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Related papers: Compact Distributed Certification of Planar Graphs

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There is no known polynomial-time algorithm for graph isomorphism testing, but elementary combinatorial "refinement" algorithms seem to be very efficient in practice. Some philosophical justification is provided by a classical theorem of…

Combinatorics · Mathematics 2025-10-17 Michael Anastos , Matthew Kwan , Benjamin Moore

We study verification (decision) problems for graph properties in distributed networks under the locally checkable labeling framework, where nodes use labels (proofs) and local neighborhoods to decide acceptance or rejection. Our focus is…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-03-24 Paweł Garncarek , Tomasz Jurdzinski , Dariusz Kowalski , Subhajit Pramanick

In this paper we study the problem of testing graph isomorphism (GI) in the CONGEST distributed model. In this setting we test whether the distributive network, $G_U$, is isomorphic to $G_K$ which is given as an input to all the nodes in…

Data Structures and Algorithms · Computer Science 2020-03-03 Reut Levi , Moti Medina

We present proof labeling schemes for graphs with bounded pathwidth that can decide any graph property expressible in monadic second-order (MSO) logic using $O(\log n)$-bit vertex labels. Examples of such properties include planarity,…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-02-04 Dan Alden Baterisna , Yi-Jun Chang

As modern computing moves towards smaller devices and powerful cloud platforms, more and more computation is being delegated to powerful service providers. Interactive proofs are a widely-used model to design efficient protocols for…

Computer Science and Game Theory · Computer Science 2018-09-14 Jing Chen , Samuel McCauley , Shikha Singh

Certifying the robustness of a graph-based machine learning model poses a critical challenge for safety. Current robustness certificates for graph classifiers guarantee output invariance with respect to the total number of node pair flips…

Machine Learning · Computer Science 2023-06-27 Pierre Osselin , Henry Kenlay , Xiaowen Dong

Two planar graphs G1 and G2 sharing some vertices and edges are `simultaneously planar' if they have planar drawings such that a shared vertex [edge] is represented by the same point [curve] in both drawings. It is an open problem whether…

Data Structures and Algorithms · Computer Science 2011-12-12 Bernhard Haeupler , Krishnam Raju Jampani , Anna Lubiw

Local certification consists in assigning labels to the nodes of a network to certify that some given property is satisfied, in such a way that the labels can be checked locally. In the last few years, certification of graph classes…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-09-14 Nicolas Bousquet , Laurent Feuilloley , Théo Pierron

We introduce the {\em certification} of solutions to graph problems when access to the input is restricted. This topic has received a lot of attention in the distributed computing setting, and we introduce it here in the context of…

Computational Complexity · Computer Science 2025-03-18 Avinandan Das , Pierre Fraigniaud , Ami Paz , Adi Rosen

In this paper, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…

Optimization and Control · Mathematics 2022-07-19 Mohammadreza Chamanbaz , Giuseppe Notarstefano , Francesco Sasso , Roland Bouffanais

In this paper we initiate the study of property testing in simultaneous and non-simultaneous multi-party communication complexity, focusing on testing triangle-freeness in graphs. We consider the $\textit{coordinator}$ model, where we have…

Data Structures and Algorithms · Computer Science 2017-05-24 Orr Fischer , Shay Gershtein , Rotem Oshman

The study of network representations of physical, biological, and social phenomena can help us better understand the structural and functional dynamics of their networks and formulate predictive models of these phenomena. However, due to…

Social and Information Networks · Computer Science 2019-05-14 Varsha Chauhan , Alexander Gutfraind , Ilya Safro

Distributed optimization requires nodes to coordinate, yet full synchronization scales poorly. When $n$ nodes collaborate through $m$ pairwise regularizers, standard methods demand $\mathcal{O}(m)$ communications per iteration. This paper…

Machine Learning · Computer Science 2025-09-19 Ying Lin , Yao Kuang , Ahmet Alacaoglu , Michael P. Friedlander

In 1994, Thomassen proved that every planar graph is 5-list-colorable. In 1995, Thomassen proved that every planar graph of girth at least five is 3-list-colorable. His proofs naturally lead to quadratic-time algorithms to find such…

Combinatorics · Mathematics 2019-11-07 Luke Postle

The intrinsic non-locality of correlations in Quantum Mechanics allow us to certify the behaviour of a quantum mechanism in a device independent way. In particular, we present a new protocol that allows an unbounded amount of randomness to…

Quantum Physics · Physics 2018-08-01 Brian Coyle , Matty J. Hoban , Elham Kashefi

We propose a simple and time-optimal algorithm for property testing a graph for its conductance in the CONGEST model. Our algorithm takes only $O(\log n)$ rounds of communication (which is known to be optimal), and consists of simply…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-03-12 Tugkan Batu , Amitabh Trehan , Chhaya Trehan

We present Proof-of-Perception (PoP), a tool-using framework that casts multimodal reasoning as an executable graph with explicit reliability guarantees. Each perception or logic node outputs a conformal set, yielding calibrated, stepwise…

Computer Vision and Pattern Recognition · Computer Science 2026-03-03 Arya Fayyazi , Haleh Akrami

The Internet of Things (IoT) is an emerging paradigm that allows to set large networks of small and independent devices. To ensure their integrity, practitioners employ so-called Remote Attestation (RA) schemes. Classic RA schemes require a…

Cryptography and Security · Computer Science 2019-12-13 Alessandro Visintin , Flavio Toffalini , Mauro Conti , Jianying Zhou

In this paper we consider a network of processors aiming at cooperatively solving linear programming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…

Optimization and Control · Mathematics 2019-08-27 Mohammadreza Chamanbaz , Giuseppe Notarstefano , Roland Bouffanais

Given a dynamic graph subject to insertions and deletions of edges, a natural question is whether the graph presently admits a planar embedding. We give a deterministic fully-dynamic algorithm for general graphs, running in amortized…

Data Structures and Algorithms · Computer Science 2019-12-11 Jacob Holm , Eva Rotenberg