Filters








123,286 Hits in 5.9 sec

An O(log N) deterministic packet-routing scheme

Eli Upfal
1992 Journal of the ACM  
A determuustlc O(log N)-time algorithm for the problem of routing an arbitrary permutation on an N-processor bounded-degree network with bounded buffers is presented.  ...  Unhke all previous deterministic solutions to this problem, our routing scheme does not reduce the routing problem to sorting and does not use the sorting network of Ajtai, et al. [1].  ...  An O(log N)-sorting network gives an O(log N) solution for the acyclic, switching network, packet-routing problem.  ... 
doi:10.1145/147508.147517 fatcat:pt37lwwnf5byvdxt5uc2ir6bli

Secure merge with O(n log log n) secure operation [article]

Brett Hemenway Falk, Rafail Ostrovsky
2020 IACR Cryptology ePrint Archive  
Using blackbox access to an O(n)-communication secure shuffle, we give the first secure merge algorithm that requires only O(n log log n) communication.  ...  The best data-oblivious sorting algorithms for sorting a list of n elements require O(n log n) comparisons.  ...  The AKS sorting network [AKS83] requires O(n log n) comparators to sort n elements.  ... 
dblp:journals/iacr/FalkO20 fatcat:rksbxv7wjjdu7m3dtjqaw3ksse

An O(n log n)-Time Algorithm for the k-Center Problem in Trees

Haitao Wang, Jingru Zhang, Marc Herbstritt
2018 International Symposium on Computational Geometry  
Comput., 1983) gave an algorithm that can solve the problem in O(n log 2 n) time by using Cole's parametric search.  ...  In this paper, we present an O(n log n) time algorithm for the problem and thus settle the open problem affirmatively.  ...  sorting network [2] .  ... 
doi:10.4230/lipics.socg.2018.72 dblp:conf/compgeom/0001Z18 fatcat:ruwgocgwjzesdchks5uv4sx4nm

Perfectly Secure Oblivious Parallel RAM with O(log 3 N/ log log N) Overhead [article]

T.-H. Hubert Chan, Wei-Kai Lin, Kartik Nayak, Elaine Shi
2020 IACR Cryptology ePrint Archive  
Similarly, Oblivious Parallel RAM (OPRAM) compiles a parallel RAM program to an oblivious counterpart.  ...  Oblivious RAM (ORAM) is a technique for compiling any RAM program to an oblivious counterpart, i.e., one whose access patterns do not leak information about the secret inputs.  ...  O(n log 2 n) work, but to sort only 0/1 elements, i.e. tight compaction, a bitonic sort augmented with counting takes only O(n log n) work).  ... 
dblp:journals/iacr/ChanLNS20 fatcat:6a427rcl6bgofpgz5cy5mv5t7q

An O(n^2 log^2 n) Time Algorithm for Minmax Regret Minsum Sink on Path Networks

Binay Bhattacharya, Yuya Higashikawa, Tsunehiko Kameda, Naoki Katoh, Michael Wagner
2018 International Symposium on Algorithms and Computation  
We want to minimize the aggregate evacuation time to an evacuation center (called a sink) on a path network with uniform edge capacities.  ...  We present the first sub-cubic time algorithm in n to solve this problem, where n is the number of vertices.  ...  [2] that an aggregate time k-sink in path networks can be found in O(kn log 3 n) (resp. O(kn 2 log 2 n)) time, if edge capacities are uniform (resp. nonuniform).  ... 
doi:10.4230/lipics.isaac.2018.14 dblp:conf/isaac/BhattacharyaHKK18 fatcat:p6y7fskgerdo3bxpils6zc53u4

Optimal parallel selection has complexity O(Log Log N)

Miklós Ajtai, János Komlós, W.L. Steiger, Endre Szemerédi
1989 Journal of computer and system sciences (Print)  
We show that in the deterministic comparison model for parallel computation, p=n processors can select the kth smallest item from a set of n numbers in O(log log n) parallel time.  ...  This optimal time bound holds even if p = o(n).  ...  The log n depth sorting network of Ajtai, Komlbs, and Szemeredi [ 1 ] implies that log n is both an upper and lower bound for sorting in this model becaue the PCT is more powerful than a network.  ... 
doi:10.1016/0022-0000(89)90035-4 fatcat:z7kk67veffhm7fttm2gxwuwwvq

Sorting Short Keys in Circuits of Size o(n log n) [article]

Gilad Asharov, Wei-Kai Lin, Elaine Shi
2020 arXiv   pre-print
Therefore, if the keys to be sorted are short, say, k < o(log n), our result is asymptotically better than the classical AKS sorting network (ignoring log^* terms); and we also overcome the n log n barrier  ...  We also show that if the Li-Li network coding conjecture is true, our upper bound is optimal, barring log^* terms, for every k as long as k = O(log n).  ...  Acknowledgments Elaine Shi would like to thank Bruce Maggs for explaining the AKS sorting network [AKS83] , for numerous extremely helpful discussions regarding the elegant Arora, Leighton, Maggs self-routing  ... 
arXiv:2010.09884v2 fatcat:ji2762hgevbpxijglqczbp5sxu

Treemap: An O(log n) algorithm for indoor simultaneous localization and mapping

Udo Frese
2006 Autonomous Robots  
When the robot moves to a different subregion a full least-square estimate for that region is computed in only O(k 3 log n) computation time for n landmarks.  ...  A global least square estimate needs O(kn) computation time with a very small constant (12.37ms for n = 11300).  ...  By definition 1.2 this holds for only O(1) leaves taking O(k log n) time.  ... 
doi:10.1007/s10514-006-9043-2 fatcat:pww3nmtyqzaafmca4rfyzsoq7u

MST construction in O(log log n) communication rounds

Zvi Lotker, Elan Pavlov, Boaz Patt-Shamir, David Peleg
2003 Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures - SPAA '03  
We consider a simple model for overlay networks, where all n processes are connected to all other processes, and each message contains at most O(log n) bits.  ...  For this model, we present a distributed algorithm that constructs a minimumweight spanning tree in O(log log n) communication rounds, where in each round any process can send a message to each other process  ...  In this paper we present an MST construction algorithm that works in O(log log n) communication rounds, where in each round each process can send O(log n) bits to each other process (more intuitively,  ... 
doi:10.1145/777412.777428 dblp:conf/spaa/LotkerPPP03 fatcat:j3krvcrcb5ca3glgpmwadwlk7q

MST construction in O(log log n) communication rounds

Zvi Lotker, Elan Pavlov, Boaz Patt-Shamir, David Peleg
2003 Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures - SPAA '03  
We consider a simple model for overlay networks, where all n processes are connected to all other processes, and each message contains at most O(log n) bits.  ...  For this model, we present a distributed algorithm that constructs a minimumweight spanning tree in O(log log n) communication rounds, where in each round any process can send a message to each other process  ...  In this paper we present an MST construction algorithm that works in O(log log n) communication rounds, where in each round each process can send O(log n) bits to each other process (more intuitively,  ... 
doi:10.1145/777426.777428 fatcat:4cdmg4apbzghxn7niolz5ovhxe

Neural Shuffle-Exchange Networks – Sequence Processing in O(n log n) Time [article]

Kārlis Freivalds, Emīls Ozoliņš, Agris Šostaks
2019 arXiv   pre-print
We introduce a new Shuffle-Exchange neural network model for sequence to sequence tasks which have O(log n) depth and O(n log n) total complexity.  ...  To this end, a vast majority of the state-of-the-art models use attention mechanism which is of O(n^2) complexity that leads to slow execution for long sequences.  ...  Although the best known sorting circuits have depth O(log n) (Ajtai et al., 1983; Seiferas, 2009) , they are huge, with estimated depth over 100 log n.  ... 
arXiv:1907.07897v3 fatcat:g644nxdyxjakhjw2t6jbnfumta

Neural Shuffle-Exchange Networks - Sequence Processing in O(n log n) Time

Karlis Freivalds, Emils Ozolins, Agris Sostaks
2019 Neural Information Processing Systems  
We introduce a new Shuffle-Exchange neural network model for sequence to sequence tasks which have O(log n) depth and O(n log n) total complexity.  ...  To this end, a vast majority of the state-of-the-art models use attention mechanism which is of O(n 2 ) complexity that leads to slow execution for long sequences.  ...  Although the best known sorting circuits have depth O(log n) (Ajtai et al., 1983; Seiferas, 2009) , they are huge, with estimated depth over 100 log n.  ... 
dblp:conf/nips/FreivaldsOS19 fatcat:ogdbdlylvjem3n3z5tcjtkbaz4

An $O(n\log ^2 n)$ Algorithm for the kth Longest Path in a Tree with Applications to Location Problems

N. Megiddo, A. Tamir, E. Zemel, R. Chandrasekaran
1981 SIAM journal on computing (Print)  
This amounts to an effort of O ( m log n l m ) = O ( n log2 n ) if one uses trimming and an inferior bound, of O ( n FIG. 1 sup,.. mini,,,, d ( x , , y).  ...  log n log -= O ( pn log2 n ). ( (lo: n ) ) n min { p log2 n, n log p } ) 8 .  ... 
doi:10.1137/0210023 fatcat:ixaxf22jvfcern7e7nrdcjpthq

Selection networks with 8n log2 n size and O(log n) depth [chapter]

Shuji Jimbo, Akira Maruoka
1992 Lecture Notes in Computer Science  
A sorting network with $n$ inputs is also caUed an n-sorter.  ...  Since n-sorters are also $(n,k)$-selectors, the existence of n-sorters with $O(n\log n)$ size and $O(\log n)$ depth, given in $[AKS83a] [AKS83b]$ , immediately implies the existence of $(n,k)$ -selectors  ... 
doi:10.1007/3-540-56279-6_69 fatcat:ftwtkip4jvcftp76vaa42mcrbq

Secure Merge in Linear Time and O(log log N) Rounds [article]

Mark Blunk, Paul Bunn, Samuel Dittmer, Steve Lu, Rafail Ostrovsky
2022 IACR Cryptology ePrint Archive  
n) communication and O(log n) round complexity.  ...  Our protocol improves on previous work of [FNO22], which gave a O(n) communication and O(n) round complexity protocol, and other "naive" approaches, such as the shuffle-sort paradigm, which has O(n log  ...  Protocol Computation Communication Rounds (Garbled) Merging Network [Folklore] O(κ • n log n) O(κ • n log n) O(1) (GMW) Merging Network [Folklore] O(n log n) O(n log n) O(log n) (FHE) Merging Network [  ... 
dblp:journals/iacr/BlunkBDLO22 fatcat:hx6yrmnfararrmybx55gq2lneq
« Previous Showing results 1 — 15 out of 123,286 results