---
_id: '273'
abstract:
- lang: eng
text: The accuracy of information retrieval systems is often measured using complex
loss functions such as the average precision (AP) or the normalized discounted
cumulative gain (NDCG). Given a set of positive and negative samples, the parameters
of a retrieval system can be estimated by minimizing these loss functions. However,
the non-differentiability and non-decomposability of these loss functions does
not allow for simple gradient based optimization algorithms. This issue is generally
circumvented by either optimizing a structured hinge-loss upper bound to the loss
function or by using asymptotic methods like the direct-loss minimization framework.
Yet, the high computational complexity of loss-augmented inference, which is necessary
for both the frameworks, prohibits its use in large training data sets. To alleviate
this deficiency, we present a novel quicksort flavored algorithm for a large class
of non-decomposable loss functions. We provide a complete characterization of
the loss functions that are amenable to our algorithm, and show that it includes
both AP and NDCG based loss functions. Furthermore, we prove that no comparison
based algorithm can improve upon the computational complexity of our approach
asymptotically. We demonstrate the effectiveness of our approach in the context
of optimizing the structured hinge loss upper bound of AP and NDCG loss for learning
models for a variety of vision tasks. We show that our approach provides significantly
better results than simpler decomposable loss functions, while requiring a comparable
training time.
article_processing_charge: No
arxiv: 1
author:
- first_name: Pritish
full_name: Mohapatra, Pritish
last_name: Mohapatra
- first_name: Michal
full_name: Rolinek, Michal
id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87
last_name: Rolinek
- first_name: C V
full_name: Jawahar, C V
last_name: Jawahar
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
- first_name: M Pawan
full_name: Kumar, M Pawan
last_name: Kumar
citation:
ama: 'Mohapatra P, Rolinek M, Jawahar CV, Kolmogorov V, Kumar MP. Efficient optimization
for rank-based loss functions. In: 2018 IEEE/CVF Conference on Computer Vision
and Pattern Recognition. IEEE; 2018:3693-3701. doi:10.1109/cvpr.2018.00389'
apa: 'Mohapatra, P., Rolinek, M., Jawahar, C. V., Kolmogorov, V., & Kumar, M.
P. (2018). Efficient optimization for rank-based loss functions. In 2018 IEEE/CVF
Conference on Computer Vision and Pattern Recognition (pp. 3693–3701). Salt
Lake City, UT, USA: IEEE. https://doi.org/10.1109/cvpr.2018.00389'
chicago: Mohapatra, Pritish, Michal Rolinek, C V Jawahar, Vladimir Kolmogorov, and
M Pawan Kumar. “Efficient Optimization for Rank-Based Loss Functions.” In 2018
IEEE/CVF Conference on Computer Vision and Pattern Recognition, 3693–3701.
IEEE, 2018. https://doi.org/10.1109/cvpr.2018.00389.
ieee: P. Mohapatra, M. Rolinek, C. V. Jawahar, V. Kolmogorov, and M. P. Kumar, “Efficient
optimization for rank-based loss functions,” in 2018 IEEE/CVF Conference on
Computer Vision and Pattern Recognition, Salt Lake City, UT, USA, 2018, pp.
3693–3701.
ista: 'Mohapatra P, Rolinek M, Jawahar CV, Kolmogorov V, Kumar MP. 2018. Efficient
optimization for rank-based loss functions. 2018 IEEE/CVF Conference on Computer
Vision and Pattern Recognition. CVPR: Conference on Computer Vision and Pattern
Recognition, 3693–3701.'
mla: Mohapatra, Pritish, et al. “Efficient Optimization for Rank-Based Loss Functions.”
2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, IEEE,
2018, pp. 3693–701, doi:10.1109/cvpr.2018.00389.
short: P. Mohapatra, M. Rolinek, C.V. Jawahar, V. Kolmogorov, M.P. Kumar, in:, 2018
IEEE/CVF Conference on Computer Vision and Pattern Recognition, IEEE, 2018, pp.
3693–3701.
conference:
end_date: 2018-06-22
location: Salt Lake City, UT, USA
name: 'CVPR: Conference on Computer Vision and Pattern Recognition'
start_date: 2018-06-18
date_created: 2018-12-11T11:45:33Z
date_published: 2018-06-28T00:00:00Z
date_updated: 2024-11-04T13:52:32Z
day: '28'
department:
- _id: VlKo
doi: 10.1109/cvpr.2018.00389
ec_funded: 1
external_id:
arxiv:
- '1604.08269'
isi:
- '000457843603087'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1604.08269
month: '06'
oa: 1
oa_version: Preprint
page: 3693-3701
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication: 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition
publication_identifier:
isbn:
- '9781538664209'
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Efficient optimization for rank-based loss functions
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2018'
...
---
_id: '18'
abstract:
- lang: eng
text: An N-superconcentrator is a directed, acyclic graph with N input nodes and
N output nodes such that every subset of the inputs and every subset of the outputs
of same cardinality can be connected by node-disjoint paths. It is known that
linear-size and bounded-degree superconcentrators exist. We prove the existence
of such superconcentrators with asymptotic density 25.3 (where the density is
the number of edges divided by N). The previously best known densities were 28
[12] and 27.4136 [17].
article_processing_charge: No
arxiv: 1
author:
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
- first_name: Michal
full_name: Rolinek, Michal
id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87
last_name: Rolinek
citation:
ama: Kolmogorov V, Rolinek M. Superconcentrators of density 25.3. Ars Combinatoria.
2018;141(10):269-304.
apa: Kolmogorov, V., & Rolinek, M. (2018). Superconcentrators of density 25.3.
Ars Combinatoria. Charles Babbage Research Centre.
chicago: Kolmogorov, Vladimir, and Michal Rolinek. “Superconcentrators of Density
25.3.” Ars Combinatoria. Charles Babbage Research Centre, 2018.
ieee: V. Kolmogorov and M. Rolinek, “Superconcentrators of density 25.3,” Ars
Combinatoria, vol. 141, no. 10. Charles Babbage Research Centre, pp. 269–304,
2018.
ista: Kolmogorov V, Rolinek M. 2018. Superconcentrators of density 25.3. Ars Combinatoria.
141(10), 269–304.
mla: Kolmogorov, Vladimir, and Michal Rolinek. “Superconcentrators of Density 25.3.”
Ars Combinatoria, vol. 141, no. 10, Charles Babbage Research Centre, 2018,
pp. 269–304.
short: V. Kolmogorov, M. Rolinek, Ars Combinatoria 141 (2018) 269–304.
date_created: 2018-12-11T11:44:11Z
date_published: 2018-10-01T00:00:00Z
date_updated: 2023-09-19T14:46:18Z
day: '01'
department:
- _id: VlKo
external_id:
arxiv:
- '1405.7828'
isi:
- '000446809500022'
intvolume: ' 141'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1405.7828
month: '10'
oa: 1
oa_version: Preprint
page: 269 - 304
publication: Ars Combinatoria
publication_identifier:
issn:
- 0381-7032
publication_status: published
publisher: Charles Babbage Research Centre
publist_id: '8037'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Superconcentrators of density 25.3
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 141
year: '2018'
...
---
_id: '193'
abstract:
- lang: eng
text: 'We show attacks on five data-independent memory-hard functions (iMHF) that
were submitted to the password hashing competition (PHC). Informally, an MHF is
a function which cannot be evaluated on dedicated hardware, like ASICs, at significantly
lower hardware and/or energy cost than evaluating a single instance on a standard
single-core architecture. Data-independent means the memory access pattern of
the function is independent of the input; this makes iMHFs harder to construct
than data-dependent ones, but the latter can be attacked by various side-channel
attacks. Following [Alwen-Blocki''16], we capture the evaluation of an iMHF as
a directed acyclic graph (DAG). The cumulative parallel pebbling complexity of
this DAG is a measure for the hardware cost of evaluating the iMHF on an ASIC.
Ideally, one would like the complexity of a DAG underlying an iMHF to be as close
to quadratic in the number of nodes of the graph as possible. Instead, we show
that (the DAGs underlying) the following iMHFs are far from this bound: Rig.v2,
TwoCats and Gambit each having an exponent no more than 1.75. Moreover, we show
that the complexity of the iMHF modes of the PHC finalists Pomelo and Lyra2 have
exponents at most 1.83 and 1.67 respectively. To show this we investigate a combinatorial
property of each underlying DAG (called its depth-robustness. By establishing
upper bounds on this property we are then able to apply the general technique
of [Alwen-Block''16] for analyzing the hardware costs of an iMHF.'
acknowledgement: Leonid Reyzin was supported in part by IST Austria and by US NSF
grants 1012910, 1012798, and 1422965; this research was performed while he was visiting
IST Austria.
article_processing_charge: No
author:
- first_name: Joel F
full_name: Alwen, Joel F
id: 2A8DFA8C-F248-11E8-B48F-1D18A9856A87
last_name: Alwen
- first_name: Peter
full_name: Gazi, Peter
last_name: Gazi
- first_name: Chethan
full_name: Kamath Hosdurg, Chethan
id: 4BD3F30E-F248-11E8-B48F-1D18A9856A87
last_name: Kamath Hosdurg
- first_name: Karen
full_name: Klein, Karen
id: 3E83A2F8-F248-11E8-B48F-1D18A9856A87
last_name: Klein
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
orcid: 0000-0002-8882-5116
- first_name: Krzysztof Z
full_name: Pietrzak, Krzysztof Z
id: 3E04A7AA-F248-11E8-B48F-1D18A9856A87
last_name: Pietrzak
orcid: 0000-0002-9139-1654
- first_name: Lenoid
full_name: Reyzin, Lenoid
last_name: Reyzin
- first_name: Michal
full_name: Rolinek, Michal
id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87
last_name: Rolinek
- first_name: Michal
full_name: Rybar, Michal
id: 2B3E3DE8-F248-11E8-B48F-1D18A9856A87
last_name: Rybar
citation:
ama: 'Alwen JF, Gazi P, Kamath Hosdurg C, et al. On the memory hardness of data
independent password hashing functions. In: Proceedings of the 2018 on Asia
Conference on Computer and Communication Security. ACM; 2018:51-65. doi:10.1145/3196494.3196534'
apa: 'Alwen, J. F., Gazi, P., Kamath Hosdurg, C., Klein, K., Osang, G. F., Pietrzak,
K. Z., … Rybar, M. (2018). On the memory hardness of data independent password
hashing functions. In Proceedings of the 2018 on Asia Conference on Computer
and Communication Security (pp. 51–65). Incheon, Republic of Korea: ACM. https://doi.org/10.1145/3196494.3196534'
chicago: Alwen, Joel F, Peter Gazi, Chethan Kamath Hosdurg, Karen Klein, Georg F
Osang, Krzysztof Z Pietrzak, Lenoid Reyzin, Michal Rolinek, and Michal Rybar.
“On the Memory Hardness of Data Independent Password Hashing Functions.” In Proceedings
of the 2018 on Asia Conference on Computer and Communication Security, 51–65.
ACM, 2018. https://doi.org/10.1145/3196494.3196534.
ieee: J. F. Alwen et al., “On the memory hardness of data independent password
hashing functions,” in Proceedings of the 2018 on Asia Conference on Computer
and Communication Security, Incheon, Republic of Korea, 2018, pp. 51–65.
ista: 'Alwen JF, Gazi P, Kamath Hosdurg C, Klein K, Osang GF, Pietrzak KZ, Reyzin
L, Rolinek M, Rybar M. 2018. On the memory hardness of data independent password
hashing functions. Proceedings of the 2018 on Asia Conference on Computer and
Communication Security. ASIACCS: Asia Conference on Computer and Communications
Security , 51–65.'
mla: Alwen, Joel F., et al. “On the Memory Hardness of Data Independent Password
Hashing Functions.” Proceedings of the 2018 on Asia Conference on Computer
and Communication Security, ACM, 2018, pp. 51–65, doi:10.1145/3196494.3196534.
short: J.F. Alwen, P. Gazi, C. Kamath Hosdurg, K. Klein, G.F. Osang, K.Z. Pietrzak,
L. Reyzin, M. Rolinek, M. Rybar, in:, Proceedings of the 2018 on Asia Conference
on Computer and Communication Security, ACM, 2018, pp. 51–65.
conference:
end_date: 2018-06-08
location: Incheon, Republic of Korea
name: 'ASIACCS: Asia Conference on Computer and Communications Security '
start_date: 2018-06-04
date_created: 2018-12-11T11:45:07Z
date_published: 2018-06-01T00:00:00Z
date_updated: 2024-11-04T13:52:29Z
day: '01'
department:
- _id: KrPi
- _id: HeEd
- _id: VlKo
doi: 10.1145/3196494.3196534
ec_funded: 1
external_id:
isi:
- '000516620100005'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://eprint.iacr.org/2016/783
month: '06'
oa: 1
oa_version: Submitted Version
page: 51 - 65
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
- _id: 258AA5B2-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '682815'
name: Teaching Old Crypto New Tricks
publication: Proceedings of the 2018 on Asia Conference on Computer and Communication
Security
publication_status: published
publisher: ACM
publist_id: '7723'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the memory hardness of data independent password hashing functions
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2018'
...
---
_id: '6032'
abstract:
- lang: eng
text: The main result of this article is a generalization of the classical blossom
algorithm for finding perfect matchings. Our algorithm can efficiently solve Boolean
CSPs where each variable appears in exactly two constraints (we call it edge CSP)
and all constraints are even Δ-matroid relations (represented by lists of tuples).
As a consequence of this, we settle the complexity classification of planar Boolean
CSPs started by Dvorak and Kupec. Using a reduction to even Δ-matroids, we then
extend the tractability result to larger classes of Δ-matroids that we call efficiently
coverable. It properly includes classes that were known to be tractable before,
namely, co-independent, compact, local, linear, and binary, with the following
caveat:We represent Δ-matroids by lists of tuples, while the last two use a representation
by matrices. Since an n ×n matrix can represent exponentially many tuples, our
tractability result is not strictly stronger than the known algorithm for linear
and binary Δ-matroids.
article_number: '22'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Alexandr
full_name: Kazda, Alexandr
id: 3B32BAA8-F248-11E8-B48F-1D18A9856A87
last_name: Kazda
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
- first_name: Michal
full_name: Rolinek, Michal
id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87
last_name: Rolinek
citation:
ama: Kazda A, Kolmogorov V, Rolinek M. Even delta-matroids and the complexity of
planar boolean CSPs. ACM Transactions on Algorithms. 2018;15(2). doi:10.1145/3230649
apa: Kazda, A., Kolmogorov, V., & Rolinek, M. (2018). Even delta-matroids and
the complexity of planar boolean CSPs. ACM Transactions on Algorithms.
ACM. https://doi.org/10.1145/3230649
chicago: Kazda, Alexandr, Vladimir Kolmogorov, and Michal Rolinek. “Even Delta-Matroids
and the Complexity of Planar Boolean CSPs.” ACM Transactions on Algorithms.
ACM, 2018. https://doi.org/10.1145/3230649.
ieee: A. Kazda, V. Kolmogorov, and M. Rolinek, “Even delta-matroids and the complexity
of planar boolean CSPs,” ACM Transactions on Algorithms, vol. 15, no. 2.
ACM, 2018.
ista: Kazda A, Kolmogorov V, Rolinek M. 2018. Even delta-matroids and the complexity
of planar boolean CSPs. ACM Transactions on Algorithms. 15(2), 22.
mla: Kazda, Alexandr, et al. “Even Delta-Matroids and the Complexity of Planar Boolean
CSPs.” ACM Transactions on Algorithms, vol. 15, no. 2, 22, ACM, 2018, doi:10.1145/3230649.
short: A. Kazda, V. Kolmogorov, M. Rolinek, ACM Transactions on Algorithms 15 (2018).
date_created: 2019-02-17T22:59:25Z
date_published: 2018-12-01T00:00:00Z
date_updated: 2025-06-04T08:46:58Z
day: '01'
department:
- _id: VlKo
doi: 10.1145/3230649
ec_funded: 1
external_id:
arxiv:
- '1602.03124'
isi:
- '000468036500007'
intvolume: ' 15'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1602.03124
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication: ACM Transactions on Algorithms
publication_status: published
publisher: ACM
quality_controlled: '1'
related_material:
record:
- id: '1192'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Even delta-matroids and the complexity of planar boolean CSPs
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 15
year: '2018'
...
---
_id: '1192'
abstract:
- lang: eng
text: The main result of this paper is a generalization of the classical blossom
algorithm for finding perfect matchings. Our algorithm can efficiently solve Boolean
CSPs where each variable appears in exactly two constraints (we call it edge CSP)
and all constraints are even Δ-matroid relations (represented by lists of tuples).
As a consequence of this, we settle the complexity classification of planar Boolean
CSPs started by Dvorak and Kupec. Knowing that edge CSP is tractable for even
Δ-matroid constraints allows us to extend the tractability result to a larger
class of Δ-matroids that includes many classes that were known to be tractable
before, namely co-independent, compact, local and binary.
article_processing_charge: No
arxiv: 1
author:
- first_name: Alexandr
full_name: Kazda, Alexandr
id: 3B32BAA8-F248-11E8-B48F-1D18A9856A87
last_name: Kazda
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
- first_name: Michal
full_name: Rolinek, Michal
id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87
last_name: Rolinek
citation:
ama: 'Kazda A, Kolmogorov V, Rolinek M. Even delta-matroids and the complexity of
planar Boolean CSPs. In: SIAM; 2017:307-326. doi:10.1137/1.9781611974782.20'
apa: 'Kazda, A., Kolmogorov, V., & Rolinek, M. (2017). Even delta-matroids and
the complexity of planar Boolean CSPs (pp. 307–326). Presented at the SODA: Symposium
on Discrete Algorithms, Barcelona, Spain: SIAM. https://doi.org/10.1137/1.9781611974782.20'
chicago: Kazda, Alexandr, Vladimir Kolmogorov, and Michal Rolinek. “Even Delta-Matroids
and the Complexity of Planar Boolean CSPs,” 307–26. SIAM, 2017. https://doi.org/10.1137/1.9781611974782.20.
ieee: 'A. Kazda, V. Kolmogorov, and M. Rolinek, “Even delta-matroids and the complexity
of planar Boolean CSPs,” presented at the SODA: Symposium on Discrete Algorithms,
Barcelona, Spain, 2017, pp. 307–326.'
ista: 'Kazda A, Kolmogorov V, Rolinek M. 2017. Even delta-matroids and the complexity
of planar Boolean CSPs. SODA: Symposium on Discrete Algorithms, 307–326.'
mla: Kazda, Alexandr, et al. Even Delta-Matroids and the Complexity of Planar
Boolean CSPs. SIAM, 2017, pp. 307–26, doi:10.1137/1.9781611974782.20.
short: A. Kazda, V. Kolmogorov, M. Rolinek, in:, SIAM, 2017, pp. 307–326.
conference:
end_date: 2017-01019
location: Barcelona, Spain
name: 'SODA: Symposium on Discrete Algorithms'
start_date: 2017-01-16
date_created: 2018-12-11T11:50:38Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2025-06-04T08:46:59Z
day: '01'
department:
- _id: VlKo
doi: 10.1137/1.9781611974782.20
ec_funded: 1
external_id:
arxiv:
- '1602.03124'
isi:
- '000426965800020'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1602.03124
month: '01'
oa: 1
oa_version: Submitted Version
page: 307 - 326
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication_identifier:
isbn:
- 978-161197478-2
publication_status: published
publisher: SIAM
publist_id: '6159'
quality_controlled: '1'
related_material:
record:
- id: '6032'
relation: later_version
status: public
status: public
title: Even delta-matroids and the complexity of planar Boolean CSPs
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2017'
...
---
_id: '644'
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 6=
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 f0;1g 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 they are NP-hard. The case when all allowed functions take only finite
values corresponds to a finitevalued 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 Živný. 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.
article_processing_charge: No
arxiv: 1
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.
SIAM Journal on Computing. 2017;46(3):1087-1110. doi:10.1137/16M1091836
apa: Kolmogorov, V., Krokhin, A., & Rolinek, M. (2017). The complexity of general-valued
CSPs. SIAM Journal on Computing. SIAM. https://doi.org/10.1137/16M1091836
chicago: Kolmogorov, Vladimir, Andrei Krokhin, and Michal Rolinek. “The Complexity
of General-Valued CSPs.” SIAM Journal on Computing. SIAM, 2017. https://doi.org/10.1137/16M1091836.
ieee: V. Kolmogorov, A. Krokhin, and M. Rolinek, “The complexity of general-valued
CSPs,” SIAM Journal on Computing, vol. 46, no. 3. SIAM, pp. 1087–1110,
2017.
ista: Kolmogorov V, Krokhin A, Rolinek M. 2017. The complexity of general-valued
CSPs. SIAM Journal on Computing. 46(3), 1087–1110.
mla: Kolmogorov, Vladimir, et al. “The Complexity of General-Valued CSPs.” SIAM
Journal on Computing, vol. 46, no. 3, SIAM, 2017, pp. 1087–110, doi:10.1137/16M1091836.
short: V. Kolmogorov, A. Krokhin, M. Rolinek, SIAM Journal on Computing 46 (2017)
1087–1110.
date_created: 2018-12-11T11:47:40Z
date_published: 2017-06-29T00:00:00Z
date_updated: 2025-09-23T13:45:56Z
day: '29'
department:
- _id: VlKo
doi: 10.1137/16M1091836
ec_funded: 1
external_id:
arxiv:
- '1502.07327'
isi:
- '000404774300010'
intvolume: ' 46'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1502.07327
month: '06'
oa: 1
oa_version: Preprint
page: 1087 - 1110
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication: SIAM Journal on Computing
publication_status: published
publisher: SIAM
publist_id: '7138'
quality_controlled: '1'
related_material:
record:
- id: '1637'
relation: other
status: public
scopus_import: '1'
status: public
title: The complexity of general-valued CSPs
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 46
year: '2017'
...
---
OA_place: publisher
_id: '992'
abstract:
- lang: eng
text: "An instance of the Constraint Satisfaction Problem (CSP) is given by a finite
set of\r\nvariables, a finite domain of labels, and a set of constraints, each
constraint acting on\r\na subset of the variables. The goal is to find an assignment
of labels to its variables\r\nthat satisfies all constraints (or decide whether
one exists). If we allow more general\r\n“soft” constraints, which come with (possibly
infinite) costs of particular assignments,\r\nwe obtain instances from a richer
class called Valued Constraint Satisfaction Problem\r\n(VCSP). There the goal
is to find an assignment with minimum total cost.\r\nIn this thesis, we focus
(assuming that P\r\n6\r\n=\r\nNP) on classifying computational com-\r\nplexity
of CSPs and VCSPs under certain restricting conditions. Two results are the core\r\ncontent
of the work. In one of them, we consider VCSPs parametrized by a constraint\r\nlanguage,
that is the set of “soft” constraints allowed to form the instances, and finish\r\nthe
complexity classification modulo (missing pieces of) complexity classification
for\r\nanalogously parametrized CSP. The other result is a generalization of Edmonds’
perfect\r\nmatching algorithm. This generalization contributes to complexity classfications
in two\r\nways. First, it gives a new (largest known) polynomial-time solvable
class of Boolean\r\nCSPs in which every variable may appear in at most two constraints
and second, it\r\nsettles full classification of Boolean CSPs with planar drawing
(again parametrized by a\r\nconstraint language)."
acknowledgement: FP7/2007-2013/ERC grant agreement no 616160
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Michal
full_name: Rolinek, Michal
id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87
last_name: Rolinek
citation:
ama: Rolinek M. Complexity of constraint satisfaction. 2017. doi:10.15479/AT:ISTA:th_815
apa: Rolinek, M. (2017). Complexity of constraint satisfaction. Institute
of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_815
chicago: Rolinek, Michal. “Complexity of Constraint Satisfaction.” Institute of
Science and Technology Austria, 2017. https://doi.org/10.15479/AT:ISTA:th_815.
ieee: M. Rolinek, “Complexity of constraint satisfaction,” Institute of Science
and Technology Austria, 2017.
ista: Rolinek M. 2017. Complexity of constraint satisfaction. Institute of Science
and Technology Austria.
mla: Rolinek, Michal. Complexity of Constraint Satisfaction. Institute of
Science and Technology Austria, 2017, doi:10.15479/AT:ISTA:th_815.
short: M. Rolinek, Complexity of Constraint Satisfaction, Institute of Science and
Technology Austria, 2017.
corr_author: '1'
date_created: 2018-12-11T11:49:35Z
date_published: 2017-05-01T00:00:00Z
date_updated: 2026-04-08T14:17:06Z
day: '01'
ddc:
- '004'
degree_awarded: PhD
department:
- _id: VlKo
doi: 10.15479/AT:ISTA:th_815
ec_funded: 1
file:
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checksum: 81761fb939acb7585c36629f765b4373
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language:
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month: '05'
oa: 1
oa_version: Published Version
page: '97'
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
publist_id: '6407'
pubrep_id: '815'
status: public
supervisor:
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
title: Complexity of constraint satisfaction
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2017'
...
---
_id: '1377'
abstract:
- lang: eng
text: We consider the problem of minimizing the continuous valued total variation
subject to different unary terms on trees and propose fast direct algorithms based
on dynamic programming to solve these problems. We treat both the convex and the
nonconvex case and derive worst-case complexities that are equal to or better
than existing methods. We show applications to total variation based two dimensional
image processing and computer vision problems based on a Lagrangian decomposition
approach. The resulting algorithms are very effcient, offer a high degree of parallelism,
and come along with memory requirements which are only in the order of the number
of image pixels.
article_processing_charge: No
arxiv: 1
author:
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
- first_name: Thomas
full_name: Pock, Thomas
last_name: Pock
- first_name: Michal
full_name: Rolinek, Michal
id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87
last_name: Rolinek
citation:
ama: Kolmogorov V, Pock T, Rolinek M. Total variation on a tree. SIAM Journal
on Imaging Sciences. 2016;9(2):605-636. doi:10.1137/15M1010257
apa: Kolmogorov, V., Pock, T., & Rolinek, M. (2016). Total variation on a tree.
SIAM Journal on Imaging Sciences. Society for Industrial and Applied Mathematics
. https://doi.org/10.1137/15M1010257
chicago: Kolmogorov, Vladimir, Thomas Pock, and Michal Rolinek. “Total Variation
on a Tree.” SIAM Journal on Imaging Sciences. Society for Industrial and
Applied Mathematics , 2016. https://doi.org/10.1137/15M1010257.
ieee: V. Kolmogorov, T. Pock, and M. Rolinek, “Total variation on a tree,” SIAM
Journal on Imaging Sciences, vol. 9, no. 2. Society for Industrial and Applied
Mathematics , pp. 605–636, 2016.
ista: Kolmogorov V, Pock T, Rolinek M. 2016. Total variation on a tree. SIAM Journal
on Imaging Sciences. 9(2), 605–636.
mla: Kolmogorov, Vladimir, et al. “Total Variation on a Tree.” SIAM Journal on
Imaging Sciences, vol. 9, no. 2, Society for Industrial and Applied Mathematics
, 2016, pp. 605–36, doi:10.1137/15M1010257.
short: V. Kolmogorov, T. Pock, M. Rolinek, SIAM Journal on Imaging Sciences 9 (2016)
605–636.
date_created: 2018-12-11T11:51:40Z
date_published: 2016-05-03T00:00:00Z
date_updated: 2025-09-22T07:34:48Z
day: '03'
department:
- _id: VlKo
doi: 10.1137/15M1010257
ec_funded: 1
external_id:
arxiv:
- '1502.07770'
isi:
- '000385275400005'
intvolume: ' 9'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1502.07770
month: '05'
oa: 1
oa_version: Preprint
page: 605 - 636
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication: SIAM Journal on Imaging Sciences
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '5834'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Total variation on a tree
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 9
year: '2016'
...
---
_id: '1636'
abstract:
- lang: eng
text: "Constraint Satisfaction Problem (CSP) is a fundamental algorithmic problem
that appears in many areas of Computer Science. It can be equivalently stated
as computing a homomorphism R→ΓΓ between two relational structures, e.g. between
two directed graphs. Analyzing its complexity has been a prominent research direction,
especially for the fixed template CSPs where the right side ΓΓ is fixed and the
left side R is unconstrained.\r\n\r\nFar fewer results are known for the hybrid
setting that restricts both sides simultaneously. It assumes that R belongs to
a certain class of relational structures (called a structural restriction in this
paper). We study which structural restrictions are effective, i.e. there exists
a fixed template ΓΓ (from a certain class of languages) for which the problem
is tractable when R is restricted, and NP-hard otherwise. We provide a characterization
for structural restrictions that are closed under inverse homomorphisms. The criterion
is based on the chromatic number of a relational structure defined in this paper;
it generalizes the standard chromatic number of a graph.\r\n\r\nAs our main tool,
we use the algebraic machinery developed for fixed template CSPs. To apply it
to our case, we introduce a new construction called a “lifted language”. We also
give a characterization for structural restrictions corresponding to minor-closed
families of graphs, extend results to certain Valued CSPs (namely conservative
valued languages), and state implications for (valued) CSPs with ordered variables
and for the maximum weight independent set problem on some restricted families
of graphs."
alternative_title:
- LNCS
article_processing_charge: No
arxiv: 1
author:
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
- first_name: Michal
full_name: Rolinek, Michal
id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87
last_name: Rolinek
- first_name: Rustem
full_name: Takhanov, Rustem
last_name: Takhanov
citation:
ama: 'Kolmogorov V, Rolinek M, Takhanov R. Effectiveness of structural restrictions
for hybrid CSPs. In: 26th International Symposium. Vol 9472. Springer Nature;
2015:566-577. doi:10.1007/978-3-662-48971-0_48'
apa: 'Kolmogorov, V., Rolinek, M., & Takhanov, R. (2015). Effectiveness of structural
restrictions for hybrid CSPs. In 26th International Symposium (Vol. 9472,
pp. 566–577). Nagoya, Japan: Springer Nature. https://doi.org/10.1007/978-3-662-48971-0_48'
chicago: Kolmogorov, Vladimir, Michal Rolinek, and Rustem Takhanov. “Effectiveness
of Structural Restrictions for Hybrid CSPs.” In 26th International Symposium,
9472:566–77. Springer Nature, 2015. https://doi.org/10.1007/978-3-662-48971-0_48.
ieee: V. Kolmogorov, M. Rolinek, and R. Takhanov, “Effectiveness of structural restrictions
for hybrid CSPs,” in 26th International Symposium, Nagoya, Japan, 2015,
vol. 9472, pp. 566–577.
ista: 'Kolmogorov V, Rolinek M, Takhanov R. 2015. Effectiveness of structural restrictions
for hybrid CSPs. 26th International Symposium. ISAAC: International Symposium
on Algorithms and Computation, LNCS, vol. 9472, 566–577.'
mla: Kolmogorov, Vladimir, et al. “Effectiveness of Structural Restrictions for
Hybrid CSPs.” 26th International Symposium, vol. 9472, Springer Nature,
2015, pp. 566–77, doi:10.1007/978-3-662-48971-0_48.
short: V. Kolmogorov, M. Rolinek, R. Takhanov, in:, 26th International Symposium,
Springer Nature, 2015, pp. 566–577.
conference:
end_date: 2015-12-11
location: Nagoya, Japan
name: 'ISAAC: International Symposium on Algorithms and Computation'
start_date: 2015-12-09
date_created: 2018-12-11T11:53:10Z
date_published: 2015-12-01T00:00:00Z
date_updated: 2025-09-23T08:39:38Z
day: '01'
department:
- _id: VlKo
doi: 10.1007/978-3-662-48971-0_48
ec_funded: 1
external_id:
arxiv:
- '1504.07067'
isi:
- '000375151300048'
intvolume: ' 9472'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1504.07067
month: '12'
oa: 1
oa_version: Preprint
page: 566 - 577
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication: 26th International Symposium
publication_identifier:
isbn:
- 978-3-662-48970-3
publication_status: published
publisher: Springer Nature
publist_id: '5519'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Effectiveness of structural restrictions for hybrid CSPs
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 9472
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
article_processing_charge: No
arxiv: 1
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
corr_author: '1'
date_created: 2018-12-11T11:53:10Z
date_published: 2015-12-01T00:00:00Z
date_updated: 2025-09-23T13:45:57Z
day: '01'
department:
- _id: VlKo
doi: 10.1109/FOCS.2015.80
ec_funded: 1
external_id:
arxiv:
- '1502.07327'
isi:
- '000379204700071'
isi: 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2015'
...
---
_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.
corr_author: '1'
date_created: 2019-11-18T15:57:05Z
date_published: 2014-06-30T00:00:00Z
date_updated: 2025-06-26T12:38:53Z
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'
...