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Three theorems regarding testing graph properties

*
Proceedings 2001 IEEE International Conference on Cluster Computing
*

We presents

doi:10.1109/sfcs.2001.959922
dblp:conf/focs/GoldreichT01
fatcat:gfek52n475alho3fvccuyuryha
*three**theorems**regarding**testing**graph**properties*in the adjacency matrix representation. ... The second*theorem*is that every*graph**property*that can be*tested*making a number of queries that is independent of the size of the*graph*can be so*tested*by uniformly selecting a set of vertices and ...*THREE**THEOREMS**REGARDING**TESTING**GRAPH**PROPERTIES*The closure operation makes this collection correspond to a*graph**property*(since it is now preserved under isomorphism). ...##
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Xor-Magic Graphs

2019
*
Recreational Mathematics Magazine
*

We classify the 3-regular xor-magic

doi:10.2478/rmm-2019-0004
fatcat:fn67hkp7hrehdc3qai6h2smorm
*graphs*on 8 and 16 vertices, and give multiple examples of 3-regular xor-magic*graphs*on 32 vertices, including the well-known Dyck*graph*. ... We show that there is at least one 3-regular xor-magic*graph*on 2n vertices for every n ⩾ 2. ...*Theorem*2. If G is xor-magic, then (*Test*1) k n, and (*Test*2) The rows of Y are all distinct.*Test*2 is particularly powerful because it applies to any basis for the nullspace. Proof. ...##
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Hierarchy Theorems for Property Testing
[chapter]

2010
*
Lecture Notes in Computer Science
*

Such results are proven in

doi:10.1007/978-3-642-16367-8_22
fatcat:27fuovq6qndpfllrj65l2c63oa
*three*standard domains often considered in*property**testing*: generic functions, adjacency predicates describing (dense)*graphs*, and incidence functions describing bounded-degree ... That is, for any relevant function q, we prove the existence of*properties*that have*testing*complexity Θ(q). ... Acknowledgments We are grateful to Ronitt Rubinfeld for asking about the existence of hierarchy*theorems*for the adjacency matrix model. ...##
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Hierarchy Theorems for Property Testing
[chapter]

2009
*
Lecture Notes in Computer Science
*

Such results are proven in

doi:10.1007/978-3-642-03685-9_38
fatcat:emgg7e2tjjgytd3kuak73fv6qm
*three*standard domains often considered in*property**testing*: generic functions, adjacency predicates describing (dense)*graphs*, and incidence functions describing bounded-degree ... That is, for any relevant function q, we prove the existence of*properties*that have*testing*complexity Θ(q). ... Acknowledgments We are grateful to Ronitt Rubinfeld for asking about the existence of hierarchy*theorems*for the adjacency matrix model. ...##
###
Hierarchy Theorems for Property Testing

2011
*
Computational Complexity
*

Such results are proven in

doi:10.1007/s00037-011-0022-4
fatcat:nbzpgk6lnzgpve3buslc5w2xmi
*three*standard domains often considered in*property**testing*: generic functions, adjacency predicates describing (dense)*graphs*, and incidence functions describing bounded-degree ... That is, for any relevant function q, we prove the existence of*properties*that have*testing*complexity Θ(q). ... Acknowledgments We are grateful to Ronitt Rubinfeld for asking about the existence of hierarchy*theorems*the adjacency matrix model. ...##
###
Page 7272 of Mathematical Reviews Vol. , Issue 2004i
[page]

2004
*
Mathematical Reviews
*

Wing-Kin Sung (SGP-SING-CSC; Singapore)
2004i:68081 68Q25 05C85 68Q17 68R10 68W20 68W25 Goldreich, Oded (IL-WEIZ-AC; Rehovot) ; Trevisan, Luca (1-CA-CDE; Berkeley, CA)

*Three**theorems**regarding**testing*... The authors offer improvements of*three*existing*theorems*con- cerning*testing*in the above setting. ...##
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Page 2335 of Mathematical Reviews Vol. , Issue 82f
[page]

1982
*
Mathematical Reviews
*

With

*regard*to planar*graphs*it is conjectured that every such*graph*is 5-choosable and that 5 is best possible. ... (Here 9,,,,, is the*graph*determined by*three*paths, two of length 2 and one of length 2m, having only end vertices in common.) ...##
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Learning from Few Positives: a Provably Accurate Metric Learning Algorithm to Deal with Imbalanced Data

2020
*
Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence
*

Unlike the state-of-the-art methods, our algorithm MLFP, for Metric Learning from Few Positives, learns a new representation that is used only when a

doi:10.24963/ijcai.2020/294
dblp:conf/ijcai/DasoulasSSV20
fatcat:zivvyy4k6jaipduk437ysirl2u
*test*query is compared to a minority training example ...*property**testing*. ...*Graph**Property**Testing*We now investigate the ability of CLIP to identify structural*graph**properties*, a task which was previously used to evaluate the expressivity of*graph*kernels and on which the Weisfeiler-Lehman ...##
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Avoidable paths in graphs
[article]

2019
*
arXiv
*
pre-print

We provide a constructive and elementary proof, relying on a single trick

arXiv:1908.03788v1
fatcat:vyldpisxcjgmhppfchicn7svwq
*regarding*the induction hypothesis. ... Avoidability generalises the notion of simpliciality best known in the context of chordal*graphs*. ... We are indebted to Michał Pilipczuk for providing helpful references*regarding*the complexity of finding an induced path of given length. ...##
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Avoidable Paths in Graphs

2020
*
Electronic Journal of Combinatorics
*

We provide a constructive and elementary proof, relying on a single trick

doi:10.37236/9030
fatcat:dova7wywhretnjonxjg735oqxe
*regarding*the induction hypothesis. ... Avoidability generalises the notion of simpliciality best known in the context of chordal*graphs*. ... We are indebted to Micha l Pilipczuk for providing helpful references*regarding*the complexity of finding an induced path of given length. ...##
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Relating counterexamples to test cases in CTL model checking specifications

2007
*
Proceedings of the 3rd international workshop on Advances in model-based testing - A-MOST '07
*

For example, it might take more than one

doi:10.1145/1291535.1291543
dblp:conf/amost/WijesekeraASF07
fatcat:xwvdh7rx3zcs5ooa4dfb3mjtpq
*test*case to "cover" a given counterexample, because not all*property*violations can be illustrated with linear counterexamples. ... This result can not only be used in the generation of a*test*set that satisfies a given*test*coverage criterion, but also in the determination of whether an extant*test*set satisfies the criterion. ... Figure 4 : 4*Three*different possible evidence*graphs*for MC/DC with*regard*to x in C = x ∧ (y ∨ z). Figure 5 : 5 An AX dangerous evidence*graph*for*property*P . ...##
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Sublinear Computation Paradigm: Constant-Time Algorithms and Sublinear Progressive Algorithms

2021
*
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
*

We present Sublinear Progressive Algorithm Theory (SPA Theory, for short), which enables to make a sublinear progressive algorithm for any

doi:10.1587/transfun.2021eai0003
fatcat:t3bm4y6i25cizkjfsxmdyxzfpq
*property*if it has a constant-time algorithm and an exact algorithm ...*Theorem*23 (SPA*Theorem*:*property**testing*version): Let P be a*property*. ... Note that in O( * ) and Θ( * ) in this*theorem*, ϵ, r, and t are*regarded*as variables. ...##
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The Subgraph Testing Model

2018
*
Innovations in Theoretical Computer Science
*

We focus on bounded-degree base

doi:10.4230/lipics.itcs.2019.37
dblp:conf/innovations/0001R19
fatcat:gwdnftxulbabtiunseob3mnzcm
*graphs*and on the relation between*testing**graph**properties*in the subgraph model and*testing*the same*properties*in the bounded-degree*graph*model. ... We initiate a study of*testing**properties*of*graphs*that are presented as subgraphs of a fixed (or an explicitly given)*graph*. ... Still, let us make a couple of comments*regarding*cases in which the subgraph*testing*model coincides with other*testing*models. The dense*graph*model is a special case of subgraph*testing*. ...##
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Every minor-closed property of sparse graphs is testable

2008
*
Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08
*

In sharp contrast to

doi:10.1145/1374376.1374433
dblp:conf/stoc/BenjaminiSS08
fatcat:ps6jlnzyjnd3fmqkoeejccni2i
*property**testing*of dense*graphs*, which is relatively well understood, very few*properties*are known to be testable in bounded degree*graphs*with a constant number of queries. ... In this paper we identify for the first time a large (and natural) family of*properties*that can be efficiently*tested*in bounded degree*graphs*, by showing that every minor-closed*graph**property*can be ... In fact, this closure*property*under these*three*basic operations holds for the*property*of a*graph*being embeddable in any specific surface. ...##
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Every minor-closed property of sparse graphs is testable

2010
*
Advances in Mathematics
*

In sharp contrast to

doi:10.1016/j.aim.2009.10.018
fatcat:zr6yivicfjclfggv7imxvazfni
*property**testing*of dense*graphs*, which is relatively well understood, very few*properties*are known to be testable in bounded degree*graphs*with a constant number of queries. ... In this paper we identify for the first time a large (and natural) family of*properties*that can be efficiently*tested*in bounded degree*graphs*, by showing that every minor-closed*graph**property*can be ... In fact, this closure*property*under these*three*basic operations holds for the*property*of a*graph*being embeddable in any specific surface. ...
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