A Combinatorial Certifying Algorithm for Linear Programming Problems with Gainfree Leontief Substitution Systems

Authors: Kei Kimura, Kazuhisa Makino

Contributors: Kei Kimura and Kazuhisa Makino

Source: Annals of Operations Research. 359:2483-2521

Subject Terms: FOS: Computer and information sciences, certifying algorithm, Computer Science - Data Structures and Algorithms, linear programming problem, Data Structures and Algorithms (cs.DS), Horn system

File Description: application/pdf

Access URL: http://arxiv.org/abs/2306.03368
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.47

Certifying Algorithms for Automated Reasoning (Dagstuhl Seminar 25231)

Authors: Nikolaj S. Bjørner and Marijn J. H. Heule and Daniela Kaufmann and Jakob Nordström and Wietze Koops, Bjørner, Nikolaj S., Heule, Marijn J. H., Kaufmann, Daniela, Nordström, Jakob, Koops, Wietze

Index Terms: ATP, Computer Algebra, DRAT, DRUP, MIP, Propagation Redundancy, QBF, SAT, SMT, Article, Text, doc-type:ResearchArticle, publishedVersion

URL: https://drops.dagstuhl.de/entities/document/10.4230/DagRep.15.6.1
Is Part Of Dagstuhl Reports, Volume 15, Issue 6 (2026)

Certifying Quantum Optimization and Circuit Cutting by Using Quantum-Classical Moment Duality

Authors: Daskin, Ammar

Subject Terms: Quantum Physics, Data Structures and Algorithms

Access URL: https://arxiv.org/abs/2606.23727

A simple certifying algorithm for 3-edge-connectivity

Authors: Tsin, Yung H. ¹

Source: In Theoretical Computer Science 24 March 2023 951

Certifying Adapters: Enabling and Enhancing the Certification of Classifier Adversarial Robustness

Authors: Deng, Jieren, Hong, Hanbin, Palmer, Aaron, Zhou, Xin, Bi, Jinbo, Mahmood, Kaleel, Hong, Yuan, Aguiar, Derek

Source: 2025 International Joint Conference on Neural Networks (IJCNN) Neural Networks (IJCNN), 2025 International Joint Conference on. :1-8 Jun, 2025

Relation: 2025 International Joint Conference on Neural Networks (IJCNN)

A Combinatorial Certifying Algorithm for Linear Programming Problems with Gainfree Leontief Substitution Systems

Authors: Kimura, Kei, Makino, Kazuhisa

Subject Terms: Computer Science - Data Structures and Algorithms

Access URL: http://arxiv.org/abs/2306.03368

Certifying and learning local quantum Hamiltonians

Authors: Bluhm, Andreas, Caro, Matthias C., Gutiérrez, Francisco Escudero, Lee, Junseo, Oufkir, Aadil, Rouzé, Cambyse, Shin, Myeongjin

Subject Terms: Quantum Physics, Computational Complexity, Data Structures and Algorithms

Access URL: http://arxiv.org/abs/2603.29809

Certifying Algorithms for Automated Reasoning (Dagstuhl Seminar 25231)

Authors: Bjørner, Nikolaj S., Heule, Marijn J. H., Kaufmann, Daniela, Nordström, Jakob, Koops, Wietze

Contributors: Nikolaj S. Bjørner and Marijn J. H. Heule and Daniela Kaufmann and Jakob Nordström and Wietze Koops

Source: Dagstuhl Reports. 15:1-31

Subject Terms: ATP, DRUP, Computer Algebra, Propagation Redundancy, SMT, DRAT, QBF, SAT, MIP

File Description: application/pdf

Access URL: https://drops.dagstuhl.de/entities/document/10.4230/DagRep.15.6.1

SoS Certificates for Sparse Singular Values and Their Applications: Robust Statistics, Subspace Distortion, and More

Additional Titles: We study sparse singular value certificates for random rectangular matrices. If M is a d × n matrix with independent Gaussian entries, we give a new family of polynomial-time algorithms which can certify upper bounds on the maximum of ||M u||, where u is a unit vector with at most η n nonzero entries for a given η ∈ (0,1). This basic algorithmic primitive lies at the heart of a wide range of problems across algorithmic statistics and theoretical computer science, including robust mean and covariance estimation, certification of distortion of random subspaces of n, certification of the 2 → p norm of a random matrix, and sparse principal component analysis. Our algorithms certify a bound which is asymptotically smaller than the naive one, given by the maximum singular value of M, for nearly the widest-possible range of n,d, and η. Efficiently certifying such a bound for a range of n,d and η which is larger by any polynomial factor than what is achieved by our algorithm would violate lower bounds in the statistical query and low-degree polynomials models. Our certification algorithm makes essential use of the Sum-of-Squares hierarchy. To prove the correctness of our algorithm, we develop a new combinatorial connection between the graph matrix approach to analyze random matrices with dependent entries, and the Efron-Stein decomposition of functions of independent random variables. As applications of our certification algorithm, we obtain new efficient algorithms for a wide range of well-studied algorithmic tasks. In algorithmic robust statistics, we obtain new algorithms for robust mean and covariance estimation with tradeoffs between breakdown point and sample complexity, which are nearly matched by statistical query and low-degree polynomial lower bounds (that we establish). We also obtain new polynomial-time guarantees for certification of ℓ1/ℓ2 distortion of random subspaces of n (also with nearly matching lower bounds), sparse principal component analysis, and cert

Authors: Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science, Diakonikolas, Ilias, Hopkins, Samuel B., Pensia, Ankit, Tiegel, Stefan

Source: Association for Computing Machinery

Index Terms: Article, http://purl.org/eprint/type/ConferencePaper

URL: https://hdl.handle.net/1721.1/164633
https://doi.org/10.1145/3717823.3718293
https://doi.org/10.1145/3717823.3718293

A linear-time certifying algorithm for recognizing generalized series–parallel graphs

Authors: Chin, Francis Y.L. ^a, Ting, Hing-Fung ^a, Tsin, Yung H. ^{b, ⁎}, Zhang, Yong ^c

Source: In Discrete Applied Mathematics 30 January 2023 325:152-171

Simple certifying algorithms for variants of the (2, 1)-colouring problem

Authors: Contreras-Mendoza, Fernando Esteban ^a, Hernández-Cruz, César ^a

Source: In Procedia Computer Science 2023 223:292-301

Efficient algorithms for certifying lower bounds on the discrepancy of random matrices

Authors: Venkat, Prayaag

Subject Terms: Computer Science - Data Structures and Algorithms, Computer Science - Computational Complexity, Computer Science - Discrete Mathematics

Access URL: http://arxiv.org/abs/2211.07503

A certifying and dynamic algorithm for the recognition of proper circular-arc graphs

Authors: Soulignac, Francisco J. ^{a, b, c, ⁎}

Source: In Theoretical Computer Science 8 October 2021 889:105-134

An Optimal Algorithm for Certifying Monotone Functions

Authors: Gupta, Meghal, Manoj, Naren Sarayu

Subject Terms: Computer Science - Data Structures and Algorithms, Computer Science - Computational Complexity

Access URL: http://arxiv.org/abs/2204.01224

Efficient Certifying Algorithms for Linear Classification

Authors: Bonifaci, Vincenzo^Aff10, Galatro, Sara^Aff10

Contributors: Goos, Gerhard, Series Editor^{Aff1, Aff3}, Hartmanis, Juris, Founding Editor^Aff2, Bertino, Elisa, Editorial Board Member^Aff4, Gao, Wen, Editorial Board Member^Aff5, Steffen, Bernhard, Editorial Board Member^Aff6, Yung, Moti, Editorial Board Member^Aff7, Finocchi, Irene, editor^Aff8, Georgiadis, Loukas, editor^Aff9

Source: Algorithms and Complexity : 14th International Conference, CIAC 2025, Rome, Italy, June 10–12, 2025, Proceedings, Part I. 15679:153-169

Certifying Fully Dynamic Algorithms for Recognition and Hamiltonicity of Threshold and Chain Graphs: Certifying fully dynamic algorithms for recognition and Hamiltonicity of threshold and chain graphs

Authors: Jesse Beisegel, Ekkehard Köhler, Robert Scheffler 0001, Martin Strehler 0001

Source: Algorithmica. 85:2454-2481

Subject Terms: Graph theory, Eulerian and Hamiltonian graphs, difference graphs, Graph algorithms (graph-theoretic aspects), Graph theory (including graph drawing) in computer science, fully dynamic algorithms, threshold graphs, Algorithms in computer science, chain graphs, Hamiltonian cycles, Hamiltonian paths

File Description: application/xml

Access URL: https://zbmath.org/7729250
https://doi.org/10.1007/s00453-023-01107-1

Certifying and learning quantum Ising Hamiltonians

Authors: Bluhm, Andreas, Caro, Matthias C., Gutiérrez, Francisco Escudero, Oufkir, Aadil, Rouzé, Cambyse

Subject Terms: Quantum Physics, Computational Complexity, Data Structures and Algorithms

Access URL: http://arxiv.org/abs/2509.10239

Certifying expressive power and algorithms of reversible primitive permutations with Lean

Authors: Maletto, Giacomo ^a, Roversi, Luca ^{b, ⁎}

Source: In Journal of Logical and Algebraic Methods in Programming January 2024 136

Certifying Combinatorial Optimization: A Unified Approach Using Pseudo-Boolean Reasoning

Authors: Oertel, Andy, Author, Lund University, Faculty of Engineering, LTH, Departments at LTH, Department of Computer Science, Parallel Systems, Lunds universitet, Lunds Tekniska Högskola, Institutioner vid LTH, Institutionen för datavetenskap, Parallella System, Originator, Lund University, Faculty of Engineering, LTH, LTH Profile areas, LTH Profile Area: AI and Digitalization, Lunds universitet, Lunds Tekniska Högskola, LTH profilområden, LTH profilområde: AI och digitalisering, Originator, Lund University, Profile areas and other strong research environments, Strategic research areas (SRA), ELLIIT: the Linköping-Lund initiative on IT and mobile communication, Lunds universitet, Profilområden och andra starka forskningsmiljöer, Strategiska forskningsområden (SFO), ELLIIT: the Linköping-Lund initiative on IT and mobile communication, Originator, Nordström, Jakob, de Rezende, Susanna

Contributors: Oertel, Andy, Author, Lund University, Faculty of Engineering, LTH, Departments at LTH, Department of Computer Science, Parallel Systems, Lunds universitet, Lunds Tekniska Högskola, Institutioner vid LTH, Institutionen för datavetenskap, Parallella System, Originator, Lund University, Faculty of Engineering, LTH, LTH Profile areas, LTH Profile Area: AI and Digitalization, Lunds universitet, Lunds Tekniska Högskola, LTH profilområden, LTH profilområde: AI och digitalisering, Originator, Lund University, Profile areas and other strong research environments, Strategic research areas (SRA), ELLIIT: the Linköping-Lund initiative on IT and mobile communication, Lunds universitet, Profilområden och andra starka forskningsmiljöer, Strategiska forskningsområden (SFO), ELLIIT: the Linköping-Lund initiative on IT and mobile communication, Originator, Nordström, Jakob, de Rezende, Susanna

Subject Terms: Natural Sciences, Computer and Information Sciences, Computer Sciences, Naturvetenskap, Data- och informationsvetenskap (Datateknik), Datavetenskap (Datalogi), Algorithms, Algoritmer

File Description: electronic

Access URL: https://lucris.lub.lu.se/ws/files/248592548/thesis-Andy_Oertel.pdf

Computational Hardness of Detecting Graph Lifts and Certifying Lift-Monotone Properties of Random Regular Graphs

Authors: Kunisky, Dmitriy, Yu, Xifan

Source: 2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS) FOCS Foundations of Computer Science (FOCS), 2024 IEEE 65th Annual Symposium on. :1621-1633 Oct, 2024

Relation: 2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)