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An O(log N) deterministic packet-routing scheme
1992
Journal of the ACM
Preserved Fulltext
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]
2020
IACR Cryptology ePrint Archive
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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
2018
International Symposium on Computational Geometry
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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]
2020
IACR Cryptology ePrint Archive
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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
2018
International Symposium on Algorithms and Computation
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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)
1989
Journal of computer and system sciences (Print)
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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]
2020
arXiv
pre-print
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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
2006
Autonomous Robots
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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
2003
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures - SPAA '03
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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
2003
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures - SPAA '03
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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]
2019
arXiv
pre-print
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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
2019
Neural Information Processing Systems
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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
1981
SIAM journal on computing (Print)
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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]
1992
Lecture Notes in Computer Science
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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]
2022
IACR Cryptology ePrint Archive
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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
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