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Complexity of the homomorphism extension problem in the random case [article]

Alexandr Kazda
2012 arXiv   pre-print
We prove that if A is a large random relational structure with at least one relation of arity at least 2 then the problem EXT(A) is almost surely NP-complete.  ...  The author would like to thank Libor Barto for suggesting this problem.  ...  Acknowledgments The research was supported by the GAČR project GAČR 201/09/H012, by the Charles University project GA UK 67410 and by the grant SVV-2011-263317.  ... 
arXiv:1106.0663v5 fatcat:o5gpi467rzfobdw2zathkg552e

Algorithmic aspects of M-Lipschitz mappings of graphs [article]

Jan Bok
2018 arXiv   pre-print
Furthermore, our problem of extending partial mappings is connected to the problem of list homomorphism and yields a better run-time complexity for a specific family of its instances.  ...  We study two natural problems regarding graph-indexed random walks. - Computing the maximum range of a graph-indexed random walk for a given graph. - Deciding if we can extend a partial GI random walk  ...  Acknowledgments This research was supported by the Charles University Grant Agency, project GA UK 1158216 and by the Center of Excellence -ITI (P202/12/G061 of GAČR).  ... 
arXiv:1801.05496v3 fatcat:sijafagz6ngmjmyhtzxk7xwow4

Quantum Query Complexity of Subgraph Isomorphism and Homomorphism [article]

Raghav Kulkarni, Supartha Podder
2015 arXiv   pre-print
Interestingly, the randomized bound of Ω(α_H · n) for f_H still remains open. We also study the Subgraph Homomorphism Problem, denoted by f_[H], and show that Q(f_[H]) = Ω(n).  ...  In this paper we show: Q(f_H) = Ω(√(α_H · n)), where Q(f_H) denotes the quantum query complexity of f_H.  ...  The authors also thank Biswaroop Maiti for the discussion in the beginning phase of this work.  ... 
arXiv:1509.06361v2 fatcat:eydgqkabuvhbhdxdxrwarfnqcu

Approximation Algorithms for Graph Homomorphism Problems [chapter]

Michael Langberg, Yuval Rabani, Chaitanya Swamy
2006 Lecture Notes in Computer Science  
Multiway uncut can be viewed as a special case of prelabeled MGH where one is also given a prelabeling ϕ : U → VH , U ⊆ VG, and the output has to be an extension of ϕ .  ...  We introduce the maximum graph homomorphism (MGH) problem: given a graph G, and a target graph H, find a mapping ϕ : VG → VH that maximizes the number of edges of G that are mapped to edges of H.  ...  Feige gave the first inapproximability results for various NP-hard optimization problems assuming the complexity of refuting random-3CNF formulas.  ... 
doi:10.1007/11830924_18 fatcat:xr642moslnckxjndlgpimcryte

Efficient and Secure Evaluation of Multivariate Polynomials and Applications [chapter]

Matthew Franklin, Payman Mohassel
2010 Lecture Notes in Computer Science  
This includes the variants of Yao's garbled circuit protocol in the malicious model such as [22, 13] in the twoparty case and works such as [17] [18] [19] in the multi-party case.  ...  in the computational complexity of the original semi-honest protocol.  ...  In case of GM encryption we show a simple way of extending it to work over any extension field of GF(2) while preserving its homomorphic properties.  ... 
doi:10.1007/978-3-642-13708-2_15 fatcat:zrp7qxsdgbdsxmzmylxhfzdzum

Page 4273 of Mathematical Reviews Vol. , Issue 83j [page]

1983 Mathematical Reviews  
From the summary: “We consider the case of automata operating within random environments.  ...  Frances 83):68056 On the average-case complexity of selecting the k th best. SIAM J. Comput. 11 (1982), no. 3, 428-447.  ... 

Somewhat homomorphic encryption scheme for arithmetic operations on large integers

Pedro Silveira Pisa, Michel Abdalla, Otto Carlos Muniz Bandeira Duarte
2012 2012 Global Information Infrastructure and Networking Symposium (GIIS)  
Even though the total number of allowed homomorphic operations is limited in our scheme, our results show that the new extension is more efficient in terms of processing and that the ratio between the  ...  In this paper, we propose a new encryption scheme oriented for calculating arithmetic functions of large integer numbers. Our proposal is an extension of the encryption scheme proposed in [1].  ...  Indeed, in our extension, the noise size is log 2 B times larger, which increases the complexity of the problem.  ... 
doi:10.1109/giis.2012.6466769 dblp:conf/giis/PisaAD12 fatcat:qd2v53zpijbcdofnfu22s5ft3a

Algebraic and model theoretic methods in constraint satisfaction [article]

Michael Pinsker
2015 arXiv   pre-print
This text is related to the tutorials I gave at the Banff International Research Station and within a "Doc-course" at Charles University Prague in the fall of 2014.  ...  It describes my current research and some of the most important open questions related to it.  ...  Classify the complexity of CSP(Γ), for all finite language reducts Γ of the random partial order. In other words, classify the complexity of Poset-SAT problems.  ... 
arXiv:1507.00931v1 fatcat:gdiqkrt7sbhjfjke4mtqx75uua

Homomorphic Encryption: Theory & Applications [article]

Jaydip Sen
2013 arXiv   pre-print
The chapter then provides a survey of some of the classical homomorphic encryption schemes existing in the current literature.  ...  The chapter then introduces the most important and recent research direction in the filed - fully homomorphic encryption.  ...  In case of symmetric schemes, we introduce a random vector in the encryption process (e.g., in the pseudo-random generator for stream ciphers, or in the operating mode for block ciphers) -generally called  ... 
arXiv:1305.5886v1 fatcat:agzyco4ehnfajiamrbp7qobo2a

A Combinatorial Classic — Sparse Graphs with High Chromatic Number [chapter]

Jaroslav Nešetřil
2013 Bolyai Society Mathematical Studies  
Acknowledgment: I thank to Martin Bálek and Andrew Goodall for the help when preparing this article.  ...  This is important for the complexity of algorithms, particularly in the context of Constraint Satisfaction Problems -CSP: For a given a relational structure H, CSP (H) denotes the following decision problem  ...  The problem of the existence of uniquely k-colorable graphs with large girth has an interesting history: the triangle-free case (i.e. l = 3) was settled in [68] and this was improved in [31] to graphs  ... 
doi:10.1007/978-3-642-39286-3_15 fatcat:plrnkchibbdv5jm3jfap4dmk5u

Page 481 of Mathematical Reviews Vol. , Issue 98A [page]

1998 Mathematical Reviews  
The investigation of communication complexity has proved to be very useful in the study of complexity of computing prob- lems of fundamental computing models as well as in the central topic of the complexity  ...  logn) messages, where n is the number of computers in the network. This paper presents a new distributed algorithm for the same problem using 2n? messages in the worst case.  ... 

Extending Oblivious Transfer with Low Communication via Key-Homomorphic PRFs [chapter]

Peter Scholl
2018 Lecture Notes in Computer Science  
Our main technique is a novel twist on the classic OT extension of Ishai et al. (Crypto 2003), using an additively key-homomorphic PRF to reduce interaction.  ...  We present a new approach to extending oblivious transfer with communication complexity that is logarithmic in the security parameter.  ...  I would like to thank Claudio Orlandi for the observation that an XOR-homomorphic PRG would imply non-interactive OT extension, which inspired this work.  ... 
doi:10.1007/978-3-319-76578-5_19 fatcat:dqrf37o2lrgxjarbhc47w2dvm4

Polynomial AND homomorphic cryptosystem and applications

Shundong Li, Sufang Zhou, Jiawei Dou, Wenli Wang
2019 Science China Information Sciences  
To solve problems such as these, we propose a polynomial AND homomorphic cryptosystem based on the ideal theory of abstract algebra; the scheme can be obtained from available multiplicatively homomorphic  ...  Exploring new homomorphic cryptosystems to solve these problems is appealing, and is of high theoretical and practical significance.  ...  Acknowledgements This work was supported by National Natural Science Foundation of China (Grant No. 62172435). We are deeply grateful to all reviewers.  ... 
doi:10.1007/s11432-018-9789-y fatcat:qipqsltknbg2rgljcqqm42dq6m

Computational Counting (Dagstuhl Seminar 18341)

Ivona Bezáková, Leslie Ann Goldberg, Mark R. Jerrum, Marc Herbstritt
2018 Dagstuhl Reports  
A total of 43 researchers from all over the world, with interests and expertise in different aspects of computational counting, actively participated in the meeting.  ...  This report documents the program and the outcomes of Dagstuhl Seminar 17341 "Computational Counting".  ...  Modular counting provides a rich setting in which to study the structure of homomorphism problems. In this talk we will discuss the complexity of counting graph homomorphisms modulo 2.  ... 
doi:10.4230/dagrep.7.8.23 dblp:journals/dagstuhl-reports/BezakovaGJ17 fatcat:yp3oqvgo4fal5lbio5yeqt4uje

Homomorphic Encryption — Theory and Application [chapter]

Jaydip Sen
2013 Theory and Practice of Cryptography and Network Security Protocols and Technologies  
In case of symmetric schemes, we introduce a random vector in the encryption process (e.g., in the pseudo-random generator for stream ciphers, or in the operating mode for block ciphers)generally called  ...  In his security analysis of BDD, Gentry has used the best known complexity bound for the approximate shortest vector problem (SVP) in lattices.  ...  Author details Jaydip Sen * Department of Computer Science, National Institute of Science & Technology, Odisha, India  ... 
doi:10.5772/56687 fatcat:amgaohpdbnal3ly6nsx4nvasmm
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