---
_id: '2271'
abstract:
- lang: eng
text: "A class of valued constraint satisfaction problems (VCSPs) is characterised
by a valued constraint language, a fixed set of cost functions on a finite domain.
Finite-valued constraint languages contain functions that take on rational costs
and general-valued constraint languages contain functions that take on rational
or infinite costs. An instance of the problem is specified by a sum of functions
from the language with the goal to minimise the sum. This framework includes and
generalises well-studied constraint satisfaction problems (CSPs) and maximum constraint
satisfaction problems (Max-CSPs).\r\nOur main result is a precise algebraic characterisation
of valued constraint languages whose instances can be solved exactly by the basic
linear programming relaxation (BLP). For a general-valued constraint language
Γ, BLP is a decision procedure for Γ if and only if Γ admits a symmetric fractional
polymorphism of every arity. For a finite-valued constraint language Γ, BLP is
a decision procedure if and only if Γ admits a symmetric fractional polymorphism
of some arity, or equivalently, if Γ admits a symmetric fractional polymorphism
of arity 2.\r\nUsing these results, we obtain tractability of several novel and
previously widely-open classes of VCSPs, including problems over valued constraint
languages that are: (1) submodular on arbitrary lattices; (2) bisubmodular (also
known as k-submodular) on arbitrary finite domains; (3) weakly (and hence strongly)
tree-submodular on arbitrary trees. "
author:
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
- first_name: Johan
full_name: Thapper, Johan
last_name: Thapper
- first_name: Stanislav
full_name: Živný, Stanislav
last_name: Živný
citation:
ama: Kolmogorov V, Thapper J, Živný S. The power of linear programming for general-valued
CSPs. SIAM Journal on Computing. 2015;44(1):1-36. doi:10.1137/130945648
apa: Kolmogorov, V., Thapper, J., & Živný, S. (2015). The power of linear programming
for general-valued CSPs. SIAM Journal on Computing. SIAM. https://doi.org/10.1137/130945648
chicago: Kolmogorov, Vladimir, Johan Thapper, and Stanislav Živný. “The Power of
Linear Programming for General-Valued CSPs.” SIAM Journal on Computing.
SIAM, 2015. https://doi.org/10.1137/130945648.
ieee: V. Kolmogorov, J. Thapper, and S. Živný, “The power of linear programming
for general-valued CSPs,” SIAM Journal on Computing, vol. 44, no. 1. SIAM,
pp. 1–36, 2015.
ista: Kolmogorov V, Thapper J, Živný S. 2015. The power of linear programming for
general-valued CSPs. SIAM Journal on Computing. 44(1), 1–36.
mla: Kolmogorov, Vladimir, et al. “The Power of Linear Programming for General-Valued
CSPs.” SIAM Journal on Computing, vol. 44, no. 1, SIAM, 2015, pp. 1–36,
doi:10.1137/130945648.
short: V. Kolmogorov, J. Thapper, S. Živný, SIAM Journal on Computing 44 (2015)
1–36.
date_created: 2018-12-11T11:56:41Z
date_published: 2015-02-01T00:00:00Z
date_updated: 2023-02-23T10:46:30Z
day: '01'
department:
- _id: VlKo
doi: 10.1137/130945648
external_id:
arxiv:
- '1311.4219'
intvolume: ' 44'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1311.4219
month: '02'
oa: 1
oa_version: Preprint
page: 1 - 36
publication: SIAM Journal on Computing
publication_status: published
publisher: SIAM
publist_id: '4673'
quality_controlled: '1'
related_material:
record:
- id: '2518'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: The power of linear programming for general-valued CSPs
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 44
year: '2015'
...
---
_id: '1637'
abstract:
- lang: eng
text: An instance of the Valued Constraint Satisfaction Problem (VCSP) is given
by a finite set of variables, a finite domain of labels, and a sum of functions,
each function depending on a subset of the variables. Each function can take finite
values specifying costs of assignments of labels to its variables or the infinite
value, which indicates an infeasible assignment. The goal is to find an assignment
of labels to the variables that minimizes the sum. We study, assuming that P ≠
NP, how the complexity of this very general problem depends on the set of functions
allowed in the instances, the so-called constraint language. The case when all
allowed functions take values in {0, ∞} corresponds to ordinary CSPs, where one
deals only with the feasibility issue and there is no optimization. This case
is the subject of the Algebraic CSP Dichotomy Conjecture predicting for which
constraint languages CSPs are tractable (i.e. solvable in polynomial time) and
for which NP-hard. The case when all allowed functions take only finite values
corresponds to finite-valued CSP, where the feasibility aspect is trivial and
one deals only with the optimization issue. The complexity of finite-valued CSPs
was fully classified by Thapper and Zivny. An algebraic necessary condition for
tractability of a general-valued CSP with a fixed constraint language was recently
given by Kozik and Ochremiak. As our main result, we prove that if a constraint
language satisfies this algebraic necessary condition, and the feasibility CSP
(i.e. the problem of deciding whether a given instance has a feasible solution)
corresponding to the VCSP with this language is tractable, then the VCSP is tractable.
The algorithm is a simple combination of the assumed algorithm for the feasibility
CSP and the standard LP relaxation. As a corollary, we obtain that a dichotomy
for ordinary CSPs would imply a dichotomy for general-valued CSPs.
alternative_title:
- 56th Annual Symposium on Foundations of Computer Science
author:
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
- first_name: Andrei
full_name: Krokhin, Andrei
last_name: Krokhin
- first_name: Michal
full_name: Rolinek, Michal
id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87
last_name: Rolinek
citation:
ama: 'Kolmogorov V, Krokhin A, Rolinek M. The complexity of general-valued CSPs.
In: IEEE; 2015:1246-1258. doi:10.1109/FOCS.2015.80'
apa: 'Kolmogorov, V., Krokhin, A., & Rolinek, M. (2015). The complexity of general-valued
CSPs (pp. 1246–1258). Presented at the FOCS: Foundations of Computer Science,
Berkeley, CA, United States: IEEE. https://doi.org/10.1109/FOCS.2015.80'
chicago: Kolmogorov, Vladimir, Andrei Krokhin, and Michal Rolinek. “The Complexity
of General-Valued CSPs,” 1246–58. IEEE, 2015. https://doi.org/10.1109/FOCS.2015.80.
ieee: 'V. Kolmogorov, A. Krokhin, and M. Rolinek, “The complexity of general-valued
CSPs,” presented at the FOCS: Foundations of Computer Science, Berkeley, CA, United
States, 2015, pp. 1246–1258.'
ista: 'Kolmogorov V, Krokhin A, Rolinek M. 2015. The complexity of general-valued
CSPs. FOCS: Foundations of Computer Science, 56th Annual Symposium on Foundations
of Computer Science, , 1246–1258.'
mla: Kolmogorov, Vladimir, et al. The Complexity of General-Valued CSPs.
IEEE, 2015, pp. 1246–58, doi:10.1109/FOCS.2015.80.
short: V. Kolmogorov, A. Krokhin, M. Rolinek, in:, IEEE, 2015, pp. 1246–1258.
conference:
end_date: 2015-10-20
location: Berkeley, CA, United States
name: 'FOCS: Foundations of Computer Science'
start_date: 2015-10-18
date_created: 2018-12-11T11:53:10Z
date_published: 2015-12-01T00:00:00Z
date_updated: 2023-02-23T12:44:26Z
day: '01'
department:
- _id: VlKo
doi: 10.1109/FOCS.2015.80
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1502.07327
month: '12'
oa: 1
oa_version: Preprint
page: 1246 - 1258
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication_status: published
publisher: IEEE
publist_id: '5518'
quality_controlled: '1'
related_material:
record:
- id: '644'
relation: other
status: public
scopus_import: 1
status: public
title: The complexity of general-valued CSPs
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2015'
...
---
_id: '1675'
abstract:
- lang: eng
text: Proofs of work (PoW) have been suggested by Dwork and Naor (Crypto’92) as
protection to a shared resource. The basic idea is to ask the service requestor
to dedicate some non-trivial amount of computational work to every request. The
original applications included prevention of spam and protection against denial
of service attacks. More recently, PoWs have been used to prevent double spending
in the Bitcoin digital currency system. In this work, we put forward an alternative
concept for PoWs - so-called proofs of space (PoS), where a service requestor
must dedicate a significant amount of disk space as opposed to computation. We
construct secure PoS schemes in the random oracle model (with one additional mild
assumption required for the proof to go through), using graphs with high “pebbling
complexity” and Merkle hash-trees. We discuss some applications, including follow-up
work where a decentralized digital currency scheme called Spacecoin is constructed
that uses PoS (instead of wasteful PoW like in Bitcoin) to prevent double spending.
The main technical contribution of this work is the construction of (directed,
loop-free) graphs on N vertices with in-degree O(log logN) such that even if one
places Θ(N) pebbles on the nodes of the graph, there’s a constant fraction of
nodes that needs Θ(N) steps to be pebbled (where in every step one can put a pebble
on a node if all its parents have a pebble).
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Stefan
full_name: Dziembowski, Stefan
last_name: Dziembowski
- first_name: Sebastian
full_name: Faust, Sebastian
last_name: Faust
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
- first_name: Krzysztof Z
full_name: Pietrzak, Krzysztof Z
id: 3E04A7AA-F248-11E8-B48F-1D18A9856A87
last_name: Pietrzak
orcid: 0000-0002-9139-1654
citation:
ama: 'Dziembowski S, Faust S, Kolmogorov V, Pietrzak KZ. Proofs of space. In: 35th
Annual Cryptology Conference. Vol 9216. Springer; 2015:585-605. doi:10.1007/978-3-662-48000-7_29'
apa: 'Dziembowski, S., Faust, S., Kolmogorov, V., & Pietrzak, K. Z. (2015).
Proofs of space. In 35th Annual Cryptology Conference (Vol. 9216, pp. 585–605).
Santa Barbara, CA, United States: Springer. https://doi.org/10.1007/978-3-662-48000-7_29'
chicago: Dziembowski, Stefan, Sebastian Faust, Vladimir Kolmogorov, and Krzysztof
Z Pietrzak. “Proofs of Space.” In 35th Annual Cryptology Conference, 9216:585–605.
Springer, 2015. https://doi.org/10.1007/978-3-662-48000-7_29.
ieee: S. Dziembowski, S. Faust, V. Kolmogorov, and K. Z. Pietrzak, “Proofs of space,”
in 35th Annual Cryptology Conference, Santa Barbara, CA, United States,
2015, vol. 9216, pp. 585–605.
ista: 'Dziembowski S, Faust S, Kolmogorov V, Pietrzak KZ. 2015. Proofs of space.
35th Annual Cryptology Conference. CRYPTO: International Cryptology Conference,
LNCS, vol. 9216, 585–605.'
mla: Dziembowski, Stefan, et al. “Proofs of Space.” 35th Annual Cryptology Conference,
vol. 9216, Springer, 2015, pp. 585–605, doi:10.1007/978-3-662-48000-7_29.
short: S. Dziembowski, S. Faust, V. Kolmogorov, K.Z. Pietrzak, in:, 35th Annual
Cryptology Conference, Springer, 2015, pp. 585–605.
conference:
end_date: 2015-08-20
location: Santa Barbara, CA, United States
name: 'CRYPTO: International Cryptology Conference'
start_date: 2015-08-16
date_created: 2018-12-11T11:53:24Z
date_published: 2015-08-01T00:00:00Z
date_updated: 2024-03-20T08:31:49Z
day: '01'
department:
- _id: VlKo
- _id: KrPi
doi: 10.1007/978-3-662-48000-7_29
ec_funded: 1
intvolume: ' 9216'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://eprint.iacr.org/2013/796.pdf
month: '08'
oa: 1
oa_version: Preprint
page: 585 - 605
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
- _id: 258C570E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '259668'
name: Provable Security for Physical Cryptography
publication: 35th Annual Cryptology Conference
publication_identifier:
isbn:
- '9783662479995'
issn:
- 0302-9743
publication_status: published
publisher: Springer
publist_id: '5474'
pubrep_id: '671'
quality_controlled: '1'
related_material:
record:
- id: '2274'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Proofs of space
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 9216
year: '2015'
...
---
_id: '2275'
abstract:
- lang: eng
text: "Energies with high-order non-submodular interactions have been shown to be
very useful in vision due to their high modeling power. Optimization of such energies,
however, is generally NP-hard. A naive approach that works for small problem instances
is exhaustive search, that is, enumeration of all possible labelings of the underlying
graph. We propose a general minimization approach for large graphs based on enumeration
of labelings of certain small patches. \r\nThis partial enumeration technique
reduces complex high-order energy formulations to pairwise Constraint Satisfaction
Problems with unary costs (uCSP), which can be efficiently solved using standard
methods like TRW-S. Our approach outperforms a number of existing state-of-the-art
algorithms on well known difficult problems (e.g. curvature regularization, stereo,
deconvolution); it gives near global minimum and better speed. \r\nOur main application
of interest is curvature regularization. In the context of segmentation, our partial
enumeration technique allows to evaluate curvature directly on small patches using
a novel integral geometry approach.\r\n"
author:
- first_name: Carl
full_name: Olsson, Carl
last_name: Olsson
- first_name: Johannes
full_name: Ulen, Johannes
last_name: Ulen
- first_name: Yuri
full_name: Boykov, Yuri
last_name: Boykov
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
citation:
ama: 'Olsson C, Ulen J, Boykov Y, Kolmogorov V. Partial enumeration and curvature
regularization. In: IEEE; 2014:2936-2943. doi:10.1109/ICCV.2013.365'
apa: 'Olsson, C., Ulen, J., Boykov, Y., & Kolmogorov, V. (2014). Partial enumeration
and curvature regularization (pp. 2936–2943). Presented at the ICCV: International
Conference on Computer Vision, Sydney, Australia: IEEE. https://doi.org/10.1109/ICCV.2013.365'
chicago: Olsson, Carl, Johannes Ulen, Yuri Boykov, and Vladimir Kolmogorov. “Partial
Enumeration and Curvature Regularization,” 2936–43. IEEE, 2014. https://doi.org/10.1109/ICCV.2013.365.
ieee: 'C. Olsson, J. Ulen, Y. Boykov, and V. Kolmogorov, “Partial enumeration and
curvature regularization,” presented at the ICCV: International Conference on
Computer Vision, Sydney, Australia, 2014, pp. 2936–2943.'
ista: 'Olsson C, Ulen J, Boykov Y, Kolmogorov V. 2014. Partial enumeration and curvature
regularization. ICCV: International Conference on Computer Vision, 2936–2943.'
mla: Olsson, Carl, et al. Partial Enumeration and Curvature Regularization.
IEEE, 2014, pp. 2936–43, doi:10.1109/ICCV.2013.365.
short: C. Olsson, J. Ulen, Y. Boykov, V. Kolmogorov, in:, IEEE, 2014, pp. 2936–2943.
conference:
end_date: 2013-12-08
location: Sydney, Australia
name: 'ICCV: International Conference on Computer Vision'
start_date: 2013-12-01
date_created: 2018-12-11T11:56:42Z
date_published: 2014-03-03T00:00:00Z
date_updated: 2021-01-12T06:56:28Z
day: '03'
ddc:
- '000'
department:
- _id: VlKo
doi: 10.1109/ICCV.2013.365
file:
- access_level: open_access
checksum: 4a74b5c92d6dcd2348c2c10ec8dd18bf
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:09:30Z
date_updated: 2020-07-14T12:45:36Z
file_id: '4754'
file_name: IST-2016-566-v1+1_iccv13_part_enumeration.pdf
file_size: 378601
relation: main_file
file_date_updated: 2020-07-14T12:45:36Z
has_accepted_license: '1'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Submitted Version
page: 2936 - 2943
publication_status: published
publisher: IEEE
publist_id: '4669'
pubrep_id: '566'
quality_controlled: '1'
scopus_import: 1
status: public
title: Partial enumeration and curvature regularization
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '7038'
article_processing_charge: No
author:
- first_name: Kristóf
full_name: Huszár, Kristóf
id: 33C26278-F248-11E8-B48F-1D18A9856A87
last_name: Huszár
orcid: 0000-0002-5445-5057
- first_name: Michal
full_name: Rolinek, Michal
id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87
last_name: Rolinek
citation:
ama: Huszár K, Rolinek M. Playful Math - An Introduction to Mathematical Games.
IST Austria
apa: Huszár, K., & Rolinek, M. (n.d.). Playful Math - An introduction to
mathematical games. IST Austria.
chicago: Huszár, Kristóf, and Michal Rolinek. Playful Math - An Introduction
to Mathematical Games. IST Austria, n.d.
ieee: K. Huszár and M. Rolinek, Playful Math - An introduction to mathematical
games. IST Austria.
ista: Huszár K, Rolinek M. Playful Math - An introduction to mathematical games,
IST Austria, 5p.
mla: Huszár, Kristóf, and Michal Rolinek. Playful Math - An Introduction to Mathematical
Games. IST Austria.
short: K. Huszár, M. Rolinek, Playful Math - An Introduction to Mathematical Games,
IST Austria, n.d.
date_created: 2019-11-18T15:57:05Z
date_published: 2014-06-30T00:00:00Z
date_updated: 2020-07-14T23:11:45Z
day: '30'
ddc:
- '510'
department:
- _id: VlKo
- _id: UlWa
file:
- access_level: open_access
checksum: 2b94e5e1f4c3fe8ab89b12806276fb09
content_type: application/pdf
creator: dernst
date_created: 2019-11-18T15:57:51Z
date_updated: 2020-07-14T12:47:48Z
file_id: '7039'
file_name: 2014_Playful_Math_Huszar.pdf
file_size: 511233
relation: main_file
file_date_updated: 2020-07-14T12:47:48Z
has_accepted_license: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: '5'
publication_status: draft
publisher: IST Austria
status: public
title: Playful Math - An introduction to mathematical games
type: working_paper
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...