithm (BHA) A Zero-Drift Framework for Scalable Quantum Architecture

Carolina Johnson · Zenodo (CERN European Organization for Nuclear Research) · 2025

Blossom Harmonic Algorithm (BHA) This paper introduces the Blossom Harmonic Algorithm, a quantum architecture that prevents error propagation through tier-gated validation. Unlike traditional error correction that reacts to errors after they occur, BHA blocks them at the source by verifying zero drift before allowing any computation to advance. The result is a 100x reduction in qubit overhead, deterministic reliability, and linear scalability. The framework is built on harmonic shell theory and can be implemented on existing quantum hardware through software changes.

Cited by 0Open access

Shared-Memory Parallel Edmonds Blossom Algorithm for Maximum Cardinality Matching in General Graphs

Gregory Schwing, Daniel Grosu, Loren Schwiebert · PubMed Central · 2024

The Edmonds Blossom algorithm is implemented here using depth-first search, which is intrinsically serial. By streamlining the code, our serial implementation is consistently three to five times faster than the previously fastest general graph matching code. By extracting parallelism across iterations of the algorithm, with coarse-grain locking, we are able to further reduce the run time on random regular graphs four-fold and obtain a two-fold reduction of run time on real-world graphs with similar topology. Solving very sparse graphs (average degree less than four) exhibiting community structure with eight threads led to a slow down of three-fold, but this slow down is replaced by marginal speed up once the average degree is greater than four. We conclude that our parallel coarse-grain locking implementation performs well when extracting parallelism from this augmenting-path-based algorithm and may work well for similar algorithms.

Cited by 1Open access

Rock the QASBA: Quantum Error Correction Acceleration via the Sparse Blossom Algorithm on FPGAs

M. Vénere, Beatrice Branchini, Davide Conficconi et al. · ACM Transactions on Reconfigurable Technology and Systems · 2025

Quantum computing is a new paradigm of computation that exploits principles from quantum mechanics to achieve an exponential speedup compared to classical logic. However, noise strongly limits current quantum hardware, reducing achievable performance and limiting the scaling of the applications. For this reason, current noisy intermediate-scale quantum devices require Quantum Error Correction (QEC) mechanisms to identify errors occurring in the computation and correct them in real time. Nevertheless, the high computational complexity of QEC algorithms is incompatible with the tight time constraints of quantum devices. Thus, hardware acceleration is paramount to achieving real-time QEC. This work presents QASBA, an FPGA-based hardware accelerator for the Sparse Blossom Algorithm (SBA), a state-of-the-art decoding algorithm. After profiling the state-of-the-art software counterpart, we developed a design methodology for hardware development based on the SBA. We also devised an automation process to help users without expertise in hardware design in deploying architectures based on QASBA. We implement QASBA on different FPGA architectures and experimentally evaluate resource usage, execution time, and energy efficiency of our solution. Our solution attains up to \(25.05\times\) speedup and \(304.16\times\) improvement in energy efficiency compared to the software baseline.

Cited by 1Open access

Blossom Harmonic Algorithm as Holonomic Monad: A Unified Framework for Topologically Protected Quantum Computation

Carolina Johnson · Zenodo (CERN European Organization for Nuclear Research) · 2025

This paper proves that the Blossom Harmonic Algorithm (BHA) is structurally isomorphic to both monadic composition in functional programming and holonomic evolution in quantum mechanics. We demonstrate that BHA's tier-gated architecture satisfies the monad laws through its zero-drift validation protocol, with tier transitions accumulating Berry phase via parallel transport in frequency space. The Law of Admissibility (n=4k), previously established for recursive systems, is shown to function as the monadic invariant ensuring drift-free composition. Key result: Monads, quantum holonomies, and harmonic shells are the same computational structure appearing in three domains. Computation, geometry, and frequency dynamics are governed by identical compositional laws. Implications: Fault-tolerant quantum architectures with topological protection by construction; type systems that verify coherence at compile time; and evidence that the deepest structures of computation and physics are unified.

Cited by 0Open access

Blossom Harmonic Algorithm as Holonomic Monad: A Unified Framework for Topologically Protected Quantum Computation

Carolina Johnson · Zenodo (CERN European Organization for Nuclear Research) · 2025

This paper proves that the Blossom Harmonic Algorithm (BHA) is structurally isomorphic to both monadic composition in functional programming and holonomic evolution in quantum mechanics. We demonstrate that BHA's tier-gated architecture satisfies the monad laws through its zero-drift validation protocol, with tier transitions accumulating Berry phase via parallel transport in frequency space. The Law of Admissibility (n=4k), previously established for recursive systems, is shown to function as the monadic invariant ensuring drift-free composition. Key result: Monads, quantum holonomies, and harmonic shells are the same computational structure appearing in three domains. Computation, geometry, and frequency dynamics are governed by identical compositional laws. Implications: Fault-tolerant quantum architectures with topological protection by construction; type systems that verify coherence at compile time; and evidence that the deepest structures of computation and physics are unified.

Cited by 0Open access

Implementation of <i>O</i> ( <i>nm</i> log <i>n</i> ) weighted matchings in general graphs

Kurt Mehlhorn, Guido Schäfer · ACM Journal of Experimental Algorithmics · 2002

We describe the implementation of an algorithm which solves the weighted matching problem in general graphs with n vertices and m edges in time O(nm log n) . Our algorithm is a variant of the algorithm of Galil, Micali and Gabow [Galil et al. 1986] and extensively uses sophisticated data structures, in particular concatenable priority queues , so as to reduce the time needed to perform dual adjustments and to find tight edges in Edmonds' blossom-shrinking algorithm.We compare our implementation to the experimentally fastest implementation, named Blossom IV , due to Cook and Rohe [Cook and Rohe 1997]. Blossom IV requires only very simple data structures and has an asymptotic running time of O(n 2 m) . Our experiments show that our new implementation is superior to Blossom IV. A closer inspection reveals that the running time of Edmonds' blossom-shrinking algorithm in practice heavily depends on the time spent to perform dual adjustments and to find tight edges. Therefore, optimizing these operations, as is done in our implementation, indeed speeds-up the practical performance of implementations of Edmonds' algorithm.

Cited by 43

Unweighted Matching in Random Graphs

Kristina Nelson · Open Collections · 2015

We study the application of Edmond’s Blossom algorithm for unweighted matching on random graphs generated with the Erdos-Renyi model. Since its publication in 1965, the blossom algorithm has been the subject of great interest and research, not only in the field of matching theory but also as a linear programming problem. In the first part of this report we introduce the background and prerequisite graph theoretic definitions before describing the operation of the blossom algorithm itself. In the second part of this essay we describe our investigations around the operational running time of the algorithm and attempts to improve this value.

Cited by 0Open access

UAV Photogrammetry-Based Apple Orchard Blossom Density Estimation and Mapping

Wenan Yuan, Weiyun Hua, Paul Heinemann et al. · Horticulturae · 2023

Thinning is an important routine for apple growers to manage crop load and improve fruit quality, which can be accomplished through manual, chemical, or mechanical manipulation of flowers and fruitlets. Traditionally, blossom thinning relies on human experts’ visual evaluation of the flower load, a leading indicator of crop load, which can be imprecise and prone to errors. This study aimed to develop an apple blossom density mapping algorithm utilizing point clouds reconstructed through unmanned aerial vehicle (UAV)-based red-green-blue (RGB) imagery and photogrammetry. The algorithm was based on grid average downsampling and white color thresholding, and it was able to generate top-view blossom density maps of user-defined tree height regions. A preliminary field experiment was carried out to evaluate the algorithm’s accuracy using manual blossom counts of apple tree row sections as ground truths, and a coefficient of determination (R2) of 0.85, a root mean square error (RMSE) of 1307, and a normalized RMSE (NRMSE) of 9.02% were achieved. The algorithm was utilized to monitor the blooming of the apple tree rows and was demonstrated to effectively show blossom density variations between different tree rows and dates. The study results suggested the potential of UAVs as a convenient tool to assist precise blossom thinning in apple orchards, while future research should further investigate the reliability of photogrammetry techniques under different image qualities and flight settings as well as the influence of blossom distribution on algorithm accuracy.

Cited by 14Open access

Research on Monocular Vision Positioning Technology Used in Water Meter Verification

Ge Yan, Jian Sun, Tao Lü · 2018 3rd International Conference on Mechanical, Control and Computer Engineering (ICMCCE) · 2018

This paper mainly studies the method of water meter plum pin precise positioning, and proposes a positioning method of water meter plum blossom needle with high positioning accuracy, anti-jamming performance and versatility. The method firstly uses the three-frame difference method to obtain the contour area of the plum blossom needle dynamically, secondly the convex hull algorithm to extract the boundary information of the plum blossom needle, and then uses the minimum encircling circle algorithm to create the circumscribed circle of the plum blossom needle. By traversing the distance between each vertex and the circumcircle pixel, we find the exact coordinate position and achieve the precise positioning of the plum blossom needle. The test results show that the precision of the water meter can reach 97.46%-99.133% by accurately positioning the plum blossom needle. On the one hand we can accurately locate the plum blossom needle with the bubble inside the dial, on the other hand, this method covers the shortage of the traditional photoelectric pulse verification method which can only detect the water meter of the plum blossom needle at the same position.

Cited by 2