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Two time-space tradeoffs for element distinctness

Mauricio Karchmer
1986 Theoretical Computer Science  
Two time-space tradeoffs for element distinctness are given. The first one shows T2S = fl(n 3) on a branching program using minimum operations.  ...  Here it is shown that their proof also holds for element distinctness, a more natural problem. 0304-3975/86/$3.50 © 1986, Elsevier Science Publishers B.V. (North-Holland)  ...  Acknowledgment I thank AI Borodin for all his suggestions and enthusiastic encouragements.  ... 
doi:10.1016/0304-3975(86)90150-7 fatcat:pbhglsl5cvflvfxrfivk5jug7i

Space Efficient Data Structures for Nearest Larger Neighbor [chapter]

Varunkumar Jayapaul, Seungbum Jo, Venkatesh Raman, Srinivasa Rao Satti
2015 Lecture Notes in Computer Science  
We consider time-space tradeoffs for the problem in both the encoding (where the input is not accessible after the data structure has been created) and indexing model, and consider cases when the input  ...  We initiate the study of this problem in two dimensions, and describe upper and lower bounds in the encoding and indexing models, distinguishing the two cases when all the elements are distinct or non-distinct  ...  We consider time-space tradeoffs for the problem in both the encoding (where the input is not accessible after the data structure has been created) and indexing model, and consider cases when the input  ... 
doi:10.1007/978-3-319-19315-1_16 fatcat:yzqm4lx4wzfulhuv22w46tsouu

A general sequential time-space tradeoff for finding unique elements

P. Beame
1989 Proceedings of the twenty-first annual ACM symposium on Theory of computing - STOC '89  
This Q(n2) tradeoff also applies to the sorting problem and thus improves the previous time-space tradeoffs for sorting.  ...  Because the Rway branching program is a such a powerful model these time-space product tradeoffs also apply to all models of sequential computation that have a fair measure of space such as off-line multi-tape  ...  Acknowledgements I would like to thank Richard Anderson, Larry RUZZO, Martin Tompa, Al Borodin, and Steve Cook for several helpful discussions and suggestions concerning these results.  ... 
doi:10.1145/73007.73026 dblp:conf/stoc/Beame89 fatcat:syznjqofgjcd7hk65skuype6f4

A general Sequential Time-Space Tradeoff for Finding Unique Elements

Paul Beame
1991 SIAM journal on computing (Print)  
This Q(n2) tradeoff also applies to the sorting problem and thus improves the previous time-space tradeoffs for sorting.  ...  Because the Rway branching program is a such a powerful model these time-space product tradeoffs also apply to all models of sequential computation that have a fair measure of space such as off-line multi-tape  ...  Acknowledgements I would like to thank Richard Anderson, Larry RUZZO, Martin Tompa, Al Borodin, and Steve Cook for several helpful discussions and suggestions concerning these results.  ... 
doi:10.1137/0220017 fatcat:zwhbbcoebrfazareyhabquaeba

The computational complexity of universal hashing

Yishay Mansour, Noam Nisan, Prasoon Tiwari
1993 Theoretical Computer Science  
As a corollary, computing a+ b * c in any field F requires a quadratic time-space tradeoff, and the bound holds for any representation of the elements of the field.  ...  Any implementation of Carter-Wegman universal hashing from n-bit strings to m-bit strings requires a time-space tradeoff of TS=n(nm).  ...  Acknowledgment We thank Paul Beame, Martin Tompa, and Avi Wigderson for helpful discussions.  ... 
doi:10.1016/0304-3975(93)90257-t fatcat:qk2acbrsovdpdkgdmefnf6uhm4

Explicit space-time codes that achieve the diversity-multiplexing gain tradeoff

P. Elia, K.R. Kumar, S.A. Pawar, P.V. Kumar, Hsiao-feng Lu
2005 Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.  
This extension thus presents rectangular D-MG optimal space-time codes that achieve the D-MG tradeoff.  ...  Taken together, the above constructions also extend the region of T for which the D-MG tradeoff is precisely known from T ≥ nt + nr − 1 to T ≥ nt.  ...  This extension thus presents rectangular D-MG optimal space-time codes that achieve the D-MG tradeoff.  ... 
doi:10.1109/isit.2005.1523467 dblp:conf/isit/EliaKPKL05 fatcat:muiooe346jhd3ns2clsugwgrpm

Quantum Time-Space Tradeoff for Finding Multiple Collision Pairs [article]

Yassine Hamoudi, Frédéric Magniez
2020 arXiv   pre-print
We further show that any improvement to our lower bound would imply a breakthrough for a related question about the Element Distinctness problem.  ...  Classically, the same question has only been settled recently by Dinur [Eurocrypt'20], who showed that the Parallel Collision Search algorithm of van Oorschot and Wiener achieves the optimal time-space  ...  Acknowledgements The authors want to thank the anonymous referees for their valuable comments and suggestions which helped to improve this paper.  ... 
arXiv:2002.08944v3 fatcat:lh2gngwqdrbcfgydj7nt2eb4dy

Improved upper bounds for time-space tradeoffs for selection with limited storage [chapter]

Venkatesh Raman, Sarnath Ramnath
1998 Lecture Notes in Computer Science  
We give new algorithms for various ranges of extra space.  ...  Our upper bounds improve the previously known bounds in the range of space s such that s is o(lg 2 n) and s > c lg lg n/lg lg lg n for some constant c.  ...  The restriction on the data movements also gives rise to interesting time-space tradeoffs for selection. Munro and Paterson [3] were the first to consider the time-space tradeoff for selection.  ... 
doi:10.1007/bfb0054361 fatcat:v6pts6idknf3topfvczco6c6va

Time-Space Tradeoffs for the Memory Game [article]

Amit Chakrabarti, Yining Chen
2018 arXiv   pre-print
We prove two time-space tradeoff lower bounds on algorithms (strategies for the player) that clear all cards in T moves while using at most S bits of memory.  ...  In this work, we study the Memory game in a space-bounded setting.  ...  Acknowledgments We would like to thank Graham Cormode and Peter Winkler for helpful discussions about the problems considered in this work.  ... 
arXiv:1712.01330v2 fatcat:ahjx7rovvvdppj2ikbgy6mfkxu

A time-space tradeoff for sorting on non-oblivious machines

Allan Borodin, Michael J. Fischer, David G. Kirkpatrick, Nancy A. Lynch, Martin Tompa
1981 Journal of computer and system sciences (Print)  
Using this model, it is demonstrated that any algorithm for sorting n inputs which is based on comparisons of individual inputs requires time-space product proportional to n*.  ...  A model of computation is introduced which permits the analysis of both the time and space requirements of non-oblivious programs.  ...  Thus there are at least three time-space tradeoffs for sorting already known [ 10, 16, 171 .  ... 
doi:10.1016/0022-0000(81)90037-4 fatcat:2lgqetqkabbircgf4gidgsit7y

A time-space tradeoff for sorting on non-oblivious machines

Allan Borodin, Michael J. Fischer, David G. Kirkpatrick, Nancy A. Lynch, Martin Tompa
1979 20th Annual Symposium on Foundations of Computer Science (sfcs 1979)  
Using this model, it is demonstrated that any algorithm for sorting n inputs which is based on comparisons of individual inputs requires time-space product proportional to n*.  ...  A model of computation is introduced which permits the analysis of both the time and space requirements of non-oblivious programs.  ...  Thus there are at least three time-space tradeoffs for sorting already known [ 10, 16, 171 .  ... 
doi:10.1109/sfcs.1979.4 dblp:conf/focs/BorodinFKLT79 fatcat:o2x2b5wwkfbl5m74siyvur4cuy

Element Distinctness, Frequency Moments, and Sliding Windows

Paul Beame, Raphael Clifford, Widad Machmouchi
2013 2013 IEEE 54th Annual Symposium on Foundations of Computer Science  
We derive new time-space tradeoff lower bounds and algorithms for exactly computing statistics of input data, including frequency moments, element distinctness, and order statistics, that are simple to  ...  In contrast, we show a time-space tradeoff lower bound of T ∈ Ω(n 2 /S) for randomized multi-way branching programs, and hence standard RAM and word-RAM models, to compute the number of distinct elements  ...  A time-space efficient algorithm for F n k : We now show that our time-space tradeoff lower bound for F n k is nearly optimal even for restricted RAM models. Theorem 3.10.  ... 
doi:10.1109/focs.2013.39 dblp:conf/focs/BeameCM13 fatcat:zjf6ehe42rb45ons7idh3gui3u

Page 6030 of Mathematical Reviews Vol. , Issue 88k [page]

1988 Mathematical Reviews  
Grzymata-Busse (1-KS-C) 88k:68025 68Q10 68Q05 68R05 Karchmer, Mauricio (IL-HEBR-C) Two time-space tradeoffs for element distinctness. Theoret. Comput. Sci. 47 (1986), no. 3, 237-246.  ...  He also obtains a tradeoff T7S = Q(n> logn) between time, T, and space, S, for the element distinctness problem on nonuniform nondeterministic multihead Turing machines.  ... 

Conditional Lower Bounds for Space/Time Tradeoffs [chapter]

Isaac Goldstein, Tsvi Kopelowitz, Moshe Lewenstein, Ely Porat
2017 Lecture Notes in Computer Science  
This hardness is shown as a tradeoff between the space consumed by the data structure and the time needed to answer queries. The tradeoff may be either smooth or admit one or more singularity points.  ...  In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems.  ...  Any data structure for the st-Reach/ BPMatch/ SC problem on sparse graphs can not haveÕ(n 1−Ω(1) ) update and query time and O(n 2−Ω(1) ) space.  ... 
doi:10.1007/978-3-319-62127-2_36 fatcat:ks2gunfmkjfmrjvk35ehnasnfm

Space efficient data structures for nearest larger neighbor

Varunkumar Jayapaul, Seungbum Jo, Rajeev Raman, Venkatesh Raman, Srinivasa Rao Satti
2016 Journal of Discrete Algorithms  
We consider time-space tradeoffs for the problem in both the encoding (where the input is not accessible after the data structure has been created) and indexing model, and consider cases when the input  ...  is in a one dimensional array, and also initiate the study of this problem on two-dimensional arrays.  ...  We give a lower bound for time-space tradeoff for NLN and NLRN queries adapting the lower bound tradeoff proof of Brodal et al. [10] for RMQ.  ... 
doi:10.1016/j.jda.2016.01.001 fatcat:mzyhgadwozhd5ipabzqrmvzm5e
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