---
_id: '10045'
abstract:
- lang: eng
text: "Given a fixed finite metric space (V,μ), the {\\em minimum 0-extension problem},
denoted as 0-Ext[μ], is equivalent to the following optimization problem: minimize
function of the form minx∈Vn∑ifi(xi)+∑ijcijμ(xi,xj) where cij,cvi are given nonnegative
costs and fi:V→R are functions given by fi(xi)=∑v∈Vcviμ(xi,v). The computational
complexity of 0-Ext[μ] has been recently established by Karzanov and by Hirai:
if metric μ is {\\em orientable modular} then 0-Ext[μ] can be solved in polynomial
time, otherwise 0-Ext[μ] is NP-hard. To prove the tractability part, Hirai developed
a theory of discrete convex functions on orientable modular graphs generalizing
several known classes of functions in discrete convex analysis, such as L♮-convex
functions. We consider a more general version of the problem in which unary functions
fi(xi) can additionally have terms of the form cuv;iμ(xi,{u,v}) for {u,v}∈F, where
set F⊆(V2) is fixed. We extend the complexity classification above by providing
an explicit condition on (μ,F) for the problem to be tractable. In order to prove
the tractability part, we generalize Hirai's theory and define a larger class
of discrete convex functions. It covers, in particular, another well-known class
of functions, namely submodular functions on an integer lattice. Finally, we improve
the complexity of Hirai's algorithm for solving 0-Ext on orientable modular graphs.\r\n"
acknowledgement: We thank the anonymous reviewers for their careful reading of our
manuscript and their many insightful comments and suggestions. Open access funding
provided by Institute of Science and Technology (IST Austria).
article_number: '2109.10203'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Martin
full_name: Dvorak, Martin
id: 40ED02A8-C8B4-11E9-A9C0-453BE6697425
last_name: Dvorak
orcid: 0000-0001-5293-214X
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
citation:
ama: Dvorak M, Kolmogorov V. Generalized minimum 0-extension problem and discrete
convexity. Mathematical Programming. 2024. doi:10.1007/s10107-024-02064-5
apa: Dvorak, M., & Kolmogorov, V. (2024). Generalized minimum 0-extension problem
and discrete convexity. Mathematical Programming. Springer Nature. https://doi.org/10.1007/s10107-024-02064-5
chicago: Dvorak, Martin, and Vladimir Kolmogorov. “Generalized Minimum 0-Extension
Problem and Discrete Convexity.” Mathematical Programming. Springer Nature,
2024. https://doi.org/10.1007/s10107-024-02064-5.
ieee: M. Dvorak and V. Kolmogorov, “Generalized minimum 0-extension problem and
discrete convexity,” Mathematical Programming. Springer Nature, 2024.
ista: Dvorak M, Kolmogorov V. 2024. Generalized minimum 0-extension problem and
discrete convexity. Mathematical Programming., 2109.10203.
mla: Dvorak, Martin, and Vladimir Kolmogorov. “Generalized Minimum 0-Extension Problem
and Discrete Convexity.” Mathematical Programming, 2109.10203, Springer
Nature, 2024, doi:10.1007/s10107-024-02064-5.
short: M. Dvorak, V. Kolmogorov, Mathematical Programming (2024).
date_created: 2021-09-27T10:48:23Z
date_published: 2024-03-07T00:00:00Z
date_updated: 2024-03-19T08:20:31Z
day: '07'
ddc:
- '004'
department:
- _id: GradSch
- _id: VlKo
doi: 10.1007/s10107-024-02064-5
external_id:
arxiv:
- '2109.10203'
file:
- access_level: open_access
checksum: e7e83065f7bc18b9c188bf93b5ca5db6
content_type: application/pdf
creator: mdvorak
date_created: 2021-09-27T10:54:51Z
date_updated: 2021-09-27T10:54:51Z
file_id: '10046'
file_name: Generalized-0-Ext.pdf
file_size: 603672
relation: main_file
success: 1
file_date_updated: 2021-09-27T10:54:51Z
has_accepted_license: '1'
keyword:
- minimum 0-extension problem
- metric labeling problem
- discrete metric spaces
- metric extensions
- computational complexity
- valued constraint satisfaction problems
- discrete convex analysis
- L-convex functions
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '03'
oa: 1
oa_version: Preprint
publication: Mathematical Programming
publication_identifier:
eissn:
- 1436-4646
issn:
- 0025-5610
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Generalized minimum 0-extension problem and discrete convexity
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_id: '14084'
abstract:
- lang: eng
text: "A central problem in computational statistics is to convert a procedure for
sampling combinatorial objects into a procedure for counting those objects, and
vice versa. We will consider sampling problems which come from Gibbs distributions,
which are families of probability distributions over a discrete space Ω with probability
mass function of the form μ^Ω_β(ω) ∝ e^{β H(ω)} for β in an interval [β_min, β_max]
and H(ω) ∈ {0} ∪ [1, n].\r\nThe partition function is the normalization factor
Z(β) = ∑_{ω ∈ Ω} e^{β H(ω)}, and the log partition ratio is defined as q = (log
Z(β_max))/Z(β_min)\r\nWe develop a number of algorithms to estimate the counts
c_x using roughly Õ(q/ε²) samples for general Gibbs distributions and Õ(n²/ε²)
samples for integer-valued distributions (ignoring some second-order terms and
parameters), We show this is optimal up to logarithmic factors. We illustrate
with improved algorithms for counting connected subgraphs and perfect matchings
in a graph."
acknowledgement: We thank Heng Guo for helpful explanations of algorithms for sampling
connected subgraphs and matchings, Maksym Serbyn for bringing to our attention the
Wang-Landau algorithm and its use in physics.
alternative_title:
- LIPIcs
article_number: '72'
article_processing_charge: Yes
author:
- first_name: David G.
full_name: Harris, David G.
last_name: Harris
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
citation:
ama: 'Harris DG, Kolmogorov V. Parameter estimation for Gibbs distributions. In:
50th International Colloquium on Automata, Languages, and Programming.
Vol 261. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:10.4230/LIPIcs.ICALP.2023.72'
apa: 'Harris, D. G., & Kolmogorov, V. (2023). Parameter estimation for Gibbs
distributions. In 50th International Colloquium on Automata, Languages, and
Programming (Vol. 261). Paderborn, Germany: Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPIcs.ICALP.2023.72'
chicago: Harris, David G., and Vladimir Kolmogorov. “Parameter Estimation for Gibbs
Distributions.” In 50th International Colloquium on Automata, Languages, and
Programming, Vol. 261. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2023. https://doi.org/10.4230/LIPIcs.ICALP.2023.72.
ieee: D. G. Harris and V. Kolmogorov, “Parameter estimation for Gibbs distributions,”
in 50th International Colloquium on Automata, Languages, and Programming,
Paderborn, Germany, 2023, vol. 261.
ista: 'Harris DG, Kolmogorov V. 2023. Parameter estimation for Gibbs distributions.
50th International Colloquium on Automata, Languages, and Programming. ICALP:
International Colloquium on Automata, Languages, and Programming, LIPIcs, vol.
261, 72.'
mla: Harris, David G., and Vladimir Kolmogorov. “Parameter Estimation for Gibbs
Distributions.” 50th International Colloquium on Automata, Languages, and Programming,
vol. 261, 72, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, doi:10.4230/LIPIcs.ICALP.2023.72.
short: D.G. Harris, V. Kolmogorov, in:, 50th International Colloquium on Automata,
Languages, and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2023.
conference:
end_date: 2023-07-14
location: Paderborn, Germany
name: 'ICALP: International Colloquium on Automata, Languages, and Programming'
start_date: 2023-07-10
date_created: 2023-08-20T22:01:14Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2023-08-21T06:49:11Z
day: '01'
ddc:
- '000'
- '510'
department:
- _id: VlKo
doi: 10.4230/LIPIcs.ICALP.2023.72
external_id:
arxiv:
- '2007.10824'
file:
- access_level: open_access
checksum: 6dee0684245bb1c524b9c955db1e933d
content_type: application/pdf
creator: dernst
date_created: 2023-08-21T06:45:16Z
date_updated: 2023-08-21T06:45:16Z
file_id: '14088'
file_name: 2023_LIPIcsICALP_Harris.pdf
file_size: 917791
relation: main_file
success: 1
file_date_updated: 2023-08-21T06:45:16Z
has_accepted_license: '1'
intvolume: ' 261'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
publication: 50th International Colloquium on Automata, Languages, and Programming
publication_identifier:
isbn:
- '9783959772785'
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Parameter estimation for Gibbs distributions
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 261
year: '2023'
...
---
_id: '13120'
abstract:
- lang: eng
text: 'We formalized general (i.e., type-0) grammars using the Lean 3 proof assistant.
We defined basic notions of rewrite rules and of words derived by a grammar, and
used grammars to show closure of the class of type-0 languages under four operations:
union, reversal, concatenation, and the Kleene star. The literature mostly focuses
on Turing machine arguments, which are possibly more difficult to formalize. For
the Kleene star, we could not follow the literature and came up with our own grammar-based
construction.'
acknowledgement: "Jasmin Blanchette: This research has received funding from the Netherlands
Organization\r\nfor Scientific Research (NWO) under the Vidi program (project No.
016.Vidi.189.037, Lean Forward).\r\n__\r\nWe thank Vladimir Kolmogorov for making
this collaboration possible. We\r\nthank Václav Končický for discussing ideas about
the Kleene star construction. We thank Patrick Johnson, Floris van Doorn, and Damiano
Testa for their small yet very valuable contributions to our code. We thank Eric
Wieser for simplifying one of our proofs. We thank Mark Summerfield for suggesting
textual improvements. We thank the anonymous reviewers for very helpful comments.
Finally, we thank the Lean community for helping us with various technical issues
and answering many questions. "
alternative_title:
- LIPIcs
article_number: '15'
article_processing_charge: No
author:
- first_name: Martin
full_name: Dvorak, Martin
id: 40ED02A8-C8B4-11E9-A9C0-453BE6697425
last_name: Dvorak
orcid: 0000-0001-5293-214X
- first_name: Jasmin
full_name: Blanchette, Jasmin
last_name: Blanchette
citation:
ama: 'Dvorak M, Blanchette J. Closure properties of general grammars - formally
verified. In: 14th International Conference on Interactive Theorem Proving.
Vol 268. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:10.4230/LIPIcs.ITP.2023.15'
apa: 'Dvorak, M., & Blanchette, J. (2023). Closure properties of general grammars
- formally verified. In 14th International Conference on Interactive Theorem
Proving (Vol. 268). Bialystok, Poland: Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPIcs.ITP.2023.15'
chicago: Dvorak, Martin, and Jasmin Blanchette. “Closure Properties of General Grammars
- Formally Verified.” In 14th International Conference on Interactive Theorem
Proving, Vol. 268. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023.
https://doi.org/10.4230/LIPIcs.ITP.2023.15.
ieee: M. Dvorak and J. Blanchette, “Closure properties of general grammars - formally
verified,” in 14th International Conference on Interactive Theorem Proving,
Bialystok, Poland, 2023, vol. 268.
ista: 'Dvorak M, Blanchette J. 2023. Closure properties of general grammars - formally
verified. 14th International Conference on Interactive Theorem Proving. ITP: International
Conference on Interactive Theorem Proving, LIPIcs, vol. 268, 15.'
mla: Dvorak, Martin, and Jasmin Blanchette. “Closure Properties of General Grammars
- Formally Verified.” 14th International Conference on Interactive Theorem
Proving, vol. 268, 15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2023, doi:10.4230/LIPIcs.ITP.2023.15.
short: M. Dvorak, J. Blanchette, in:, 14th International Conference on Interactive
Theorem Proving, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023.
conference:
end_date: 2023-08-04
location: Bialystok, Poland
name: 'ITP: International Conference on Interactive Theorem Proving'
start_date: 2023-07-31
date_created: 2023-06-05T07:29:05Z
date_published: 2023-07-27T00:00:00Z
date_updated: 2023-09-25T11:04:29Z
day: '27'
ddc:
- '000'
department:
- _id: GradSch
- _id: VlKo
doi: 10.4230/LIPIcs.ITP.2023.15
external_id:
arxiv:
- '2302.06420'
file:
- access_level: open_access
checksum: 773a0197f05b67feaa6cb1e17ec3642d
content_type: application/pdf
creator: dernst
date_created: 2023-08-07T11:55:43Z
date_updated: 2023-08-07T11:55:43Z
file_id: '13982'
file_name: 2023_LIPIcS_Dvorak.pdf
file_size: 715976
relation: main_file
success: 1
file_date_updated: 2023-08-07T11:55:43Z
has_accepted_license: '1'
intvolume: ' 268'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
publication: 14th International Conference on Interactive Theorem Proving
publication_identifier:
eissn:
- 1868-8969
isbn:
- '9783959772846'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/madvorak/grammars/tree/publish
scopus_import: '1'
status: public
title: Closure properties of general grammars - formally verified
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 268
year: '2023'
...
---
_id: '14448'
abstract:
- lang: eng
text: We consider the problem of solving LP relaxations of MAP-MRF inference problems,
and in particular the method proposed recently in [16], [35]. As a key computational
subroutine, it uses a variant of the Frank-Wolfe (FW) method to minimize a smooth
convex function over a combinatorial polytope. We propose an efficient implementation
of this subroutine based on in-face Frank-Wolfe directions, introduced in [4]
in a different context. More generally, we define an abstract data structure for
a combinatorial subproblem that enables in-face FW directions, and describe its
specialization for tree-structured MAP-MRF inference subproblems. Experimental
results indicate that the resulting method is the current state-of-art LP solver
for some classes of problems. Our code is available at pub.ist.ac.at/~vnk/papers/IN-FACE-FW.html.
article_processing_charge: No
author:
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
citation:
ama: 'Kolmogorov V. Solving relaxations of MAP-MRF problems: Combinatorial in-face
Frank-Wolfe directions. In: Proceedings of the IEEE Computer Society Conference
on Computer Vision and Pattern Recognition. Vol 2023. IEEE; 2023:11980-11989.
doi:10.1109/CVPR52729.2023.01153'
apa: 'Kolmogorov, V. (2023). Solving relaxations of MAP-MRF problems: Combinatorial
in-face Frank-Wolfe directions. In Proceedings of the IEEE Computer Society
Conference on Computer Vision and Pattern Recognition (Vol. 2023, pp. 11980–11989).
Vancouver, Canada: IEEE. https://doi.org/10.1109/CVPR52729.2023.01153'
chicago: 'Kolmogorov, Vladimir. “Solving Relaxations of MAP-MRF Problems: Combinatorial
in-Face Frank-Wolfe Directions.” In Proceedings of the IEEE Computer Society
Conference on Computer Vision and Pattern Recognition, 2023:11980–89. IEEE,
2023. https://doi.org/10.1109/CVPR52729.2023.01153.'
ieee: 'V. Kolmogorov, “Solving relaxations of MAP-MRF problems: Combinatorial in-face
Frank-Wolfe directions,” in Proceedings of the IEEE Computer Society Conference
on Computer Vision and Pattern Recognition, Vancouver, Canada, 2023, vol.
2023, pp. 11980–11989.'
ista: 'Kolmogorov V. 2023. Solving relaxations of MAP-MRF problems: Combinatorial
in-face Frank-Wolfe directions. Proceedings of the IEEE Computer Society Conference
on Computer Vision and Pattern Recognition. CVPR: Conference on Computer Vision
and Pattern Recognition vol. 2023, 11980–11989.'
mla: 'Kolmogorov, Vladimir. “Solving Relaxations of MAP-MRF Problems: Combinatorial
in-Face Frank-Wolfe Directions.” Proceedings of the IEEE Computer Society Conference
on Computer Vision and Pattern Recognition, vol. 2023, IEEE, 2023, pp. 11980–89,
doi:10.1109/CVPR52729.2023.01153.'
short: V. Kolmogorov, in:, Proceedings of the IEEE Computer Society Conference on
Computer Vision and Pattern Recognition, IEEE, 2023, pp. 11980–11989.
conference:
end_date: 2023-06-24
location: Vancouver, Canada
name: 'CVPR: Conference on Computer Vision and Pattern Recognition'
start_date: 2023-06-17
date_created: 2023-10-22T22:01:16Z
date_published: 2023-08-22T00:00:00Z
date_updated: 2023-10-31T12:01:24Z
day: '22'
department:
- _id: VlKo
doi: 10.1109/CVPR52729.2023.01153
external_id:
arxiv:
- '2010.09567'
intvolume: ' 2023'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2010.09567'
month: '08'
oa: 1
oa_version: Preprint
page: 11980-11989
publication: Proceedings of the IEEE Computer Society Conference on Computer Vision
and Pattern Recognition
publication_identifier:
isbn:
- '9798350301298'
issn:
- 1063-6919
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Solving relaxations of MAP-MRF problems: Combinatorial in-face Frank-Wolfe
directions'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2023
year: '2023'
...
---
_id: '10737'
abstract:
- lang: eng
text: We consider two models for the sequence labeling (tagging) problem. The first
one is a Pattern-Based Conditional Random Field (PB), in which the energy of a
string (chain labeling) x=x1…xn∈Dn is a sum of terms over intervals [i,j] where
each term is non-zero only if the substring xi…xj equals a prespecified word
w∈Λ. The second model is a Weighted Context-Free Grammar (WCFG) frequently used
for natural language processing. PB and WCFG encode local and non-local interactions
respectively, and thus can be viewed as complementary. We propose a Grammatical
Pattern-Based CRF model (GPB) that combines the two in a natural way. We argue
that it has certain advantages over existing approaches such as the Hybrid model
of Benedí and Sanchez that combines N-grams and WCFGs. The focus of this paper
is to analyze the complexity of inference tasks in a GPB such as computing MAP.
We present a polynomial-time algorithm for general GPBs and a faster version for
a special case that we call Interaction Grammars.
article_processing_charge: No
article_type: original
author:
- first_name: Rustem
full_name: Takhanov, Rustem
id: 2CCAC26C-F248-11E8-B48F-1D18A9856A87
last_name: Takhanov
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
citation:
ama: Takhanov R, Kolmogorov V. Combining pattern-based CRFs and weighted context-free
grammars. Intelligent Data Analysis. 2022;26(1):257-272. doi:10.3233/IDA-205623
apa: Takhanov, R., & Kolmogorov, V. (2022). Combining pattern-based CRFs and
weighted context-free grammars. Intelligent Data Analysis. IOS Press. https://doi.org/10.3233/IDA-205623
chicago: Takhanov, Rustem, and Vladimir Kolmogorov. “Combining Pattern-Based CRFs
and Weighted Context-Free Grammars.” Intelligent Data Analysis. IOS Press,
2022. https://doi.org/10.3233/IDA-205623.
ieee: R. Takhanov and V. Kolmogorov, “Combining pattern-based CRFs and weighted
context-free grammars,” Intelligent Data Analysis, vol. 26, no. 1. IOS
Press, pp. 257–272, 2022.
ista: Takhanov R, Kolmogorov V. 2022. Combining pattern-based CRFs and weighted
context-free grammars. Intelligent Data Analysis. 26(1), 257–272.
mla: Takhanov, Rustem, and Vladimir Kolmogorov. “Combining Pattern-Based CRFs and
Weighted Context-Free Grammars.” Intelligent Data Analysis, vol. 26, no.
1, IOS Press, 2022, pp. 257–72, doi:10.3233/IDA-205623.
short: R. Takhanov, V. Kolmogorov, Intelligent Data Analysis 26 (2022) 257–272.
date_created: 2022-02-06T23:01:32Z
date_published: 2022-01-14T00:00:00Z
date_updated: 2023-08-02T14:09:41Z
day: '14'
department:
- _id: VlKo
doi: 10.3233/IDA-205623
external_id:
arxiv:
- '1404.5475'
isi:
- '000749997700015'
intvolume: ' 26'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1404.5475
month: '01'
oa: 1
oa_version: Preprint
page: 257-272
publication: Intelligent Data Analysis
publication_identifier:
eissn:
- 1571-4128
issn:
- 1088-467X
publication_status: published
publisher: IOS Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Combining pattern-based CRFs and weighted context-free grammars
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 26
year: '2022'
...