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Yes, There is an Oblivious RAM Lower Bound! [chapter]

Kasper Green Larsen, Jesper Buus Nielsen
2018 Lecture Notes in Computer Science  
However, as pointed out by Boyle and Naor [ITCS'16] in the paper "Is there an oblivious RAM lower bound?"  ...  An Oblivious RAM (ORAM) introduced by Goldreich and Ostrovsky [JACM'96] is a (possibly randomized) RAM, for which the memory access pattern reveals no information about the operations performed.  ...  Acknowledgment Kasper Green Larsen wishes to thank Vinod Vaikuntanathan for introducing him to oblivious RAMs and oblivious data structures during a visit at MIT, eventually leading to the results in this  ... 
doi:10.1007/978-3-319-96881-0_18 fatcat:zmm5kkfvsbapncpihh7oih6jua

Lower Bounds for Oblivious Near-Neighbor Search [article]

Kasper Green Larsen and Tal Malkin and Omri Weinstein and Kevin Yeo
2019 arXiv   pre-print
For the natural setting of d = Θ( n), our result implies an Ω̃(^2 n) lower bound, which is a quadratic improvement over the highest (non-oblivious) cell-probe lower bound for ANN.  ...  We prove an Ω(d n/ ( n)^2) lower bound on the dynamic cell-probe complexity of statistically oblivious approximate-near-neighbor search (ANN) over the d-dimensional Hamming cube.  ...  There have been many previous works on lower bounds for non-oblivious near(est)-neighbors problems.  ... 
arXiv:1904.04828v1 fatcat:r3hafauyw5cuhfdvsejv3narsm

Inductive Time-Space Lower Bounds for Sat and Related Problems

Ryan Williams
2006 Computational Complexity  
We extend the above four-step argument in a significant way, leading to improved lower bounds in several computational models. Lower bounds for SAT on subpolynomial-space RAMs.  ...  Therefore, proving such a non-containment also proves a lower bound for an explicit and natural problem in NP.  ...  By the oblivious TM simulation of Pippenger and Fischer [21], there is a Boolean circuit C M of O(n log n) gates such that M (x, y) accepts iff C M (x, y) = 1.  ... 
doi:10.1007/s00037-007-0221-1 fatcat:w7go66suzjgpfelyymw3zouz5a

Logarithmic Lower Bounds in the Cell-Probe Model [article]

Mihai Patrascu, Erik D. Demaine
2005 arXiv   pre-print
We also prove matching upper and lower bounds for partial sums when parameterized by the word size and the maximum additive change in an update.  ...  This technique enables us to prove an amortized randomized Omega(lg n) lower bound per operation for several data structural problems on n elements, including partial sums, dynamic connectivity among disjoint  ...  Then, assuming δ ≥ 2, there is an absolute constant ε such that the second term of the lower bound is a constant fraction of the first term. We thus obtain E[c] = Ω(L) − O s b .  ... 
arXiv:cs/0502041v2 fatcat:z2ez6y6qp5fbpiuredfeehzhau

Top-k bounded diversification

Piero Fraternali, Davide Martinenghi, Marco Tagliasacchi
2012 Proceedings of the 2012 international conference on Management of Data - SIGMOD '12  
An interesting case is provided by spatial Web objects, which are produced in great quantity by location-based services that let users attach content to places, and arise also in trip planning, news analysis  ...  queries are a particular case of diversified top-k queries, for which existing methods are too costly, as they evaluate diversity by accessing and scanning all relevant objects, even if only a small subset is  ...  All the algorithms have been executed on a PC with the Windows 7 operating system, an Intel R Core2-Duo processor at 2.4GHz and 4Gb RAM.  ... 
doi:10.1145/2213836.2213884 dblp:conf/sigmod/FraternaliMT12 fatcat:hkfdwtjpjbdfxiqfx6oqvfeowm

Time-space trade-off lower bounds for randomized computation of decision problems

Paul Beame, Michael Saks, Xiaodong Sun, Erik Vee
2003 Journal of the ACM  
In the case of boolean domain, Ajtai exhibited an explicit class of functions, and proved that any deterministic Boolean branching program or RAM using space Ë Ó´Òµ requires time Ì that is superlinear.  ...  We prove the first time-space lower bound tradeoffs for randomized computation of decision problems.  ...  The best lower bounds in the oblivious case have all been obtained using some form of communication complexity.  ... 
doi:10.1145/636865.636867 fatcat:b3qhthfo2za5dexzlsfftlt33u

Sharply Bounded Alternation and Quasilinear Time

S. A. Bloch
1998 Theory of Computing Systems  
We de ne the sharply bounded hierarchy, SBH (QL), a hierarchy of classes within P , using quasilinear-time computation and quanti cation over strings of length log n.  ...  Thanks to James Otto for pointing out an error in an earlier version of our tiered-parameter de nition.  ...  Set s = d = b = 1 s is the stage number, E A d is the next machine we will diagonalize against, and b is a lower bound on the lengths of strings eligible for diagonalization.  ... 
doi:10.1007/s002240000085 fatcat:gjbauruklvbu3ho6izosgxgjfu

Structural Sparsity of Complex Networks: Bounded Expansion in Random Models and Real-World Graphs [article]

Erik D. Demaine and Felix Reidl and Peter Rossmanith and Fernando Sanchez Villaamil and Somnath Sikdar and Blair D. Sullivan
2018 arXiv   pre-print
of bounded expansion.  ...  This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network  ...  The answer is yes: consider the class of graphs consisting of Θ( √ n) copies of S √ n .  ... 
arXiv:1406.2587v6 fatcat:re6o4v32wjdavhlgtdjpnhdhwu

BIOS ORAM: Improved Privacy-Preserving Data Access for Parameterized Outsourced Storage [article]

Michael T. Goodrich
2017 arXiv   pre-print
Algorithms for oblivious random access machine (ORAM) simulation allow a client, Alice, to obfuscate a pattern of data accesses with a server, Bob, who is maintaining Alice's outsourced data while trying  ...  , where n is the size of Alice's outsourced memory.  ...  Interestingly, Goldreich and Ostrofsky [9] give a lower-bound argument that the I/O overhead for an ORAM scheme must be Ω(log n) when M is O(1), but their lower bound does not apply to larger values  ... 
arXiv:1709.06534v1 fatcat:g4n6waniuvc6je2s3qlqeuvhji

Exploring Differential Obliviousness

Amos Beimel, Kobbi Nissim, Mohammad Zaheri, Michael Wagner
2019 International Workshop on Approximation Algorithms for Combinatorial Optimization  
the bounded degree model.  ...  Our examples suggest that there would be benefits in further exploring which class of computational tasks are amenable to differential obliviousness.  ...  while retaining efficiency by using an Oblivious RAM protocol (ORAM) [10, 30, 13] .  ... 
doi:10.4230/lipics.approx-random.2019.65 dblp:conf/approx/BeimelNZ19 fatcat:krxpfa4ovnhmfce66rni25fo5i

Exploring Differential Obliviousness [article]

Amos Beimel, Kobbi Nissim, Mohammad Zaheri
2019 arXiv   pre-print
the bounded degree model.  ...  Our examples suggest that there would be benefits in further exploring which class of computational tasks are amenable to differential obliviousness.  ...  while retaining efficiency by using an Oblivious RAM protocol (ORAM) [10, 30, 13] .  ... 
arXiv:1905.01373v2 fatcat:d2n3clr2uncwrhrb7cafxf7zta

Geometric BWT: Compressed Text Indexing via Sparse Suffixes and Range Searching

Yu-Feng Chien, Wing-Kai Hon, Rahul Shah, Sharma V. Thankachan, Jeffrey Scott Vitter
2013 Algorithmica  
Many classical results on data structures and lower bounds exist under various models including pointer machine, RAM, external memory, and cache-oblivious models [1, 4].  ...  We also show lower bounds for these problems and for the problem of text indexing in general. These are the first known lower bounds (hardness results) in this area.  ...  Many classical results on data structures and lower bounds exist under various models including pointer machine, RAM, external memory, and cache-oblivious models [1, 4] .  ... 
doi:10.1007/s00453-013-9792-1 fatcat:adgwlm4ncjcjrpikomxo7eppsi

Making deterministic signatures quickly

Milan Ružić
2009 ACM Transactions on Algorithms  
We give several new results on static dictionaries in different computational models: the Word RAM, the Practical RAM, and the cache-oblivious model.  ...  binary strings that in the cache-oblivious model has a query performance of O( |s| B + log |s|) I/Os, for query argument s.  ...  helpful discussions on this subject, and in particular for pointing out that dot product with a constant vector can be easily computed in O(1) time; Rasmus Pagh for useful comments and suggestions; and an  ... 
doi:10.1145/1541885.1541887 fatcat:vasu3njvvjfpddpxqsexb5rwdq

Cache-Oblivious Planar Shortest Paths [chapter]

Hema Jampala, Norbert Zeh
2005 Lecture Notes in Computer Science  
This is the first cache-oblivious algorithm for this problem that incurs o(N ) block transfers.  ...  We present an efficient cache-oblivious implementation of the shortest-path algorithm for planar graphs by Klein et al., and prove that it incurs no more than O'N B 1/2− + N B log N´block transfers on  ...  The answer to question (3) is most definitely no because this would violate the Ω(perm(N )) lower bound for shortest paths [13] , which is Ω(sort(N )) in the cache-oblivious model.  ... 
doi:10.1007/11523468_46 fatcat:nzeuh6sckzb3zgclz575fiskr4

Constructive Separations and Their Consequences [article]

Lijie Chen, Ce Jin, Rahul Santhanam, Ryan Williams
2022 arXiv   pre-print
Put another way, constructiveness is the opposite of a complexity barrier: it is a property we want lower bounds to have. Our results fall into three broad categories. 1.  ...  We observe that for all super-polynomially growing functions t, there are no constructive separations for detecting high t-time Kolmogorov complexity (a task which is known to be not in P) from any complexity  ...  In fact, we show that there is an oblivious list-refuter R that outputs a quasipoly-size set of strings of length N.  ... 
arXiv:2203.14379v1 fatcat:hrfzpzilljdf5i73eq5u2ci2su
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