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A TimeSpace Tradeoff for Sorting on NonOblivious Machines
, 1981
"... This paper adopts the latter strategy in order to pursue the complexity of sorting ..."
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Cited by 24 (2 self)
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This paper adopts the latter strategy in order to pursue the complexity of sorting
Optimal TimeSpace TradeOffs for Sorting
 IN PROC. 39TH IEEE SYMPOS. FOUND. COMPUT. SCI
, 1998
"... We study the fundamental problem of sorting in a sequential model of computation and in particular consider the timespace tradeoff (product of time and space) for this problem. Beame has ..."
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Cited by 10 (0 self)
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We study the fundamental problem of sorting in a sequential model of computation and in particular consider the timespace tradeoff (product of time and space) for this problem. Beame has
An Exponential Lower Bound on the Size of Algebraic Decision Trees for MAX
, 1995
"... We prove an exponential lower bound on the size of any fixeddegree algebraic decision tree for solving MAX, the problem of finding the maximum of n real numbers. This complements the n \Gamma 1 lower bound of Rabin [R72] on the depth of algebraic decision trees for this problem. The proof in fac ..."
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Cited by 7 (6 self)
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We prove an exponential lower bound on the size of any fixeddegree algebraic decision tree for solving MAX, the problem of finding the maximum of n real numbers. This complements the n \Gamma 1 lower bound of Rabin [R72] on the depth of algebraic decision trees for this problem. The proof in fact gives an exponential lower bound on size for the polyhedral decision problem MAX= of testing whether the jth number is the maximum among a list of n real numbers. Previously, except for linear decision trees, no nontrivial lower bounds on the size of algebraic decision trees for any familiar problems are known. We also establish an interesting connection between our lower bound and the maximum number of minimal cutsets for any rankd hypergraphs on n vertices.
Randomized Complexity of Linear Arrangements and Polyhedra
, 1999
"... We survey some of the recent results on the complexity of recognizing ndimensional linear arrangements and convex polyhedra by randomized algebraic decision trees. We give also a number of concrete applications of these results. In particular, we derive first nontrivial, in fact quadratic, randomi ..."
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We survey some of the recent results on the complexity of recognizing ndimensional linear arrangements and convex polyhedra by randomized algebraic decision trees. We give also a number of concrete applications of these results. In particular, we derive first nontrivial, in fact quadratic, randomized lower bounds on the problems like Knapsack and Bounded Integer Programming. We formulate further several open problems and possible directions for future research. 1 Introduction. Linear search algorithms, algebraic decision trees, and computation trees were introduced early to simulate random access machines (RAM) model. They are also a very useful and simplified abstraction of various other RAMrelated computations cf. [AHU74], [DL78], [Y81], [SP82], [M84], [M85a], [KM90], and a useful tool in computational geometry. The same applies for the randomized models of computation. Starting with the papers of Manber and Tompa [MT85], Snir [S85], Meyer auf der Heide [M85a], [M85c] there wa...
TimeSpace Tradeoffs for Set Operations
, 1994
"... This paper considers timespace tradeoffs for various set operations. Denoting the time requirement of an algorithm by T and its space requirement by S, it is shown that TS =\Omega (n 2 ) for set complementation and TS =\Omega \Gamma n 3=2 \Delta for set intersection, in the Rway branch ..."
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This paper considers timespace tradeoffs for various set operations. Denoting the time requirement of an algorithm by T and its space requirement by S, it is shown that TS =\Omega (n 2 ) for set complementation and TS =\Omega \Gamma n 3=2 \Delta for set intersection, in the Rway branching program model. In the more restricted model of comparison branching programs, the paper provides two additional types of results. A tradeoff of TS =\Omega \Gamma n 2\Gammaffl(n) \Delta , derived from Yao's lower bound for element distinctness, is shown for set disjointness, set union and set intersection (where ffl(n) = O \Gamma (log n) \Gamma1=2 \Delta ). A bound of TS =\Omega \Gamma n 3=2 \Delta is shown for deciding set equality and set inclusion. Finally, a classification of set operations is presented, and it is shown that all problems of a large naturally arising class are as hard as the problems bounded in this paper.