Results 1 
4 of
4
Quantum timespace tradeoffs for sorting
 Proceedings of 35th ACM STOC
, 2003
"... We investigate the complexity of sorting in the model of sequential quantum circuits. While it is known that a quantum algorithm based on comparisons alone cannot outperform classical sorting algorithms by more than a constant factor in time complexity, this is wrong in a space bounded setting. We o ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
We investigate the complexity of sorting in the model of sequential quantum circuits. While it is known that a quantum algorithm based on comparisons alone cannot outperform classical sorting algorithms by more than a constant factor in time complexity, this is wrong in a space bounded setting. We observe that for all storage bounds S, one can devise a quantum algorithm that sorts n numbers (using comparisons only) in time T = O(n
Quantum and Classical CommunicationSpace Tradeoffs from Rectangle Bounds
"... We derive bounds on the product of the communication C and space S for communicating circuits. The first bound applies to quantum circuits and follows from a "bipartite product" result for the discrepancy of communication problems. If for any problem f : XY the multicolor discrepancy of the co ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
We derive bounds on the product of the communication C and space S for communicating circuits. The first bound applies to quantum circuits and follows from a "bipartite product" result for the discrepancy of communication problems. If for any problem f : XY the multicolor discrepancy of the communication matrix of f is 1/2 then the problem in which Alice receives some l inputs, Bob r inputs, and their task is to compute f(x i , y j ) for the l r pairs of inputs (x i , y j ), has a quantum communicationspace tradeo# CS (lrd log Z).
ComparisonBased Time–Space Lower Bounds for Selection
"... We establish the first nontrivial lower bounds on timespace tradeoffs for the selection problem. We prove that any comparisonbased randomized algorithm for finding the median requires Ω(n log logS n) expected time in the RAM model (or more generally in the comparison branching program model), if we ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
We establish the first nontrivial lower bounds on timespace tradeoffs for the selection problem. We prove that any comparisonbased randomized algorithm for finding the median requires Ω(n log logS n) expected time in the RAM model (or more generally in the comparison branching program model), if we have S bits of extra space besides the readonly input array. This bound is tight for all S ≫ log n, and remains true even if the array is given in a random order. Our result thus answers a 16yearold question of Munro and Raman, and also complements recent lower bounds that are restricted to sequential access, as in the multipass streaming model [Chakrabarti et al., SODA 2008]. We also prove that any comparisonbased, deterministic, multipass streaming algorithm for finding the median requires Ω(n log ∗ (n/s) + n log s n) worstcase time (in scanning plus comparisons), if we have s cells of space. This bound is also tight for all s ≫ log 2 n. We get deterministic lower bounds for I/Oefficient algorithms as well. All proofs in this paper involve “elementary ” techniques only. 1
Priority Queues and Sorting for ReadOnly Data
"... Abstract. We revisit the randomaccessmachine model in which the input is given on a readonly randomaccess media, the output is to be produced to a writeonly sequentialaccess media, and in addition there is a limited randomaccess workspace. The length of the input is N elements, the length of ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. We revisit the randomaccessmachine model in which the input is given on a readonly randomaccess media, the output is to be produced to a writeonly sequentialaccess media, and in addition there is a limited randomaccess workspace. The length of the input is N elements, the length of the output is limited by the computation itself, and the capacity of the workspace is O(S + w) bits,whereS is a parameter specified by the user and w is the number of bits per machine word. We present a stateoftheart priority queue—called an adjustable navigation pile—for this model. Under some reasonable assumptions, our priority queue supports minimum and insert in O(1) worstcase time and extract in O(N/S +lgS) worstcase time, where lg N ≤ S ≤ N / lg N. We also show how to use this data structure to simplify the existing optimal O(N 2 /S + N lg S)time sorting algorithm for this model. 1